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\hypersetup{pdftitle=Logiweb codex of kvanti}

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\begin {document}\raggedright

\makebox [0mm][l]{\makebox [\linewidth ][r]{\includegraphics [0mm,18.5mm][16.5mm,19mm]{/home/disk07/grue/logiweb/20060417/html/logiweb/doc/logiweb.eps}}}%
{\bf {\Large Logiweb codex of $\rm kvanti$}}

\vspace {12.5mm}

\href {../index.html}{Up}
\href {http://www.diku.dk/~grue/logiweb/20060417/logiweb/doc/browser/codex/index.html}{Help}


\begin {flushleft}\hyperlink {url:1808490373749049856838801749754674032079431248934152926926024270046521601:99}{$\rm 
\exists \ast
\colon \ast$},
\hyperlink {url:1808490373749049856838801749754674032079431248934152926926024270046521601:102}{$\rm \ast
\Rightarrow \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:0}{$\rm kvanti$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:1}{$\rm UniqueMember$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:2}{$\rm UniqueMember(Type)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:3}{$\rm SameSeries$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:4}{$\rm A4$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:5}{$\rm SameMember$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:6}{$\rm Qclosed(Addition)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:7}{$\rm Qclosed(Multiplication)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:8}{$\rm FromCartProd(1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:9}{$\rm 
\mbox{1rule fromCartProd(2)}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:10}{$\rm constantRationalSeries(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:11}{$\rm cartProd(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:12}{$\rm Power(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:13}{$\rm binaryUnion(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:14}{$\rm SetOfRationalSeries$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:15}{$\rm IsSubset(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:16}{$\rm (p\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:17}{$\rm (s\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:18}{$\rm (\cdots{})$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:19}{$\rm \texttt{Objekt-var}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:20}{$\rm \texttt{Ex-var}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:21}{$\rm \texttt{Ph-var}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:22}{$\rm \texttt{V\ae{}rdi}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:23}{$\rm \texttt{Variabel}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:24}{$\rm Op(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:25}{$\rm Op(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:26}{$\rm \ast
 \mathrel {\ddot {==}} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:27}{$\rm ContainsEmpty(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:28}{$\rm Nat(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:29}{$\rm 
Dedu(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:30}{$\rm 
Dedu_0(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:31}{$\rm Dedu_{s}(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:32}{$\rm 
Dedu_1(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:33}{$\rm 
Dedu_2(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:34}{$\rm 
Dedu_3(\ast
,\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:35}{$\rm 
Dedu_4(\ast
,\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:36}{$\rm 
Dedu_4^*(\ast
,\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:37}{$\rm 
Dedu_5(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:38}{$\rm 
Dedu_6(\ast
,\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:39}{$\rm 
Dedu_6^*(\ast
,\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:40}{$\rm 
Dedu_7(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:41}{$\rm 
Dedu_8(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:42}{$\rm 
Dedu_8^*(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:43}{$\rm Ex_{1}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:44}{$\rm Ex_{2}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:45}{$\rm Ex3$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:46}{$\rm Ex_{10}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:47}{$\rm Ex_{20}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:48}{$\rm \ast
 _{Ex}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:49}{$\rm \ast
 ^{Ex}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:50}{$\rm \langle \ast
{\equiv} \ast
| \ast
{:==} \ast
\rangle_{Ex} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:51}{$\rm \langle \ast
{\equiv}^0 \ast
| \ast
{:==} \ast
\rangle_{Ex} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:52}{$\rm \langle \ast
{\equiv}^1 \ast
| \ast
{:==} \ast
\rangle_{Ex} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:53}{$\rm \langle \ast
{\equiv}^* \ast
| \ast
{:==} \ast
\rangle_{Ex} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:54}{$\rm ph_{1}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:55}{$\rm ph_{2}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:56}{$\rm ph_{3}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:57}{$\rm \ast
 _{Ph} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:58}{$\rm \ast
 ^{Ph}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:59}{$\rm \langle \ast
{\equiv} \ast
| \ast
{:==} \ast
\rangle_{Ph} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:60}{$\rm \langle \ast
{\equiv}^0 \ast
| \ast
{:==} \ast
\rangle_{Ph} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:61}{$\rm \langle \ast
{\equiv}^1 \ast
| \ast
{:==} \ast
\rangle_{Ph} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:62}{$\rm \langle \ast
{\equiv}^* \ast
| \ast
{:==} \ast
\rangle_{Ph} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:63}{$\rm \langle \ast
{\equiv} \ast
| \ast
{:==} \ast
\rangle_{Me}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:64}{$\rm \langle \ast
{\equiv}^1 \ast
| \ast
{:==} \ast
\rangle_{Me} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:65}{$\rm \langle \ast
{\equiv}^* \ast
| \ast
{:==} \ast
\rangle_{Me} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:66}{$\rm \mathsf {bs}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:67}{$\rm  \mathsf {OBS}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:68}{$\rm {\cal BS}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:69}{$\rm \mathrm{\O}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:70}{$\rm SystemQ$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:71}{$\rm MP$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:72}{$\rm Gen$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:73}{$\rm Repetition$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:74}{$\rm Neg$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:75}{$\rm Ded$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:76}{$\rm ExistIntro$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:77}{$\rm Extensionality$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:78}{$\rm \O{}def$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:79}{$\rm PairDef$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:80}{$\rm UnionDef$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:81}{$\rm PowerDef$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:82}{$\rm SeparationDef$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:83}{$\rm AddDoubleNeg$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:84}{$\rm RemoveDoubleNeg$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:85}{$\rm AndCommutativity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:86}{$\rm AutoImply$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:87}{$\rm Contrapositive$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:88}{$\rm FirstConjunct$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:89}{$\rm SecondConjunct$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:90}{$\rm FromContradiction$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:91}{$\rm FromDisjuncts$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:92}{$\rm IffCommutativity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:93}{$\rm IffFirst$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:94}{$\rm IffSecond$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:95}{$\rm ImplyTransitivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:96}{$\rm JoinConjuncts$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:97}{$\rm MP2$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:98}{$\rm MP3$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:99}{$\rm MP4$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:100}{$\rm MP5$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:101}{$\rm MT$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:102}{$\rm NegativeMT$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:103}{$\rm Technicality$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:104}{$\rm Weakening$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:105}{$\rm WeakenOr1$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:106}{$\rm WeakenOr2$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:107}{$\rm Formula2Pair$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:108}{$\rm Pair2Formula$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:109}{$\rm Formula2Union$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:110}{$\rm Union2Formula$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:111}{$\rm Formula2Sep$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:112}{$\rm Sep2Formula$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:113}{$\rm Formula2Power$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:114}{$\rm SubsetInPower$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:115}{$\rm HelperPowerIsSub$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:116}{$\rm PowerIsSub$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:117}{$\rm (Switch)HelperPowerIsSub$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:118}{$\rm (Switch)PowerIsSub$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:119}{$\rm ToSetEquality$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:120}{$\rm HelperToSetEquality(t)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:121}{$\rm ToSetEquality(t)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:122}{$\rm HelperFromSetEquality$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:123}{$\rm FromSetEquality$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:124}{$\rm HelperReflexivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:125}{$\rm Reflexivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:126}{$\rm HelperSymmetry$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:127}{$\rm Symmetry$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:128}{$\rm HelperTransitivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:129}{$\rm Transitivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:130}{$\rm ERisReflexive$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:131}{$\rm ERisSymmetric$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:132}{$\rm ERisTransitive$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:133}{$\rm \O{}isSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:134}{$\rm HelperMemberNot\O{}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:135}{$\rm MemberNot\O{}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:136}{$\rm HelperUnique\O{}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:137}{$\rm Unique\O{}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:138}{$\rm ==\!{}Reflexivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:139}{$\rm ==\!{}Symmetry$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:140}{$\rm Helper\!{}==\!{}Transitivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:141}{$\rm \!{}==\!{}Transitivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:142}{$\rm HelperTransferNotEq$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:143}{$\rm TransferNotEq$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:144}{$\rm HelperPairSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:145}{$\rm Helper(2)PairSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:146}{$\rm PairSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:147}{$\rm SamePair$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:148}{$\rm SameSingleton$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:149}{$\rm UnionSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:150}{$\rm SameUnion$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:151}{$\rm SeparationSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:152}{$\rm SameSeparation$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:153}{$\rm SameBinaryUnion$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:154}{$\rm IntersectionSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:155}{$\rm SameIntersection$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:156}{$\rm AutoMember$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:157}{$\rm HelperEqSysNot\O{}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:158}{$\rm EqSysNot\O{}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:159}{$\rm HelperEqSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:160}{$\rm EqSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:161}{$\rm HelperEqNecessary$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:162}{$\rm EqNecessary$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:163}{$\rm HelperNoneEqNecessary$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:164}{$\rm Helper(2)NoneEqNecessary$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:165}{$\rm NoneEqNecessary$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:166}{$\rm EqClassIsSubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:167}{$\rm EqClassesAreDisjoint$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:168}{$\rm AllDisjoint$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:169}{$\rm AllDisjointImply$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:170}{$\rm BSsubset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:171}{$\rm Union(BS/R)subset$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:172}{$\rm UnionIdentity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:173}{$\rm EqSysIsPartition$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:174}{$\rm (x1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:175}{$\rm (x2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:176}{$\rm (y1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:177}{$\rm (y2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:178}{$\rm (v1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:179}{$\rm (v2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:180}{$\rm (v3)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:181}{$\rm (v4)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:182}{$\rm (v2n)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:183}{$\rm (m1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:184}{$\rm (m2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:185}{$\rm (n1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:186}{$\rm (n2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:187}{$\rm (n3)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:188}{$\rm (\epsilon)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:189}{$\rm (\epsilon)_{1}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:190}{$\rm (\epsilon 2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:191}{$\rm (fep)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:192}{$\rm (fx)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:193}{$\rm (fy)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:194}{$\rm (fz)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:195}{$\rm (fu)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:196}{$\rm (fv)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:197}{$\rm (fw)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:198}{$\rm (rx)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:199}{$\rm (ry)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:200}{$\rm (rz)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:201}{$\rm (ru)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:202}{$\rm (sx)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:203}{$\rm (sx1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:204}{$\rm (sy)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:205}{$\rm (sy1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:206}{$\rm (sz)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:207}{$\rm (sz1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:208}{$\rm (su)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:209}{$\rm (su1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:210}{$\rm (fxs)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:211}{$\rm (fys)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:212}{$\rm (crs1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:213}{$\rm (f1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:214}{$\rm (f2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:215}{$\rm (f3)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:216}{$\rm (f4)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:217}{$\rm (op1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:218}{$\rm (op2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:219}{$\rm (r1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:220}{$\rm (s1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:221}{$\rm (s2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:222}{$\rm X_{1}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:223}{$\rm X_{2}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:224}{$\rm Y_{1}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:225}{$\rm Y_{2}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:226}{$\rm V_{1}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:227}{$\rm V_{2}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:228}{$\rm V_{3}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:229}{$\rm V_{4}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:230}{$\rm V_{2n}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:231}{$\rm M_{1}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:232}{$\rm M_{2}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:233}{$\rm N_{1} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:234}{$\rm N_{2} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:235}{$\rm N_{3} $},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:236}{$\rm \epsilon$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:237}{$\rm \epsilon 1$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:238}{$\rm \epsilon 2$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:239}{$\rm FX$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:240}{$\rm FY$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:241}{$\rm FZ$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:242}{$\rm FU$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:243}{$\rm FV$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:244}{$\rm FW$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:245}{$\rm FEP$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:246}{$\rm RX$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:247}{$\rm RY$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:248}{$\rm RZ$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:249}{$\rm RU$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:250}{$\rm (SX)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:251}{$\rm (SX1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:252}{$\rm (SY)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:253}{$\rm (SY1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:254}{$\rm (SZ)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:255}{$\rm (SZ1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:256}{$\rm (SU)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:257}{$\rm (SU1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:258}{$\rm FXS$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:259}{$\rm FYS$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:260}{$\rm (F1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:261}{$\rm (F2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:262}{$\rm (F3)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:263}{$\rm (F4)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:264}{$\rm (OP1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:265}{$\rm (OP2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:266}{$\rm (R1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:267}{$\rm (S1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:268}{$\rm (S2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:269}{$\rm (EPob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:270}{$\rm (CRS1ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:271}{$\rm (F1ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:272}{$\rm (F2ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:273}{$\rm (F3ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:274}{$\rm (F4ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:275}{$\rm (N1ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:276}{$\rm (N2ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:277}{$\rm (OP1ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:278}{$\rm (OP2ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:279}{$\rm (R1ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:280}{$\rm (S1ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:281}{$\rm (S2ob)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:282}{$\rm ph_{4}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:283}{$\rm ph_{5}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:284}{$\rm ph_{6}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:285}{$\rm NAT$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:286}{$\rm RATIONAL_SERIES$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:287}{$\rm SERIES$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:288}{$\rm SetOfReals$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:289}{$\rm SetOfFxs$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:290}{$\rm N$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:291}{$\rm Q$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:292}{$\rm X$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:293}{$\rm xs$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:294}{$\rm xaF$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:295}{$\rm ysF$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:296}{$\rm us$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:297}{$\rm usFoelge$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:298}{$\rm 0$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:299}{$\rm 1$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:300}{$\rm (-1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:301}{$\rm 2$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:302}{$\rm 3$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:303}{$\rm 1/2$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:304}{$\rm 1/3$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:305}{$\rm 2/3$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:306}{$\rm 0f$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:307}{$\rm 
\mbox{1f}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:308}{$\rm 00$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:309}{$\rm 
\mbox{01}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:310}{$\rm (--01)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:311}{$\rm 02$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:312}{$\rm 01//02$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:313}{$\rm PlusAssociativity(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:314}{$\rm PlusAssociativity(R)XX$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:315}{$\rm Plus0(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:316}{$\rm Negative(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:317}{$\rm Times1(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:318}{$\rm lessAddition(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:319}{$\rm PlusCommutativity(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:320}{$\rm LeqAntisymmetry(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:321}{$\rm LeqTransitivity(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:322}{$\rm leqAddition(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:323}{$\rm Distribution(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:324}{$\rm A4(Axiom)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:325}{$\rm InductionAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:326}{$\rm EqualityAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:327}{$\rm EqLeqAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:328}{$\rm EqAdditionAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:329}{$\rm EqMultiplicationAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:330}{$\rm QisClosed(Reciprocal)(Imply)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:331}{$\rm QisClosed(Reciprocal)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:332}{$\rm QisClosed(Negative)(Imply)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:333}{$\rm QisClosed(Negative)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:334}{$\rm leqReflexivity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:335}{$\rm leqAntisymmetryAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:336}{$\rm leqTransitivityAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:337}{$\rm leqTotality$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:338}{$\rm leqAdditionAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:339}{$\rm leqMultiplicationAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:340}{$\rm plusAssociativity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:341}{$\rm plusCommutativity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:342}{$\rm Negative$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:343}{$\rm plus0$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:344}{$\rm timesAssociativity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:345}{$\rm timesCommutativity$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:346}{$\rm ReciprocalAxiom$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:347}{$\rm times1$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:348}{$\rm Distribution$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:349}{$\rm 0not1$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:350}{$\rm 
\mbox{lemma eqLeq(R)}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:351}{$\rm TimesAssociativity(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:352}{$\rm TimesCommutativity(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:353}{$\rm (Adgic)SameR$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:354}{$\rm Separation2formula(1)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:355}{$\rm Separation2formula(2)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:356}{$\rm Cauchy$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:357}{$\rm PlusF$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:358}{$\rm ReciprocalF$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:359}{$\rm From==$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:360}{$\rm To==$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:361}{$\rm FromInR$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:362}{$\rm PlusR(Sym)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:363}{$\rm ReciprocalR(Axiom)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:364}{$\rm LessMinus1(N)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:365}{$\rm Nonnegative(N)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:366}{$\rm US0$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:367}{$\rm NextXS(UpperBound)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:368}{$\rm NextXS(NoUpperBound)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:369}{$\rm NextUS(UpperBound)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:370}{$\rm NextUS(NoUpperBound)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:371}{$\rm ExpZero$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:372}{$\rm ExpPositive$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:373}{$\rm ExpZero(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:374}{$\rm ExpPositive(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:375}{$\rm BSzero$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:376}{$\rm BSpositive$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:377}{$\rm UStelescope(Zero)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:378}{$\rm UStelescope(Positive)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:379}{$\rm EqAddition(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:380}{$\rm FromLimit$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:381}{$\rm ToUpperBound$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:382}{$\rm FromUpperBound$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:383}{$\rm USisUpperBound$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:384}{$\rm 0not1(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:385}{$\rm ExpUnbounded(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:386}{$\rm FromLeq(Advanced)(N)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:387}{$\rm FromLeastUpperBound$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:388}{$\rm ToLeastUpperBound$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:389}{$\rm XSisNotUpperBound$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:390}{$\rm ysFGreater$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:391}{$\rm ysFLess$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:392}{$\rm SmallInverse$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:393}{$\rm NatType$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:394}{$\rm RationalType$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:395}{$\rm SeriesType$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:396}{$\rm Max$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:397}{$\rm Numerical$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:398}{$\rm NumericalF$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:399}{$\rm MemberOfSeries(Imply)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:400}{$\rm JoinConjuncts(2conditions)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:401}{$\rm 
\mbox{prop lemma imply negation}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:402}{$\rm TND$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:403}{$\rm FromNegatedImply$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:404}{$\rm ToNegatedImply$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:405}{$\rm FromNegated(2*Imply)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:406}{$\rm FromNegatedAnd$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:407}{$\rm FromNegatedOr$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:408}{$\rm ToNegatedOr$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:409}{$\rm FromNegations$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:410}{$\rm From3Disjuncts$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:411}{$\rm From2*2Disjuncts$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:412}{$\rm NegateDisjunct1$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:413}{$\rm NegateDisjunct2$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:414}{$\rm ExpandDisjuncts$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:415}{$\rm SENC1$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:416}{$\rm SENC2$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:417}{$\rm LessLeq(R)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:418}{$\rm MemberOfSeries$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:419}{$\rm memberOfSeries(Type)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:420}{$\rm  \ast
 (exp) \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:421}{$\rm R(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:422}{$\rm --R(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:423}{$\rm rec\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:424}{$\rm \ast
 / \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:425}{$\rm \ast
 \cap \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:426}{$\rm \ast
[\ast
]$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:427}{$\rm \cup \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:428}{$\rm \ast
 \mathrel{\cup} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:429}{$\rm P(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:430}{$\rm \{\ast
\}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:431}{$\rm StateExpand(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:432}{$\rm extractSeries(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:433}{$\rm SetOfSeries(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:434}{$\rm --Macro(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:435}{$\rm ExpandList(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:436}{$\rm **Macro(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:437}{$\rm ++Macro(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:438}{$\rm <<Macro(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:439}{$\rm ||Macro(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:440}{$\rm 01//Macro(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:441}{$\rm UB(\ast
, \ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:442}{$\rm LUB(\ast
, \ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:443}{$\rm BS(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:444}{$\rm UStelescope(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:445}{$\rm (\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:446}{$\rm |f\ast
|$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:447}{$\rm |r\ast
|$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:448}{$\rm Limit(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:449}{$\rm Union(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:450}{$\rm IsOrderedPair(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:451}{$\rm IsRelation(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:452}{$\rm isFunction(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:453}{$\rm IsSeries(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:454}{$\rm IsNatural(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:455}{$\rm OrderedPair(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:456}{$\rm TypeNat(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:457}{$\rm TypeNat0(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:458}{$\rm TypeRational(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:459}{$\rm TypeRational0(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:460}{$\rm TypeSeries(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:461}{$\rm Typeseries0(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:462}{$\rm \{\ast
,\ast
\}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:463}{$\rm \langle \ast
,\ast
\rangle$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:464}{$\rm (-u\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:465}{$\rm -_{f}\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:466}{$\rm (--\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:467}{$\rm 1f/\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:468}{$\rm 01//temp\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:469}{$\rm \ast
(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:470}{$\rm ReflRel(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:471}{$\rm SymRel(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:472}{$\rm TransRel(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:473}{$\rm EqRel(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:474}{$\rm [\ast
 \mathrel{\in} \ast
]_{\ast
}$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:475}{$\rm Partition(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:476}{$\rm (\ast
*\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:477}{$\rm \ast
*_{f}\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:478}{$\rm \ast
**\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:479}{$\rm (\ast
+\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:480}{$\rm (\ast
-\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:481}{$\rm \ast
+_{f}\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:482}{$\rm \ast
-_{f}\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:483}{$\rm \ast
++\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:484}{$\rm R(\ast
) -- R(\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:485}{$\rm \ast
 \mathrel{\in} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:486}{$\rm |\ast
|$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:487}{$\rm if(\ast
,\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:488}{$\rm Max(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:489}{$\rm Max(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:490}{$\rm \ast
 = \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:491}{$\rm \ast
 \neq \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:492}{$\rm \ast
 <= \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:493}{$\rm \ast
 < \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:494}{$\rm \ast
<_{f}\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:495}{$\rm \ast
\leq_{f}\ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:496}{$\rm SF(\ast
,\ast
)$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:497}{$\rm \ast
 == \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:498}{$\rm \ast
 !!== \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:499}{$\rm \ast
 << \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:500}{$\rm \ast
 <<== \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:501}{$\rm \ast
\!\mathrel{==}\! \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:502}{$\rm \ast
 \mathrel{\subseteq} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:503}{$\rm \dot{\neg}\,(\ast
)n$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:504}{$\rm \ast
 \mathrel{\notin} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:505}{$\rm \ast
 \mathrel{\neq} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:506}{$\rm \ast
\mathrel{\dot{\wedge}} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:507}{$\rm \ast
 \mathrel{\dot{\vee}} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:508}{$\rm 
\exists \ast
\colon \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:509}{$\rm \ast
\mathrel{\dot{\Leftrightarrow}} \ast$},
\hyperlink {url:1808490782658911215215844543754112306433607076424339373311695870409267457:510}{$\rm  \{ ph \mathrel{\in} \ast
\mid \ast
\}$},
\end {flushleft}

\hypertarget {url:1808490373749049856838801749754674032079431248934152926926024270046521601:99}{}\section* {$\rm 
\exists \ast
\colon \ast$}

$\rm
[
\exists 
\mathsf{x}
\colon 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(AARRGGHH!
\mbox{-}exist
\mbox{-}bug!)
\mbox{''}
]$

\hypertarget {url:1808490373749049856838801749754674032079431248934152926926024270046521601:102}{}\section* {$\rm \ast
\Rightarrow \ast$}

$\rm
[
\mathsf{x}
\Rightarrow 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(i
\#1.
\newline 
\mbox {$\backslash $}Rightarrow
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline )i
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:0}{}\section* {$\rm kvanti$}

$\rm
[kvanti
\stackrel{
\mathrm{prio}
}{\rightarrow}
\newline \mathbf {Preassociative} \newline 
[kvanti
] , \linebreak [0] 
[
\mbox{base}
] , \linebreak [0] 
[
\mbox{bracket $
\ast $ end bracket}
] , \linebreak [0] 
[
\mbox{big bracket $
\ast $ end bracket}
] , \linebreak [0] 
[
\ \$
\ast \$\linebreak[0]\ 
] , \linebreak [0] 
[
\mathbf{flush\ left\ }[ 
\ast 
]
] , \linebreak [0] 
[
\mathsf{x}
] , \linebreak [0] 
[
\mathsf{y}
] , \linebreak [0] 
[
\mathsf{z}
] , \linebreak [0] 
[
[
\ast 
\bowtie
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\stackrel{
\ast 
}{\rightarrow}
\ast 
]
] , \linebreak [0] 
[
\mathrm{pyk}
] , \linebreak [0] 
[
\mathrm{tex}
] , \linebreak [0] 
[
\mathrm{name}
] , \linebreak [0] 
[
\mathrm{prio}
] , \linebreak [0] 
[
\ast 
] , \linebreak [0] 
[
\mathsf {T}
] , \linebreak [0] 
[
\mathrm {if}(
\ast 
,\linebreak [0]
\ast 
,\linebreak [0]
\ast 
)
] , \linebreak [0] 
[
[
\ast 
\stackrel {
\ast 
}{\Rightarrow }
\ast 
]
] , \linebreak [0] 
[
\mathrm {val}
] , \linebreak [0] 
[
\mathrm {claim}
] , \linebreak [0] 
[
\bot 
] , \linebreak [0] 
[
f(
\ast 
)
] , \linebreak [0] 
[
(
\ast 
){}^{I} 
] , \linebreak [0] 
[
\mathsf {F}
] , \linebreak [0] 
[
\underline {0}
] , \linebreak [0] 
[
\underline {1}
] , \linebreak [0] 
[
\underline {2}
] , \linebreak [0] 
[
\underline {3}
] , \linebreak [0] 
[
\underline {4}
] , \linebreak [0] 
[
\underline {5}
] , \linebreak [0] 
[
\underline {6}
] , \linebreak [0] 
[
\underline {7}
] , \linebreak [0] 
[
\underline {8}
] , \linebreak [0] 
[
\underline {9}
] , \linebreak [0] 
[
0
] , \linebreak [0] 
[
1
] , \linebreak [0] 
[
2
] , \linebreak [0] 
[
3
] , \linebreak [0] 
[
4
] , \linebreak [0] 
[
5
] , \linebreak [0] 
[
6
] , \linebreak [0] 
[
7
] , \linebreak [0] 
[
8
] , \linebreak [0] 
[
9
] , \linebreak [0] 
[
\mathsf {a}
] , \linebreak [0] 
[
\mathsf {b}
] , \linebreak [0] 
[
\mathsf {c}
] , \linebreak [0] 
[
\mathsf {d}
] , \linebreak [0] 
[
\mathsf {e}
] , \linebreak [0] 
[
\mathsf {f}
] , \linebreak [0] 
[
\mathsf {g}
] , \linebreak [0] 
[
\mathsf {h}
] , \linebreak [0] 
[
\mathsf {i}
] , \linebreak [0] 
[
\mathsf {j}
] , \linebreak [0] 
[
\mathsf {k}
] , \linebreak [0] 
[
\mathsf {l}
] , \linebreak [0] 
[
\mathsf {m}
] , \linebreak [0] 
[
\mathsf {n}
] , \linebreak [0] 
[
\mathsf {o}
] , \linebreak [0] 
[
\mathsf {p}
] , \linebreak [0] 
[
\mathsf {q}
] , \linebreak [0] 
[
\mathsf {r}
] , \linebreak [0] 
[
\mathsf {s}
] , \linebreak [0] 
[
\mathsf {t}
] , \linebreak [0] 
[
\mathsf {u}
] , \linebreak [0] 
[
\mathsf {v}
] , \linebreak [0] 
[
\mathsf {w}
] , \linebreak [0] 
[
(
\ast 
)^M
] , \linebreak [0] 
[
\mathrm {If}(
\ast 
,\linebreak [0]
\ast 
,\linebreak [0]
\ast 
)
] , \linebreak [0] 
[\mathrm {array}\{
\ast 
\}
\ast 
\mathrm {end\ array}
] , \linebreak [0] 
[
l
] , \linebreak [0] 
[
c
] , \linebreak [0] 
[
r
] , \linebreak [0] 
[
\mathrm {empty}
] , \linebreak [0] 
[
\langle 
\ast 
\,{|}
\ast 
{:=}\,
\ast 
\rangle 
] , \linebreak [0] 
[
{\cal M}(
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal U}}(
\ast 
)
] , \linebreak [0] 
[
{\cal U}(
\ast 
)
] , \linebreak [0] 
[
{\cal U}^M(
\ast 
)
] , \linebreak [0] 
[
\mathbf {apply}(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathbf {apply}_1(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
identifier( 
\ast 
)
] , \linebreak [0] 
[
identifier_{1}( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
array\mbox{-}\linebreak[0]plus( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
array\mbox{-}\linebreak[0]remove( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
array\mbox{-}\linebreak[0]put( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
array\mbox{-}\linebreak[0]add( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
bit( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
bit_1( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
rack
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {vector}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {bibliography}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {dictionary}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {body}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {codex}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {expansion}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {code}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {cache}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {diagnose}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {pyk}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {tex}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {texname}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {value}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {message}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {macro}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {definition}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {unpack}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {claim}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {priority}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {lambda}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {apply}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {true}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {if}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {quote}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {proclaim}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {define}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {introduce}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {hide}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {pre}\mbox {\tt \char34}
] , \linebreak [0] 
[
\mbox {\tt \char34}\mathrm {post}\mbox {\tt \char34}
] , \linebreak [0] 
[
{\cal E}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal E}_2(
\ast 
,
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal E}_3(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal E}_4(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathbf {lookup}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathbf {abstract}(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\lceil 
\ast 
\rceil 
] , \linebreak [0] 
[
{\cal M}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal M}_2(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
{\cal M}^*(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathrm {macro}
] , \linebreak [0] 
[
s_0
] , \linebreak [0] 
[
\mathbf {zip}(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\mathbf {assoc}_1(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[(
\ast 
)^{\mathbf {p}}
] , \linebreak [0] 
[
\mbox{self}
] , \linebreak [0] 
[
[
\ast 
\mathrel {\ddot {=}}
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\mathrel {\dot {=}}
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\mathrel {\acute {=}}
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\stackrel {\mathrm {pyk}}{=} 
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\stackrel {\mathrm {tex}}{=} 
\ast 
]
] , \linebreak [0] 
[
[
\ast 
\stackrel {\mathrm {name}}{=} 
\ast 
]
] , \linebreak [0] 
[
\mathbf{Priority\ table} [ 
\ast 
]
] , \linebreak [0] 
[
\tilde {{\cal M}}_1
] , \linebreak [0] 
[
\tilde {{\cal M}}_2(
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal M}}_3(
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal M}}_4(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal M}}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal Q}}(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal Q}}_2(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal Q}}_3(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\tilde {{\cal Q}}^*(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
(
\ast 
)
] , \linebreak [0] 
[
\left( 
\ast 
\right) 
] , \linebreak [0] 
[
display(
\ast 
)
] , \linebreak [0] 
[
statement(
\ast 
)
] , \linebreak [0] 
[
[
\ast 
]^{\cdot}
] , \linebreak [0] 
[
[
\ast 
]^-
] , \linebreak [0] 
[
\mathbf{aspect}( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{aspect}( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\langle 
\ast 
\rangle 
] , \linebreak [0] 
[
\mathbf {tuple}_1( 
\ast 
) 
] , \linebreak [0] 
[
\mathbf {tuple}_2( 
\ast 
) 
] , \linebreak [0] 
[
let_2( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
let_1( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
[
\ast 
\stackrel {claim}{=}
\ast 
]
] , \linebreak [0] 
[
\mbox{checker}
] , \linebreak [0] 
[
\mathbf{check}( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{check}_2( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{check}_3( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{check}^*( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\mathbf{check}^*_2( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
\relax [ 
\ast 
\relax ]^{\cdot} 
] , \linebreak [0] 
[
\relax [ 
\ast 
\relax ]^{-} 
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[
\relax [ 
\ast 
\relax ]^{\circ} 
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[
msg
] , \linebreak [0] 
[
[
\ast 
\stackrel {msg}{=} 
\ast 
]
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[
{<}stmt{>}
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[
stmt
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[
[
\ast 
\stackrel {stmt}{=}
\ast 
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[
HeadNil'
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[
HeadPair'
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[
Transitivity'
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[
{\makebox [0mm][l]{$\bot $}\,{\bot }}
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[
Contra'
] , \linebreak [0] 
[
T'_{E}
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[
L_{1}
] , \linebreak [0] 
[\underline{
\ast }
] , \linebreak [0] 
[{\cal A}
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[{\cal B}
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[{\cal C}
] , \linebreak [0] 
[{\cal D}
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[{\cal E}
] , \linebreak [0] 
[{\cal F}
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[{\cal G}
] , \linebreak [0] 
[{\cal H}
] , \linebreak [0] 
[{\cal I}
] , \linebreak [0] 
[{\cal J}
] , \linebreak [0] 
[{\cal K}
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[{\cal L}
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[{\cal M}
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[{\cal N}
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[{\cal O}
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[{\cal P}
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[{\cal Q}
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[{\cal R}
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[{\cal S}
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[{\cal T}
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[{\cal U}
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[{\cal V}
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[{\cal W}
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[{\cal X}
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[{\cal Y}
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[{\cal Z}
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[
\langle 
\ast 
\,{\protect\vert}
\ast 
{:=}\,
\ast 
\rangle 
] , \linebreak [0] 
[
\langle ^ { \ast } 
\ast 
\,{\protect\vert}
\ast 
{:=}\,
\ast 
\rangle 
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[
\emptyset 
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[
Remainder
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[
( 
\ast 
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[
intro(
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\ast 
,
\ast 
,
\ast 
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[
intro(
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\ast 
,
\ast 
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[
error(
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\ast 
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[
error_{2}(
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\ast 
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[
proof( 
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\ast 
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\ast 
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[
proof_{2}( 
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\ast 
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[
{\cal S}(
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\ast 
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[
{\cal S}^{I}(
\ast 
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\ast 
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[
{\cal S}^{\rhd}(
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[
{\cal S}_{1}^{\rhd}(
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[
{\cal S}^{E}(
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[
{\cal S}_{1}^{E}(
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\ast 
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\ast 
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[
{\cal S}^{+}(
\ast 
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\ast 
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[
{\cal S}_{1}^{+}(
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, 
\ast 
, 
\ast 
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[
{\cal S}^{-}(
\ast 
, 
\ast 
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[
{\cal S}_{1}^{-}(
\ast 
, 
\ast 
, 
\ast 
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[
{\cal S}^{\ast}(
\ast 
, 
\ast 
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[
{\cal S}_{1}^{\ast}(
\ast 
, 
\ast 
, 
\ast 
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[
{\cal S}_{2}^{\ast}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
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[
{\cal S}^{\char64}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\char64}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\vdash}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\vdash}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\makebox [0mm][l]{\scriptsize $\vdash $}\,{\vdash }}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\makebox [0mm][l]{\scriptsize $\vdash $}\,{\vdash }}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{i.e.}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{i.e.}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{2}^{i.e.}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{\forall}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{\forall}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}^{;}(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{1}^{;}(
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal S}_{2}^{;}(
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal T}( 
\ast 
)
] , \linebreak [0] 
[
claims( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
claims_2( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{<}proof{>}
] , \linebreak [0] 
[
proof
] , \linebreak [0] 
[
[ \mathbf{Lemma\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ \mathbf{Proof\ of\ }
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ 
\ast 
\mathbf{\ lemma\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ 
\ast 
\mathbf{\ antilemma\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ 
\ast 
\mathbf{\ rule\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
[ 
\ast 
\mathbf{\ antirule\ } 
\ast 
\colon 
\ast 
]
] , \linebreak [0] 
[
\mbox{verifier}
] , \linebreak [0] 
[
{\cal V}_1( 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_2( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_3( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_4( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_5( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_6( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
{\cal V}_7( 
\ast 
, 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
Cut( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
Head_{\oplus} ( 
\ast 
)
] , \linebreak [0] 
[
Tail_{\oplus} ( 
\ast 
)
] , \linebreak [0] 
[
rule_1( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
rule( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
Rule\ tactic
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[
Plus( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
[ \mathbf{Theory\ } 
\ast 
]
] , \linebreak [0] 
[
theory_2( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
theory_3( 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
theory_4( 
\ast 
, 
\ast 
, 
\ast 
)
] , \linebreak [0] 
[
HeadNil''
] , \linebreak [0] 
[
HeadPair''
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[
Transitivity''
] , \linebreak [0] 
[
Contra''
] , \linebreak [0] 
[
HeadNil
] , \linebreak [0] 
[
HeadPair
] , \linebreak [0] 
[
Transitivity
] , \linebreak [0] 
[
Contra
] , \linebreak [0] 
[
T_E
] , \linebreak [0] 
[
ragged\ right
] , \linebreak [0] 
[
ragged\ right\ expansion\ 
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[
parm(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
parm^*(
\ast 
,
\ast 
,
\ast 
)
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[
inst(
\ast 
,
\ast 
)
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[
inst^*(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
occur(
\ast 
,
\ast 
,
\ast 
)
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[
occur^*(
\ast 
,
\ast 
,
\ast 
)
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[
unify(
\ast 
=
\ast 
,
\ast 
)
] , \linebreak [0] 
[
unify^*(
\ast 
=
\ast 
,
\ast 
)
] , \linebreak [0] 
[
unify_2(
\ast 
=
\ast 
,
\ast 
)
] , \linebreak [0] 
[L_a
] , \linebreak [0] 
[L_b
] , \linebreak [0] 
[L_c
] , \linebreak [0] 
[L_d
] , \linebreak [0] 
[L_e
] , \linebreak [0] 
[L_f
] , \linebreak [0] 
[L_g
] , \linebreak [0] 
[L_h
] , \linebreak [0] 
[L_i
] , \linebreak [0] 
[L_j
] , \linebreak [0] 
[L_k
] , \linebreak [0] 
[L_l
] , \linebreak [0] 
[L_m
] , \linebreak [0] 
[L_n
] , \linebreak [0] 
[L_o
] , \linebreak [0] 
[L_p
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[L_q
] , \linebreak [0] 
[L_r
] , \linebreak [0] 
[L_s
] , \linebreak [0] 
[L_t
] , \linebreak [0] 
[L_u
] , \linebreak [0] 
[L_v
] , \linebreak [0] 
[L_w
] , \linebreak [0] 
[L_x
] , \linebreak [0] 
[L_y
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[L_z
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[L_A
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[L_B
] , \linebreak [0] 
[L_C
] , \linebreak [0] 
[L_D
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[L_E
] , \linebreak [0] 
[L_F
] , \linebreak [0] 
[L_G
] , \linebreak [0] 
[L_H
] , \linebreak [0] 
[L_I
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[L_J
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[L_K
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[L_L
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[L_M
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[L_N
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[L_O
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[L_P
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[L_Q
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[L_R
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[L_S
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[L_T
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[L_U
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[L_V
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[L_W
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[L_X
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[L_Y
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[L_Z
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[L_?
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[
Reflexivity
] , \linebreak [0] 
[
Reflexivity_1
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[
Commutativity
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[
Commutativity_1
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[
{<}tactic{>}
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[
tactic
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[
[
\ast 
\stackrel {tactic}{=}
\ast 
]
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[
{\cal P}( 
\ast 
, 
\ast 
, 
\ast 
)
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[
{\cal P}^*( 
\ast 
, 
\ast 
, 
\ast 
)
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[
p_0
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[
conclude_1 ( 
\ast 
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\ast 
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[
conclude_2 ( 
\ast 
, 
\ast 
, 
\ast 
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[
conclude_3 ( 
\ast 
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\ast 
, 
\ast 
, 
\ast 
)
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[
conclude_4 ( 
\ast 
, 
\ast 
)
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[
\mbox{check}
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[
[
\ast 
\stackrel {\circ}{=}
\ast 
]
] , \linebreak [0] 
[
RootVisible(
\ast 
)
] , \linebreak [0] 
[
A
] , \linebreak [0] 
[
R
] , \linebreak [0] 
[
C
] , \linebreak [0] 
[
T
] , \linebreak [0] 
[
L
] , \linebreak [0] 
[
\{
\ast 
\}
] , \linebreak [0] 
[\overline{
\ast }
] , \linebreak [0] 
[
\mathit{a}
] , \linebreak [0] 
[
\mathit{b}
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[
\mathit{c}
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[
\mathit{d}
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[
\mathit{e}
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[
\mathit{f}
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[
\mathit{g}
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[
\mathit{h}
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[
\mathit{i}
] , \linebreak [0] 
[
\mathit{j}
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[
\mathit{k}
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[
\mathit{l}
] , \linebreak [0] 
[
\mathit{m}
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[
\mathit{n}
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[
\mathit{o}
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[
\mathit{p}
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[
\mathit{q}
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[
\mathit{r}
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[
\mathit{s}
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[
\mathit{t}
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[
\mathit{u}
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[
\mathit{v}
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[
\mathit{w}
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[
\mathit{x}
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[
\mathit{y}
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[
\mathit{z}
] , \linebreak [0] 
[
\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
] , \linebreak [0] 
[
\langle 
\ast 
{\equiv}^0 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
] , \linebreak [0] 
[
\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
] , \linebreak [0] 
[
\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:=} 
\ast 
\rangle 
] , \linebreak [0] 
[
Ded(
\ast 
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\ast 
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[
Ded_0(
\ast 
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\ast 
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Ded_1(
\ast 
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\ast 
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\ast 
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Ded_2(
\ast 
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Ded_3(
\ast 
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\ast 
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\ast 
,
\ast 
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[
Ded_4(
\ast 
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\ast 
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\ast 
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\ast 
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[
Ded_4^*(
\ast 
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\ast 
,
\ast 
,
\ast 
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[
Ded_5(
\ast 
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\ast 
,
\ast 
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[
Ded_6(
\ast 
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\ast 
,
\ast 
,
\ast 
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[
Ded_6^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
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[
Ded_7(
\ast 
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[
Ded_8(
\ast 
,
\ast 
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[
Ded_8^*(
\ast 
,
\ast 
)
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[
S
] , \linebreak [0] 
[
Neg
] , \linebreak [0] 
[
MP
] , \linebreak [0] 
[
Gen
] , \linebreak [0] 
[
Ded
] , \linebreak [0] 
[
S1
] , \linebreak [0] 
[
S2
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[
S3
] , \linebreak [0] 
[
S4
] , \linebreak [0] 
[
S5
] , \linebreak [0] 
[
S6
] , \linebreak [0] 
[
S7
] , \linebreak [0] 
[
S8
] , \linebreak [0] 
[
S9
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[
Repetition
] , \linebreak [0] 
[
A1'
] , \linebreak [0] 
[
A2'
] , \linebreak [0] 
[
A4'
] , \linebreak [0] 
[
A5'
] , \linebreak [0] 
[
Prop\ 3.2a
] , \linebreak [0] 
[
Prop\ 3.2b
] , \linebreak [0] 
[
Prop\ 3.2c
] , \linebreak [0] 
[
Prop\ 3.2d
] , \linebreak [0] 
[
Prop\ 3.2e_1
] , \linebreak [0] 
[
Prop\ 3.2e_2
] , \linebreak [0] 
[
Prop\ 3.2e
] , \linebreak [0] 
[
Prop\ 3.2f_1
] , \linebreak [0] 
[
Prop\ 3.2f_2
] , \linebreak [0] 
[
Prop\ 3.2f
] , \linebreak [0] 
[
Prop\ 3.2g_1
] , \linebreak [0] 
[
Prop\ 3.2g_2
] , \linebreak [0] 
[
Prop\ 3.2g
] , \linebreak [0] 
[
Prop\ 3.2h_1
] , \linebreak [0] 
[
Prop\ 3.2h_2
] , \linebreak [0] 
[
Prop\ 3.2h
] , \linebreak [0] 
[
Block_1(
\ast 
,
\ast 
,
\ast 
)
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[
Block_2(
\ast 
)
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[UniqueMember
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[UniqueMember(Type)
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[SameSeries
] , \linebreak [0] 
[A4
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[SameMember
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[Qclosed(Addition)
] , \linebreak [0] 
[Qclosed(Multiplication)
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[FromCartProd(1)
] , \linebreak [0] 
[
\mbox{1rule fromCartProd(2)}
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[constantRationalSeries(
\ast 
)
] , \linebreak [0] 
[cartProd(
\ast 
)
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[Power(
\ast 
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[binaryUnion(
\ast 
,
\ast 
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[SetOfRationalSeries
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[IsSubset(
\ast 
,
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)
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[(p
\ast 
,
\ast 
)
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[(s
\ast 
)
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[(\cdots{})
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[\texttt{Objekt-var}
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[\texttt{Ex-var}
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[\texttt{Ph-var}
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[\texttt{V\ae{}rdi}
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[\texttt{Variabel}
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[Op(
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[Op(
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,
\ast 
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[
\ast 
 \mathrel {\ddot {==}} 
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[ContainsEmpty(
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[Nat(
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[
Dedu(
\ast 
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\ast 
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[
Dedu_0(
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\ast 
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[Dedu_{s}(
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\ast 
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\ast 
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[
Dedu_1(
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[
Dedu_2(
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[
Dedu_3(
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[
Dedu_4(
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,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Dedu_4^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Dedu_5(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Dedu_6(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Dedu_6^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Dedu_7(
\ast 
)
] , \linebreak [0] 
[
Dedu_8(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
Dedu_8^*(
\ast 
,
\ast 
)
] , \linebreak [0] 
[Ex_{1}
] , \linebreak [0] 
[Ex_{2}
] , \linebreak [0] 
[Ex3
] , \linebreak [0] 
[Ex_{10}
] , \linebreak [0] 
[Ex_{20}
] , \linebreak [0] 
[
\ast 
 _{Ex}
] , \linebreak [0] 
[
\ast 
 ^{Ex}
] , \linebreak [0] 
[\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ex} 
] , \linebreak [0] 
[\langle 
\ast 
{\equiv}^0 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ex} 
] , \linebreak [0] 
[\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ex} 
] , \linebreak [0] 
[\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ex} 
] , \linebreak [0] 
[ph_{1}
] , \linebreak [0] 
[ph_{2}
] , \linebreak [0] 
[ph_{3}
] , \linebreak [0] 
[
\ast 
 _{Ph} 
] , \linebreak [0] 
[
\ast 
 ^{Ph}
] , \linebreak [0] 
[\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ph} 
] , \linebreak [0] 
[\langle 
\ast 
{\equiv}^0 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ph} 
] , \linebreak [0] 
[\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ph} 
] , \linebreak [0] 
[\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ph} 
] , \linebreak [0] 
[\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Me}
] , \linebreak [0] 
[\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Me} 
] , \linebreak [0] 
[\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Me} 
] , \linebreak [0] 
[\mathsf {bs}
] , \linebreak [0] 
[ \mathsf {OBS}
] , \linebreak [0] 
[{\cal BS}
] , \linebreak [0] 
[\mathrm{\O}
] , \linebreak [0] 
[SystemQ
] , \linebreak [0] 
[MP
] , \linebreak [0] 
[Gen
] , \linebreak [0] 
[Repetition
] , \linebreak [0] 
[Neg
] , \linebreak [0] 
[Ded
] , \linebreak [0] 
[ExistIntro
] , \linebreak [0] 
[Extensionality
] , \linebreak [0] 
[\O{}def
] , \linebreak [0] 
[PairDef
] , \linebreak [0] 
[UnionDef
] , \linebreak [0] 
[PowerDef
] , \linebreak [0] 
[SeparationDef
] , \linebreak [0] 
[AddDoubleNeg
] , \linebreak [0] 
[RemoveDoubleNeg
] , \linebreak [0] 
[AndCommutativity
] , \linebreak [0] 
[AutoImply
] , \linebreak [0] 
[Contrapositive
] , \linebreak [0] 
[FirstConjunct
] , \linebreak [0] 
[SecondConjunct
] , \linebreak [0] 
[FromContradiction
] , \linebreak [0] 
[FromDisjuncts
] , \linebreak [0] 
[IffCommutativity
] , \linebreak [0] 
[IffFirst
] , \linebreak [0] 
[IffSecond
] , \linebreak [0] 
[ImplyTransitivity
] , \linebreak [0] 
[JoinConjuncts
] , \linebreak [0] 
[MP2
] , \linebreak [0] 
[MP3
] , \linebreak [0] 
[MP4
] , \linebreak [0] 
[MP5
] , \linebreak [0] 
[MT
] , \linebreak [0] 
[NegativeMT
] , \linebreak [0] 
[Technicality
] , \linebreak [0] 
[Weakening
] , \linebreak [0] 
[WeakenOr1
] , \linebreak [0] 
[WeakenOr2
] , \linebreak [0] 
[Formula2Pair
] , \linebreak [0] 
[Pair2Formula
] , \linebreak [0] 
[Formula2Union
] , \linebreak [0] 
[Union2Formula
] , \linebreak [0] 
[Formula2Sep
] , \linebreak [0] 
[Sep2Formula
] , \linebreak [0] 
[Formula2Power
] , \linebreak [0] 
[SubsetInPower
] , \linebreak [0] 
[HelperPowerIsSub
] , \linebreak [0] 
[PowerIsSub
] , \linebreak [0] 
[(Switch)HelperPowerIsSub
] , \linebreak [0] 
[(Switch)PowerIsSub
] , \linebreak [0] 
[ToSetEquality
] , \linebreak [0] 
[HelperToSetEquality(t)
] , \linebreak [0] 
[ToSetEquality(t)
] , \linebreak [0] 
[HelperFromSetEquality
] , \linebreak [0] 
[FromSetEquality
] , \linebreak [0] 
[HelperReflexivity
] , \linebreak [0] 
[Reflexivity
] , \linebreak [0] 
[HelperSymmetry
] , \linebreak [0] 
[Symmetry
] , \linebreak [0] 
[HelperTransitivity
] , \linebreak [0] 
[Transitivity
] , \linebreak [0] 
[ERisReflexive
] , \linebreak [0] 
[ERisSymmetric
] , \linebreak [0] 
[ERisTransitive
] , \linebreak [0] 
[\O{}isSubset
] , \linebreak [0] 
[HelperMemberNot\O{}
] , \linebreak [0] 
[MemberNot\O{}
] , \linebreak [0] 
[HelperUnique\O{}
] , \linebreak [0] 
[Unique\O{}
] , \linebreak [0] 
[==\!{}Reflexivity
] , \linebreak [0] 
[==\!{}Symmetry
] , \linebreak [0] 
[Helper\!{}==\!{}Transitivity
] , \linebreak [0] 
[\!{}==\!{}Transitivity
] , \linebreak [0] 
[HelperTransferNotEq
] , \linebreak [0] 
[TransferNotEq
] , \linebreak [0] 
[HelperPairSubset
] , \linebreak [0] 
[Helper(2)PairSubset
] , \linebreak [0] 
[PairSubset
] , \linebreak [0] 
[SamePair
] , \linebreak [0] 
[SameSingleton
] , \linebreak [0] 
[UnionSubset
] , \linebreak [0] 
[SameUnion
] , \linebreak [0] 
[SeparationSubset
] , \linebreak [0] 
[SameSeparation
] , \linebreak [0] 
[SameBinaryUnion
] , \linebreak [0] 
[IntersectionSubset
] , \linebreak [0] 
[SameIntersection
] , \linebreak [0] 
[AutoMember
] , \linebreak [0] 
[HelperEqSysNot\O{}
] , \linebreak [0] 
[EqSysNot\O{}
] , \linebreak [0] 
[HelperEqSubset
] , \linebreak [0] 
[EqSubset
] , \linebreak [0] 
[HelperEqNecessary
] , \linebreak [0] 
[EqNecessary
] , \linebreak [0] 
[HelperNoneEqNecessary
] , \linebreak [0] 
[Helper(2)NoneEqNecessary
] , \linebreak [0] 
[NoneEqNecessary
] , \linebreak [0] 
[EqClassIsSubset
] , \linebreak [0] 
[EqClassesAreDisjoint
] , \linebreak [0] 
[AllDisjoint
] , \linebreak [0] 
[AllDisjointImply
] , \linebreak [0] 
[BSsubset
] , \linebreak [0] 
[Union(BS/R)subset
] , \linebreak [0] 
[UnionIdentity
] , \linebreak [0] 
[EqSysIsPartition
] , \linebreak [0] 
[(x1)
] , \linebreak [0] 
[(x2)
] , \linebreak [0] 
[(y1)
] , \linebreak [0] 
[(y2)
] , \linebreak [0] 
[(v1)
] , \linebreak [0] 
[(v2)
] , \linebreak [0] 
[(v3)
] , \linebreak [0] 
[(v4)
] , \linebreak [0] 
[(v2n)
] , \linebreak [0] 
[(m1)
] , \linebreak [0] 
[(m2)
] , \linebreak [0] 
[(n1)
] , \linebreak [0] 
[(n2)
] , \linebreak [0] 
[(n3)
] , \linebreak [0] 
[(\epsilon)
] , \linebreak [0] 
[(\epsilon)_{1}
] , \linebreak [0] 
[(\epsilon 2)
] , \linebreak [0] 
[(fep)
] , \linebreak [0] 
[(fx)
] , \linebreak [0] 
[(fy)
] , \linebreak [0] 
[(fz)
] , \linebreak [0] 
[(fu)
] , \linebreak [0] 
[(fv)
] , \linebreak [0] 
[(fw)
] , \linebreak [0] 
[(rx)
] , \linebreak [0] 
[(ry)
] , \linebreak [0] 
[(rz)
] , \linebreak [0] 
[(ru)
] , \linebreak [0] 
[(sx)
] , \linebreak [0] 
[(sx1)
] , \linebreak [0] 
[(sy)
] , \linebreak [0] 
[(sy1)
] , \linebreak [0] 
[(sz)
] , \linebreak [0] 
[(sz1)
] , \linebreak [0] 
[(su)
] , \linebreak [0] 
[(su1)
] , \linebreak [0] 
[(fxs)
] , \linebreak [0] 
[(fys)
] , \linebreak [0] 
[(crs1)
] , \linebreak [0] 
[(f1)
] , \linebreak [0] 
[(f2)
] , \linebreak [0] 
[(f3)
] , \linebreak [0] 
[(f4)
] , \linebreak [0] 
[(op1)
] , \linebreak [0] 
[(op2)
] , \linebreak [0] 
[(r1)
] , \linebreak [0] 
[(s1)
] , \linebreak [0] 
[(s2)
] , \linebreak [0] 
[X_{1}
] , \linebreak [0] 
[X_{2}
] , \linebreak [0] 
[Y_{1}
] , \linebreak [0] 
[Y_{2}
] , \linebreak [0] 
[V_{1}
] , \linebreak [0] 
[V_{2}
] , \linebreak [0] 
[V_{3}
] , \linebreak [0] 
[V_{4}
] , \linebreak [0] 
[V_{2n}
] , \linebreak [0] 
[M_{1}
] , \linebreak [0] 
[M_{2}
] , \linebreak [0] 
[N_{1} 
] , \linebreak [0] 
[N_{2} 
] , \linebreak [0] 
[N_{3} 
] , \linebreak [0] 
[\epsilon
] , \linebreak [0] 
[\epsilon 1
] , \linebreak [0] 
[\epsilon 2
] , \linebreak [0] 
[FX
] , \linebreak [0] 
[FY
] , \linebreak [0] 
[FZ
] , \linebreak [0] 
[FU
] , \linebreak [0] 
[FV
] , \linebreak [0] 
[FW
] , \linebreak [0] 
[FEP
] , \linebreak [0] 
[RX
] , \linebreak [0] 
[RY
] , \linebreak [0] 
[RZ
] , \linebreak [0] 
[RU
] , \linebreak [0] 
[(SX)
] , \linebreak [0] 
[(SX1)
] , \linebreak [0] 
[(SY)
] , \linebreak [0] 
[(SY1)
] , \linebreak [0] 
[(SZ)
] , \linebreak [0] 
[(SZ1)
] , \linebreak [0] 
[(SU)
] , \linebreak [0] 
[(SU1)
] , \linebreak [0] 
[FXS
] , \linebreak [0] 
[FYS
] , \linebreak [0] 
[(F1)
] , \linebreak [0] 
[(F2)
] , \linebreak [0] 
[(F3)
] , \linebreak [0] 
[(F4)
] , \linebreak [0] 
[(OP1)
] , \linebreak [0] 
[(OP2)
] , \linebreak [0] 
[(R1)
] , \linebreak [0] 
[(S1)
] , \linebreak [0] 
[(S2)
] , \linebreak [0] 
[(EPob)
] , \linebreak [0] 
[(CRS1ob)
] , \linebreak [0] 
[(F1ob)
] , \linebreak [0] 
[(F2ob)
] , \linebreak [0] 
[(F3ob)
] , \linebreak [0] 
[(F4ob)
] , \linebreak [0] 
[(N1ob)
] , \linebreak [0] 
[(N2ob)
] , \linebreak [0] 
[(OP1ob)
] , \linebreak [0] 
[(OP2ob)
] , \linebreak [0] 
[(R1ob)
] , \linebreak [0] 
[(S1ob)
] , \linebreak [0] 
[(S2ob)
] , \linebreak [0] 
[ph_{4}
] , \linebreak [0] 
[ph_{5}
] , \linebreak [0] 
[ph_{6}
] , \linebreak [0] 
[NAT
] , \linebreak [0] 
[RATIONAL_SERIES
] , \linebreak [0] 
[SERIES
] , \linebreak [0] 
[SetOfReals
] , \linebreak [0] 
[SetOfFxs
] , \linebreak [0] 
[N
] , \linebreak [0] 
[Q
] , \linebreak [0] 
[X
] , \linebreak [0] 
[xs
] , \linebreak [0] 
[xaF
] , \linebreak [0] 
[ysF
] , \linebreak [0] 
[us
] , \linebreak [0] 
[usFoelge
] , \linebreak [0] 
[0
] , \linebreak [0] 
[1
] , \linebreak [0] 
[(-1)
] , \linebreak [0] 
[2
] , \linebreak [0] 
[3
] , \linebreak [0] 
[1/2
] , \linebreak [0] 
[1/3
] , \linebreak [0] 
[2/3
] , \linebreak [0] 
[0f
] , \linebreak [0] 
[
\mbox{1f}
] , \linebreak [0] 
[00
] , \linebreak [0] 
[
\mbox{01}
] , \linebreak [0] 
[(--01)
] , \linebreak [0] 
[02
] , \linebreak [0] 
[01//02
] , \linebreak [0] 
[PlusAssociativity(R)
] , \linebreak [0] 
[PlusAssociativity(R)XX
] , \linebreak [0] 
[Plus0(R)
] , \linebreak [0] 
[Negative(R)
] , \linebreak [0] 
[Times1(R)
] , \linebreak [0] 
[lessAddition(R)
] , \linebreak [0] 
[PlusCommutativity(R)
] , \linebreak [0] 
[LeqAntisymmetry(R)
] , \linebreak [0] 
[LeqTransitivity(R)
] , \linebreak [0] 
[leqAddition(R)
] , \linebreak [0] 
[Distribution(R)
] , \linebreak [0] 
[A4(Axiom)
] , \linebreak [0] 
[InductionAxiom
] , \linebreak [0] 
[EqualityAxiom
] , \linebreak [0] 
[EqLeqAxiom
] , \linebreak [0] 
[EqAdditionAxiom
] , \linebreak [0] 
[EqMultiplicationAxiom
] , \linebreak [0] 
[QisClosed(Reciprocal)(Imply)
] , \linebreak [0] 
[QisClosed(Reciprocal)
] , \linebreak [0] 
[QisClosed(Negative)(Imply)
] , \linebreak [0] 
[QisClosed(Negative)
] , \linebreak [0] 
[leqReflexivity
] , \linebreak [0] 
[leqAntisymmetryAxiom
] , \linebreak [0] 
[leqTransitivityAxiom
] , \linebreak [0] 
[leqTotality
] , \linebreak [0] 
[leqAdditionAxiom
] , \linebreak [0] 
[leqMultiplicationAxiom
] , \linebreak [0] 
[plusAssociativity
] , \linebreak [0] 
[plusCommutativity
] , \linebreak [0] 
[Negative
] , \linebreak [0] 
[plus0
] , \linebreak [0] 
[timesAssociativity
] , \linebreak [0] 
[timesCommutativity
] , \linebreak [0] 
[ReciprocalAxiom
] , \linebreak [0] 
[times1
] , \linebreak [0] 
[Distribution
] , \linebreak [0] 
[0not1
] , \linebreak [0] 
[
\mbox{lemma eqLeq(R)}
] , \linebreak [0] 
[TimesAssociativity(R)
] , \linebreak [0] 
[TimesCommutativity(R)
] , \linebreak [0] 
[(Adgic)SameR
] , \linebreak [0] 
[Separation2formula(1)
] , \linebreak [0] 
[Separation2formula(2)
] , \linebreak [0] 
[Cauchy
] , \linebreak [0] 
[PlusF
] , \linebreak [0] 
[ReciprocalF
] , \linebreak [0] 
[From==
] , \linebreak [0] 
[To==
] , \linebreak [0] 
[FromInR
] , \linebreak [0] 
[PlusR(Sym)
] , \linebreak [0] 
[ReciprocalR(Axiom)
] , \linebreak [0] 
[LessMinus1(N)
] , \linebreak [0] 
[Nonnegative(N)
] , \linebreak [0] 
[US0
] , \linebreak [0] 
[NextXS(UpperBound)
] , \linebreak [0] 
[NextXS(NoUpperBound)
] , \linebreak [0] 
[NextUS(UpperBound)
] , \linebreak [0] 
[NextUS(NoUpperBound)
] , \linebreak [0] 
[ExpZero
] , \linebreak [0] 
[ExpPositive
] , \linebreak [0] 
[ExpZero(R)
] , \linebreak [0] 
[ExpPositive(R)
] , \linebreak [0] 
[BSzero
] , \linebreak [0] 
[BSpositive
] , \linebreak [0] 
[UStelescope(Zero)
] , \linebreak [0] 
[UStelescope(Positive)
] , \linebreak [0] 
[EqAddition(R)
] , \linebreak [0] 
[FromLimit
] , \linebreak [0] 
[ToUpperBound
] , \linebreak [0] 
[FromUpperBound
] , \linebreak [0] 
[USisUpperBound
] , \linebreak [0] 
[0not1(R)
] , \linebreak [0] 
[ExpUnbounded(R)
] , \linebreak [0] 
[FromLeq(Advanced)(N)
] , \linebreak [0] 
[FromLeastUpperBound
] , \linebreak [0] 
[ToLeastUpperBound
] , \linebreak [0] 
[XSisNotUpperBound
] , \linebreak [0] 
[ysFGreater
] , \linebreak [0] 
[ysFLess
] , \linebreak [0] 
[SmallInverse
] , \linebreak [0] 
[NatType
] , \linebreak [0] 
[RationalType
] , \linebreak [0] 
[SeriesType
] , \linebreak [0] 
[Max
] , \linebreak [0] 
[Numerical
] , \linebreak [0] 
[NumericalF
] , \linebreak [0] 
[MemberOfSeries(Imply)
] , \linebreak [0] 
[JoinConjuncts(2conditions)
] , \linebreak [0] 
[
\mbox{prop lemma imply negation}
] , \linebreak [0] 
[TND
] , \linebreak [0] 
[FromNegatedImply
] , \linebreak [0] 
[ToNegatedImply
] , \linebreak [0] 
[FromNegated(2*Imply)
] , \linebreak [0] 
[FromNegatedAnd
] , \linebreak [0] 
[FromNegatedOr
] , \linebreak [0] 
[ToNegatedOr
] , \linebreak [0] 
[FromNegations
] , \linebreak [0] 
[From3Disjuncts
] , \linebreak [0] 
[From2*2Disjuncts
] , \linebreak [0] 
[NegateDisjunct1
] , \linebreak [0] 
[NegateDisjunct2
] , \linebreak [0] 
[ExpandDisjuncts
] , \linebreak [0] 
[SENC1
] , \linebreak [0] 
[SENC2
] , \linebreak [0] 
[LessLeq(R)
] , \linebreak [0] 
[MemberOfSeries
] , \linebreak [0] 
[memberOfSeries(Type)
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\_\{
\ast 
\}
] , \linebreak [0] 
[
\ast 
/indexintro(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast 
/intro(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast 
/bothintro(
\ast 
,
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast 
/nameintro(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast '
] , \linebreak [0] 
[
\ast 
{[}
\ast 
{]}
] , \linebreak [0] 
[
\ast 
[ 
\ast 
{\rightarrow} 
\ast 
]
] , \linebreak [0] 
[
\ast 
[ 
\ast 
{\Rightarrow} 
\ast 
]
] , \linebreak [0] 
[
\ast 
0
] , \linebreak [0] 
[
\ast 
1
] , \linebreak [0] 
[
0 \mathrm {b}
] , \linebreak [0] 
[
\ast 
\mbox {-color}( 
\ast 
)
] , \linebreak [0] 
[
\ast 
\mbox {-color}^{\ast}( 
\ast 
)
] , \linebreak [0] 
[
\ast 
{}^H
] , \linebreak [0] 
[
\ast 
{}^T
] , \linebreak [0] 
[
\ast 
{}^U
] , \linebreak [0] 
[
\ast 
{}^h
] , \linebreak [0] 
[
\ast 
{}^t
] , \linebreak [0] 
[
\ast 
{}^s
] , \linebreak [0] 
[
\ast 
{}^c
] , \linebreak [0] 
[
\ast 
{}^d
] , \linebreak [0] 
[
\ast 
{}^a
] , \linebreak [0] 
[
\ast 
{}^C
] , \linebreak [0] 
[
\ast 
{}^M
] , \linebreak [0] 
[
\ast 
{}^B
] , \linebreak [0] 
[
\ast 
{}^{r}
] , \linebreak [0] 
[
\ast 
{}^{i}
] , \linebreak [0] 
[
\ast 
{}^{d}
] , \linebreak [0] 
[
\ast 
{}^{R}
] , \linebreak [0] 
[
\ast 
{}^{0}
] , \linebreak [0] 
[
\ast 
{}^{1}
] , \linebreak [0] 
[
\ast 
{}^{2}
] , \linebreak [0] 
[
\ast 
{}^{3}
] , \linebreak [0] 
[
\ast 
{}^{4}
] , \linebreak [0] 
[
\ast 
{}^{5}
] , \linebreak [0] 
[
\ast 
{}^{6}
] , \linebreak [0] 
[
\ast 
{}^{7}
] , \linebreak [0] 
[
\ast 
{}^{8}
] , \linebreak [0] 
[
\ast 
{}^{9}
] , \linebreak [0] 
[
\ast 
{} ^ { E }
] , \linebreak [0] 
[
\ast 
{} ^ {\cal V}
] , \linebreak [0] 
[
\ast 
{} ^ {\cal C}
] , \linebreak [0] 
[
\ast 
{} ^ {{\cal C} ^ { \ast }}
] , \linebreak [0] 
[
\ast 
{}^{hide}
]
; 
\newline \mathbf {Preassociative} \newline 
[
\mbox{``}
\ast 
\mbox{''}
] , \linebreak [0] 
[
] , \linebreak [0] 
[
(
\ast 
)^{\bf t}
] , \linebreak [0] 
[
\mbox{string}(
\ast 
)+
\ast 
] , \linebreak [0] 
[\mbox{string}(
\ast 
)\mathrel{++}
\ast 
] , \linebreak [0] 
[
\newline 
\ast 
] , \linebreak [0] 
[
\linebreak [0]\ \hskip0em plus2.0em{}
\ast 
] , \linebreak [0] 
[!
\ast 
] , \linebreak [0] 
[
\mbox {\tt \char34}
\ast 
] , \linebreak [0] 
[
\#
\ast 
] , \linebreak [0] 
[
\$
\ast 
] , \linebreak [0] 
[
\%
\ast 
] , \linebreak [0] 
[
\&
\ast 
] , \linebreak [0] 
[
\mbox {'}
\ast 
] , \linebreak [0] 
[(
\ast 
] , \linebreak [0] 
[)
\ast 
] , \linebreak [0] 
[
{*}
\ast 
] , \linebreak [0] 
[
{+}
\ast 
] , \linebreak [0] 
[,
\ast 
] , \linebreak [0] 
[
\mbox{-}
\ast 
] , \linebreak [0] 
[.
\ast 
] , \linebreak [0] 
[/
\ast 
] , \linebreak [0] 
[0
\ast 
] , \linebreak [0] 
[1
\ast 
] , \linebreak [0] 
[2
\ast 
] , \linebreak [0] 
[3
\ast 
] , \linebreak [0] 
[4
\ast 
] , \linebreak [0] 
[5
\ast 
] , \linebreak [0] 
[6
\ast 
] , \linebreak [0] 
[7
\ast 
] , \linebreak [0] 
[8
\ast 
] , \linebreak [0] 
[9
\ast 
] , \linebreak [0] 
[
{:}
\ast 
] , \linebreak [0] 
[;
\ast 
] , \linebreak [0] 
[
{<}
\ast 
] , \linebreak [0] 
[
{=}
\ast 
] , \linebreak [0] 
[
{>}
\ast 
] , \linebreak [0] 
[?
\ast 
] , \linebreak [0] 
[@
\ast 
] , \linebreak [0] 
[A
\ast 
] , \linebreak [0] 
[B
\ast 
] , \linebreak [0] 
[C
\ast 
] , \linebreak [0] 
[D
\ast 
] , \linebreak [0] 
[E
\ast 
] , \linebreak [0] 
[F
\ast 
] , \linebreak [0] 
[G
\ast 
] , \linebreak [0] 
[H
\ast 
] , \linebreak [0] 
[I
\ast 
] , \linebreak [0] 
[J
\ast 
] , \linebreak [0] 
[K
\ast 
] , \linebreak [0] 
[L
\ast 
] , \linebreak [0] 
[M
\ast 
] , \linebreak [0] 
[N
\ast 
] , \linebreak [0] 
[O
\ast 
] , \linebreak [0] 
[P
\ast 
] , \linebreak [0] 
[Q
\ast 
] , \linebreak [0] 
[R
\ast 
] , \linebreak [0] 
[S
\ast 
] , \linebreak [0] 
[T
\ast 
] , \linebreak [0] 
[U
\ast 
] , \linebreak [0] 
[V
\ast 
] , \linebreak [0] 
[W
\ast 
] , \linebreak [0] 
[X
\ast 
] , \linebreak [0] 
[Y
\ast 
] , \linebreak [0] 
[Z
\ast 
] , \linebreak [0] 
[[
\ast 
] , \linebreak [0] 
[
\mbox {$\backslash $}
\ast 
] , \linebreak [0] 
[]
\ast 
] , \linebreak [0] 
[
{\char94}
\ast 
] , \linebreak [0] 
[
\_
\ast 
] , \linebreak [0] 
[
\mbox {`}
\ast 
] , \linebreak [0] 
[a
\ast 
] , \linebreak [0] 
[b
\ast 
] , \linebreak [0] 
[c
\ast 
] , \linebreak [0] 
[d
\ast 
] , \linebreak [0] 
[e
\ast 
] , \linebreak [0] 
[f
\ast 
] , \linebreak [0] 
[g
\ast 
] , \linebreak [0] 
[h
\ast 
] , \linebreak [0] 
[i
\ast 
] , \linebreak [0] 
[j
\ast 
] , \linebreak [0] 
[k
\ast 
] , \linebreak [0] 
[l
\ast 
] , \linebreak [0] 
[m
\ast 
] , \linebreak [0] 
[n
\ast 
] , \linebreak [0] 
[o
\ast 
] , \linebreak [0] 
[p
\ast 
] , \linebreak [0] 
[q
\ast 
] , \linebreak [0] 
[r
\ast 
] , \linebreak [0] 
[s
\ast 
] , \linebreak [0] 
[t
\ast 
] , \linebreak [0] 
[u
\ast 
] , \linebreak [0] 
[v
\ast 
] , \linebreak [0] 
[w
\ast 
] , \linebreak [0] 
[x
\ast 
] , \linebreak [0] 
[y
\ast 
] , \linebreak [0] 
[z
\ast 
] , \linebreak [0] 
[
\{
\ast 
] , \linebreak [0] 
[|
\ast 
] , \linebreak [0] 
[
\}
\ast 
] , \linebreak [0] 
[
\char126 
\ast 
] , \linebreak [0] 
[
\mathbf{Preassociative}\,
\ast 
; 
\ast 
] , \linebreak [0] 
[
\mathbf{Postassociative}\,
\ast 
; 
\ast 
] , \linebreak [0] 
[
[
\ast 
] , \linebreak [0] 
\ast 
] , \linebreak [0] 
[
\mathrm{priority} \,
\ast 
\, \mathrm{end}
] , \linebreak [0] 
[
newline\ 
\ast 
] , \linebreak [0] 
[
macro\ newline\ 
\ast 
] , \linebreak [0] 
[
MacroIndent(
\ast 
)
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\mathbin {\mbox {'}}
\ast 
] , \linebreak [0] 
[
\ast 
\mathbin {\mbox {`}}
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[ 
\ast 
 (exp) 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
{}'
] , \linebreak [0] 
[R(
\ast 
)
] , \linebreak [0] 
[--R(
\ast 
)
] , \linebreak [0] 
[rec
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
 / 
\ast 
] , \linebreak [0] 
[
\ast 
 \cap 
\ast 
] , \linebreak [0] 
[
\ast 
[
\ast 
]
]
; 
\newline \mathbf {Preassociative} \newline 
[\cup 
\ast 
] , \linebreak [0] 
[
\ast 
 \mathrel{\cup} 
\ast 
] , \linebreak [0] 
[P(
\ast 
)
]
; 
\newline \mathbf {Preassociative} \newline 
[\{
\ast 
\}
] , \linebreak [0] 
[StateExpand(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[extractSeries(
\ast 
)
] , \linebreak [0] 
[SetOfSeries(
\ast 
)
] , \linebreak [0] 
[--Macro(
\ast 
)
] , \linebreak [0] 
[ExpandList(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[**Macro(
\ast 
)
] , \linebreak [0] 
[++Macro(
\ast 
)
] , \linebreak [0] 
[<<Macro(
\ast 
)
] , \linebreak [0] 
[||Macro(
\ast 
)
] , \linebreak [0] 
[01//Macro(
\ast 
)
] , \linebreak [0] 
[UB(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[LUB(
\ast 
, 
\ast 
)
] , \linebreak [0] 
[BS(
\ast 
,
\ast 
)
] , \linebreak [0] 
[UStelescope(
\ast 
,
\ast 
)
] , \linebreak [0] 
[(
\ast 
)
] , \linebreak [0] 
[|f
\ast 
|
] , \linebreak [0] 
[|r
\ast 
|
] , \linebreak [0] 
[Limit(
\ast 
,
\ast 
)
] , \linebreak [0] 
[Union(
\ast 
)
] , \linebreak [0] 
[IsOrderedPair(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[IsRelation(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[isFunction(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[IsSeries(
\ast 
,
\ast 
)
] , \linebreak [0] 
[IsNatural(
\ast 
,\ast
)
] , \linebreak [0] 
[OrderedPair(
\ast 
,
\ast 
)
] , \linebreak [0] 
[TypeNat(
\ast 
)
] , \linebreak [0] 
[TypeNat0(
\ast 
)
] , \linebreak [0] 
[TypeRational(
\ast 
)
] , \linebreak [0] 
[TypeRational0(
\ast 
)
] , \linebreak [0] 
[TypeSeries(
\ast 
,
\ast 
)
] , \linebreak [0] 
[Typeseries0(
\ast 
,
\ast 
)
]
; 
\newline \mathbf {Preassociative} \newline 
[\{
\ast 
,
\ast 
\}
] , \linebreak [0] 
[\langle 
\ast 
,
\ast 
\rangle
] , \linebreak [0] 
[(-u
\ast 
)
] , \linebreak [0] 
[-_{f}
\ast 
] , \linebreak [0] 
[(--
\ast 
)
] , \linebreak [0] 
[1f/
\ast 
] , \linebreak [0] 
[01//temp
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
(
\ast 
,
\ast 
)
] , \linebreak [0] 
[ReflRel(
\ast 
,
\ast 
)
] , \linebreak [0] 
[SymRel(
\ast 
,
\ast 
)
] , \linebreak [0] 
[TransRel(
\ast 
,
\ast 
)
] , \linebreak [0] 
[EqRel(
\ast 
,
\ast 
)
] , \linebreak [0] 
[[
\ast 
 \mathrel{\in} 
\ast 
]_{
\ast 
}
] , \linebreak [0] 
[Partition(
\ast 
,
\ast 
)
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\cdot 
\ast 
] , \linebreak [0] 
[
\ast 
\cdot_0 
\ast 
] , \linebreak [0] 
[(
\ast 
*
\ast 
)
] , \linebreak [0] 
[
\ast 
*_{f}
\ast 
] , \linebreak [0] 
[
\ast 
**
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
+ 
\ast 
] , \linebreak [0] 
[
\ast 
\mathop{+_0} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathop{+_1} 
\ast 
] , \linebreak [0] 
[
\ast 
- 
\ast 
] , \linebreak [0] 
[
\ast 
\mathop{-_0} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathop{-_1} 
\ast 
] , \linebreak [0] 
[(
\ast 
+
\ast 
)
] , \linebreak [0] 
[(
\ast 
-
\ast 
)
] , \linebreak [0] 
[
\ast 
+_{f}
\ast 
] , \linebreak [0] 
[
\ast 
-_{f}
\ast 
] , \linebreak [0] 
[
\ast 
++
\ast 
] , \linebreak [0] 
[R(
\ast 
) -- R(
\ast 
)
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
 \mathrel{\in} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[|
\ast 
|
] , \linebreak [0] 
[if(
\ast 
,
\ast 
,
\ast 
)
] , \linebreak [0] 
[Max(
\ast 
,
\ast 
)
] , \linebreak [0] 
[Max(
\ast 
,
\ast 
)
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
 = 
\ast 
] , \linebreak [0] 
[
\ast 
 \neq 
\ast 
] , \linebreak [0] 
[
\ast 
 <= 
\ast 
] , \linebreak [0] 
[
\ast 
 < 
\ast 
] , \linebreak [0] 
[
\ast 
<_{f}
\ast 
] , \linebreak [0] 
[
\ast 
\leq_{f}
\ast 
] , \linebreak [0] 
[SF(
\ast 
,
\ast 
)
] , \linebreak [0] 
[
\ast 
 == 
\ast 
] , \linebreak [0] 
[
\ast 
 !!== 
\ast 
] , \linebreak [0] 
[
\ast 
 << 
\ast 
] , \linebreak [0] 
[
\ast 
 <<== 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\cup \{ 
\ast 
\}
] , \linebreak [0] 
[
\ast 
\cup 
\ast 
] , \linebreak [0] 
[
\ast 
\backslash \{ 
\ast 
\}
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel { \dot { . \, . } }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { \underline { \dot { . \, . } } }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { \underline { : \, : } }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { \underline { {+} 2 \ast } }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { : \, : }
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel { {+} 2 \ast }
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
,\linebreak [0] 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\stackrel {B}{\approx }
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {D}{\approx }
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {C}{\approx }
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {P}{\approx }
\ast 
] , \linebreak [0] 
[
\ast 
\approx 
\ast 
] , \linebreak [0] 
[
\ast 
=
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {+}{\rightarrow }
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {t}{=}
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel {t^*}{=}
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel{r}{=} 
\ast 
] , \linebreak [0] 
[
\ast 
\in_t 
\ast 
] , \linebreak [0] 
[
\ast 
\subseteq_T 
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel{T}{=} 
\ast 
] , \linebreak [0] 
[
\ast 
\stackrel{s}{=} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {free\ in} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {free\ in}^{\ast} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {free\ for} 
\ast 
\mathrel {in} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {free\ for}^{\ast} 
\ast 
\mathrel {in} 
\ast 
] , \linebreak [0] 
[
\ast 
\in_c 
\ast 
] , \linebreak [0] 
[
\ast 
< 
\ast 
] , \linebreak [0] 
[
\ast 
<' 
\ast 
] , \linebreak [0] 
[
\ast 
\le' 
\ast 
] , \linebreak [0] 
[
\ast 
= 
\ast 
] , \linebreak [0] 
[
\ast 
\neq 
\ast 
] , \linebreak [0] 
[
\ast 
{}^{var}
] , \linebreak [0] 
[
\ast 
\#^0
\ast 
] , \linebreak [0] 
[
\ast 
\#^1
\ast 
] , \linebreak [0] 
[
\ast 
\#^*
\ast 
] , \linebreak [0] 
[
\ast 
\!\mathrel{==}\! 
\ast 
] , \linebreak [0] 
[
\ast 
 \mathrel{\subseteq} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
{\neg }
\ast 
] , \linebreak [0] 
[\dot{\neg}\,(
\ast 
)n
] , \linebreak [0] 
[
\ast 
 \mathrel{\notin} 
\ast 
] , \linebreak [0] 
[
\ast 
 \mathrel{\neq} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\wedge 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{\ddot{\wedge}} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{\tilde{\wedge}} 
\ast 
] , \linebreak [0] 
[
\ast 
\wedge_c 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{\dot{\wedge}} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\vee 
\ast 
] , \linebreak [0] 
[
\ast 
\parallel 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{\ddot{\vee}} 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
 \mathrel{\dot{\vee}} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\exists 
\ast 
\colon 
\ast 
] , \linebreak [0] 
[
\forall 
\ast 
\colon 
\ast 
] , \linebreak [0] 
[
\forall_{obj} 
\ast 
\colon 
\ast 
] , \linebreak [0] 
[
\exists 
\ast 
\colon 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel{\ddot{\Rightarrow}} 
\ast 
] , \linebreak [0] 
[
\ast 
\Rightarrow 
\ast 
] , \linebreak [0] 
[
\ast 
\Leftrightarrow 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{\dot{\Leftrightarrow}} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[ \{ ph \mathrel{\in} 
\ast 
\mid 
\ast 
\}
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
:
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{spy}
\ast 
] , \linebreak [0] 
[
\ast 
!
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\left\{\protect \begin {array}{l}
\ast 
\\
\ast 
\protect \end {array}\right.
]
; 
\newline \mathbf {Preassociative} \newline 
[
\lambda 
\ast 
.
\ast 
] , \linebreak [0] 
[
\Lambda 
\ast 
. 
\ast 
] , \linebreak [0] 
[
\Lambda 
\ast 
] , \linebreak [0] 
[
{\bf if} \ 
\ast 
\ {\bf then} \ 
\ast 
\ {\bf else} \ 
\ast 
] , \linebreak [0] 
[
\mathbf{let\ } 
\ast 
= 
\ast 
\mathbf{\ in\ } 
\ast 
] , \linebreak [0] 
[
\mathbf{let\ } 
\ast 
\mathrel{\ddot{=}} 
\ast 
\mathrel{\ in\ } 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\#
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
{} ^ { I }
] , \linebreak [0] 
[
\ast 
{} ^ { \rhd }
] , \linebreak [0] 
[
\ast 
{} ^ { V } 
] , \linebreak [0] 
[
\ast 
{} ^ { + } 
] , \linebreak [0] 
[
\ast 
{} ^ { - } 
] , \linebreak [0] 
[
\ast 
{} ^ { \ast } 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\mathop {\char64} 
\ast 
] , \linebreak [0] 
[
\ast 
\rhd 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {\makebox [0mm][l]{$\rhd $}\,{\rhd }} 
\ast 
] , \linebreak [0] 
[
\ast 
\gg 
\ast 
] , \linebreak [0] 
[
\ast 
\unrhd 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\vdash 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel {i.e.} 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\forall 
\ast 
\colon 
\ast 
] , \linebreak [0] 
[
\Pi 
\ast 
\colon 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel {\oplus} 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
; 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\ proves\ 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\mathbf{\ proof\ of\ } 
\ast 
: 
\ast 
] , \linebreak [0] 
[
Line \, 
\ast 
: 
\ast 
\gg 
\ast 
; 
\ast 
] , \linebreak [0] 
[
Last\ line \, 
\ast 
\gg 
\ast 
\,\Box
] , \linebreak [0] 
[
Line \, 
\ast 
: Premise \gg 
\ast 
;
\ast 
] , \linebreak [0] 
[
Line \, 
\ast 
: \mbox{Side-condition} \gg 
\ast 
; 
\ast 
] , \linebreak [0] 
[
Arbitrary \gg 
\ast 
;
\ast 
] , \linebreak [0] 
[
Local \gg 
\ast 
= 
\ast 
; 
\ast 
] , \linebreak [0] 
[
Begin \, 
\ast 
 ; 
\ast 
 : End ; 
\ast 
] , \linebreak [0] 
[
Last\ block\ line \, 
\ast 
\gg 
\ast 
\,;
] , \linebreak [0] 
[
Arbitrary \gg 
\ast 
;
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel{|} 
\ast 
]
; 
\newline\mathbf{Postassociative} \newline 
[
\ast 
\mathrel{\mathrm{,}}
\ast 
] , \linebreak [0] 
[
\ast 
{[}
\ast 
{]}
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\& 
\ast 
]
; 
\newline \mathbf {Preassociative} \newline 
[
\ast 
\backslash \backslash 
\ast 
] , \linebreak [0] 
[
\ast 
\mathrel{linebreak[4]} 
\ast 
] , \linebreak [0] 
[
\ast 
\backslash \backslash 
\ast 
]
; 
]$

$\rm
[kvanti
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}kvanti
\mbox{''}
]$

$\rm
[kvanti
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}kvanti
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:1}{}\section* {$\rm UniqueMember$}

$\rm
[UniqueMember
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UniqueMember
\mbox{''}
]$

$\rm
[UniqueMember
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}uniqueMember
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:2}{}\section* {$\rm UniqueMember(Type)$}

$\rm
[UniqueMember(Type)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UniqueMember(Type)
\mbox{''}
]$

$\rm
[UniqueMember(Type)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}uniqueMember(Type)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:3}{}\section* {$\rm SameSeries$}

$\rm
[SameSeries
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SameSeries
\mbox{''}
]$

$\rm
[SameSeries
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}sameSeries
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:4}{}\section* {$\rm A4$}

$\rm
[A4
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}A4
\mbox{''}
]$

$\rm
[A4
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}a4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:5}{}\section* {$\rm SameMember$}

$\rm
[SameMember
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SameMember
\mbox{''}
]$

$\rm
[SameMember
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}sameMember
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:6}{}\section* {$\rm Qclosed(Addition)$}

$\rm
[Qclosed(Addition)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Qclosed(Addition)
\mbox{''}
]$

$\rm
[Qclosed(Addition)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}Qclosed(Addition)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:7}{}\section* {$\rm Qclosed(Multiplication)$}

$\rm
[Qclosed(Multiplication)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Qclosed(Multiplication)
\mbox{''}
]$

$\rm
[Qclosed(Multiplication)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}Qclosed(Multiplication)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:8}{}\section* {$\rm FromCartProd(1)$}

$\rm
[FromCartProd(1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromCartProd(1)
\mbox{''}
]$

$\rm
[FromCartProd(1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}fromCartProd(1)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:9}{}\section* {$\rm 
\mbox{1rule fromCartProd(2)}$}

$\rm
[
\mbox{1rule fromCartProd(2)}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}fromCartProd(2)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:10}{}\section* {$\rm constantRationalSeries(\ast
)$}

$\rm
[constantRationalSeries(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}constantRationalSeries(
\#1.
\newline )
\mbox{''}
]$

$\rm
[constantRationalSeries(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}constantRationalSeries(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:11}{}\section* {$\rm cartProd(\ast
)$}

$\rm
[cartProd(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}cartProd(
\#1.
\newline )
\mbox{''}
]$

$\rm
[cartProd(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}cartProd(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:12}{}\section* {$\rm Power(\ast
)$}

$\rm
[Power(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Power(
\#1.
\newline )
\mbox{''}
]$

$\rm
[Power(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}P(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:13}{}\section* {$\rm binaryUnion(\ast
,\ast
)$}

$\rm
[binaryUnion(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}binaryUnion(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[binaryUnion(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}binaryUnion(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:14}{}\section* {$\rm SetOfRationalSeries$}

$\rm
[SetOfRationalSeries
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SetOfRationalSeries
\mbox{''}
]$

$\rm
[SetOfRationalSeries
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}setOfRationalSeries
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:15}{}\section* {$\rm IsSubset(\ast
,\ast
)$}

$\rm
[IsSubset(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IsSubset(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[IsSubset(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}isSubset(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:16}{}\section* {$\rm (p\ast
,\ast
)$}

$\rm
[(p
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(p
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[(p
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}(p
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:17}{}\section* {$\rm (s\ast
)$}

$\rm
[(s
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(s
\#1.
\newline )
\mbox{''}
]$

$\rm
[(s
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}(s
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:18}{}\section* {$\rm (\cdots{})$}

$\rm
[(\cdots{})
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\mbox {$\backslash $}cdots
\{
\})
\mbox{''}
]$

$\rm
[(\cdots{})
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}cdots
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:19}{}\section* {$\rm \texttt{Objekt-var}$}

$\rm
[\texttt{Objekt-var}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}texttt
\{Objekt
\mbox{-}var
\}
\mbox{''}
]$

$\rm
[\texttt{Objekt-var}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\mbox{-}var
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:20}{}\section* {$\rm \texttt{Ex-var}$}

$\rm
[\texttt{Ex-var}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}texttt
\{Ex
\mbox{-}var
\}
\mbox{''}
]$

$\rm
[\texttt{Ex-var}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ex
\mbox{-}var
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:21}{}\section* {$\rm \texttt{Ph-var}$}

$\rm
[\texttt{Ph-var}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}texttt
\{Ph
\mbox{-}var
\}
\mbox{''}
]$

$\rm
[\texttt{Ph-var}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph
\mbox{-}var
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:22}{}\section* {$\rm \texttt{V\ae{}rdi}$}

$\rm
[\texttt{V\ae{}rdi}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}texttt
\{V
\mbox {$\backslash $}ae
\{
\}rdi
\}
\mbox{''}
]$

$\rm
[\texttt{V\ae{}rdi}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}vaerdi
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:23}{}\section* {$\rm \texttt{Variabel}$}

$\rm
[\texttt{Variabel}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}texttt
\{Variabel
\}
\mbox{''}
]$

$\rm
[\texttt{Variabel}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}variabel
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:24}{}\section* {$\rm Op(\ast
)$}

$\rm
[Op(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Op(
\#1.
\newline )
\mbox{''}
]$

$\rm
[Op(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}op
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}op
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:25}{}\section* {$\rm Op(\ast
,\ast
)$}

$\rm
[Op(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Op(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[Op(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}op2
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}comma
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}op2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:26}{}\section* {$\rm \ast
 \mathrel {\ddot {==}} \ast$}

$\rm
[
\mathsf{x}
 \mathrel {\ddot {==}} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\linebreak [0]\ \hskip0em plus2.0em{}
\{
\mbox {$\backslash $}ddot
\linebreak [0]\ \hskip0em plus2.0em{}
\{
{=}
{=}
\}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \mathrel {\ddot {==}} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}define
\mbox{-}equal
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}comma
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}equal
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:27}{}\section* {$\rm ContainsEmpty(\ast
)$}

$\rm
[ContainsEmpty(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ContainsEmpty(
\#1.
\newline )
\mbox{''}
]$

$\rm
[ContainsEmpty(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}contains
\mbox{-}empty
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}empty
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:28}{}\section* {$\rm Nat(\ast
)$}

$\rm
[Nat(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Nat(
\#1.
\newline )
\mbox{''}
]$

$\rm
[Nat(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}Nat(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:29}{}\section* {$\rm 
Dedu(\ast
,\ast
)$}

$\rm
[
Dedu(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[
Dedu(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:30}{}\section* {$\rm 
Dedu_0(\ast
,\ast
)$}

$\rm
[
Dedu_0(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_0(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_0(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}zero
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:31}{}\section* {$\rm Dedu_{s}(\ast
,\ast
,\ast
)$}

$\rm
[Dedu_{s}(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Dedu
\_
\{s
\}(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[Dedu_{s}(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}side
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:32}{}\section* {$\rm 
Dedu_1(\ast
,\ast
,\ast
)$}

$\rm
[
Dedu_1(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_1(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_1(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}one
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:33}{}\section* {$\rm 
Dedu_2(\ast
,\ast
,\ast
)$}

$\rm
[
Dedu_2(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_2(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_2(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:34}{}\section* {$\rm 
Dedu_3(\ast
,\ast
,\ast
,\ast
)$}

$\rm
[
Dedu_3(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
,
\mathsf {u}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_3(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_3(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:35}{}\section* {$\rm 
Dedu_4(\ast
,\ast
,\ast
,\ast
)$}

$\rm
[
Dedu_4(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
,
\mathsf {u}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_4(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_4(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:36}{}\section* {$\rm 
Dedu_4^*(\ast
,\ast
,\ast
,\ast
)$}

$\rm
[
Dedu_4^*(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
,
\mathsf {u}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_4
{\char94}
{*}(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_4^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}four
\linebreak [0]\ \hskip0em plus2.0em{}star
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:37}{}\section* {$\rm 
Dedu_5(\ast
,\ast
,\ast
)$}

$\rm
[
Dedu_5(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_5(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_5(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}five
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}condition
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:38}{}\section* {$\rm 
Dedu_6(\ast
,\ast
,\ast
,\ast
)$}

$\rm
[
Dedu_6(
\mathsf {p}
,
\mathsf {c}
,
\mathsf {e}
,
\mathsf {b}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_6(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_6(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}six
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}exception
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:39}{}\section* {$\rm 
Dedu_6^*(\ast
,\ast
,\ast
,\ast
)$}

$\rm
[
Dedu_6^*(
\mathsf {p}
,
\mathsf {c}
,
\mathsf {e}
,
\mathsf {b}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_6
{\char94}
{*}(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline ,
\#4.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_6^*(
\ast 
,
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}six
\linebreak [0]\ \hskip0em plus2.0em{}star
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}conclude
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}exception
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:40}{}\section* {$\rm 
Dedu_7(\ast
)$}

$\rm
[
Dedu_7(
\mathsf {p}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_7(
\#1.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_7(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}seven
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:41}{}\section* {$\rm 
Dedu_8(\ast
,\ast
)$}

$\rm
[
Dedu_8(
\mathsf {p}
,
\mathsf {b}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_8(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_8(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}eight
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:42}{}\section* {$\rm 
Dedu_8^*(\ast
,\ast
)$}

$\rm
[
Dedu_8^*(
\mathsf {p}
,
\mathsf {b}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline Dedu
\_8
{\char94}
{*}(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[
Dedu_8^*(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1deduction
\linebreak [0]\ \hskip0em plus2.0em{}eight
\linebreak [0]\ \hskip0em plus2.0em{}star
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}bound
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}1deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:43}{}\section* {$\rm Ex_{1}$}

$\rm
[Ex_{1}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[Ex_{1}
\mathrel {\ddot {=}}
\mathsf {a}
 _{Ex}
]
\rceil 
)
]$

$\rm
[Ex_{1}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Ex
\_
\{1
\}
\mbox{''}
]$

$\rm
[Ex_{1}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ex1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:44}{}\section* {$\rm Ex_{2}$}

$\rm
[Ex_{2}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[Ex_{2}
\mathrel {\ddot {=}}
\mathsf {b}
 _{Ex}
]
\rceil 
)
]$

$\rm
[Ex_{2}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Ex
\_
\{2
\}
\mbox{''}
]$

$\rm
[Ex_{2}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ex2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:45}{}\section* {$\rm Ex3$}

$\rm
[Ex3
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[Ex3
\mathrel {\ddot {=}}
\mathsf {c}
 _{Ex}
]
\rceil 
)
]$

$\rm
[Ex3
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Ex3
\mbox{''}
]$

$\rm
[Ex3
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ex3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:46}{}\section* {$\rm Ex_{10}$}

$\rm
[Ex_{10}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[Ex_{10}
\mathrel {\ddot {=}}
\mathsf {j}
 _{Ex}
]
\rceil 
)
]$

$\rm
[Ex_{10}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Ex
\_
\{10
\}
\mbox{''}
]$

$\rm
[Ex_{10}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ex10
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:47}{}\section* {$\rm Ex_{20}$}

$\rm
[Ex_{20}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[Ex_{20}
\mathrel {\ddot {=}}
\mathsf {t}
 _{Ex}
]
\rceil 
)
]$

$\rm
[Ex_{20}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Ex
\_
\{20
\}
\mbox{''}
]$

$\rm
[Ex_{20}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ex20
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:48}{}\section* {$\rm \ast
 _{Ex}$}

$\rm
[
\mathsf{x}
 _{Ex}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\_
\{Ex
\}
\mbox{''}
]$

$\rm
[
\ast 
 _{Ex}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}existential
\linebreak [0]\ \hskip0em plus2.0em{}var
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}var
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:49}{}\section* {$\rm \ast
 ^{Ex}$}

$\rm
[
\mathsf{x}
 ^{Ex}
\stackrel{
\mathrm {val}
}{\rightarrow}
\mathsf{x}
\stackrel{r}{=} 
\lceil 
\mathsf{x}
 _{Ex}
\rceil 
]$

$\rm
[
\mathsf{x}
 ^{Ex}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{\char94}
\{Ex
\}
\mbox{''}
]$

$\rm
[
\ast 
 ^{Ex}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}existential
\linebreak [0]\ \hskip0em plus2.0em{}var
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:50}{}\section* {$\rm \langle \ast
{\equiv} \ast
| \ast
{:==} \ast
\rangle_{Ex} $}

$\rm
[\langle 
\mathsf {a}
{\equiv} 
\mathsf {b}
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[\langle 
\mathsf {a}
{\equiv} 
\mathsf {b}
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
\mathrel {\ddot {=}}\langle 
\lceil 
\mathsf {a}
\rceil 
{\equiv}^0 
\lceil 
\mathsf {b}
\rceil 
| 
\lceil 
\mathsf{x}
\rceil 
{:==} 
\lceil 
\mathsf {t}
\rceil 
\rangle_{Ex} 
]
\rceil 
)
]$

$\rm
[\langle 
\mathsf{x}
{\equiv} 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Ex} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Ex
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ex} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}exist
\mbox{-}sub
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:51}{}\section* {$\rm \langle \ast
{\equiv}^0 \ast
| \ast
{:==} \ast
\rangle_{Ex} $}

$\rm
[\langle 
\mathsf {a}
{\equiv}^0 
\mathsf {b}
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
\stackrel{
\mathrm {val}
}{\rightarrow}
\lambda 
\mathsf {c}
.
\mathsf{x}
 ^{Ex}
\wedge \langle 
\mathsf {a}
{\equiv}^1 
\mathsf {b}
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
]$

$\rm
[\langle 
\mathsf{x}
{\equiv}^0 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Ex} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}0
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Ex
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv}^0 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ex} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}exist
\mbox{-}sub0
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:52}{}\section* {$\rm \langle \ast
{\equiv}^1 \ast
| \ast
{:==} \ast
\rangle_{Ex} $}

$\rm
[\langle 
\mathsf {a}
{\equiv}^1 
\mathsf {b}
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
\stackrel{
\mathrm {val}
}{\rightarrow}
\mathsf {a}
!
\mathsf{x}
!
\mathsf {t}
!
\newline 
\mathrm {If}(
\mathsf {b}
\stackrel{r}{=} 
\lceil 
\forall_{obj} 
\mathsf {u}
\colon 
\mathsf {v}
\rceil 
,\linebreak [0]
\mathsf {F}
,\linebreak [0]
\newline 
\mathrm {If}(
\mathsf {b}
 ^{Ex}
\wedge 
\mathsf {b}
\stackrel {t}{=}
\mathsf{x}
,\linebreak [0]
\mathsf {a}
\stackrel {t}{=}
\mathsf {t}
,\linebreak [0]
\mathrm {If}(
\newline 
\mathsf {a}
\stackrel{r}{=} 
\mathsf {b}
,\linebreak [0]\langle 
\mathsf {a}
{}^t
{\equiv}^* 
\mathsf {b}
{}^t
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
,\linebreak [0]
\mathsf {F}
)
)
)
]$

$\rm
[\langle 
\mathsf{x}
{\equiv}^1 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Ex} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}1
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Ex
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ex} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}exist
\mbox{-}sub1
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:53}{}\section* {$\rm \langle \ast
{\equiv}^* \ast
| \ast
{:==} \ast
\rangle_{Ex} $}

$\rm
[\langle 
\mathsf {a}
{\equiv}^* 
\mathsf {b}
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
\stackrel{
\mathrm {val}
}{\rightarrow}
\mathsf {b}
!
\mathsf{x}
!
\mathsf {t}
!
\mathrm {If}(
\mathsf {a}
,\linebreak [0]
\mathsf {T}
,\linebreak [0]
\mathrm {If}(\langle 
\mathsf {a}
{}^h
{\equiv}^1 
\mathsf {b}
{}^h
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
,\linebreak [0]\langle 
\mathsf {a}
{}^t
{\equiv}^* 
\mathsf {b}
{}^t
| 
\mathsf{x}
{:==} 
\mathsf {t}
\rangle_{Ex} 
,\linebreak [0]
\mathsf {F}
)
)
]$

$\rm
[\langle 
\mathsf{x}
{\equiv}^* 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Ex} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Ex
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ex} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}exist
\mbox{-}sub
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:54}{}\section* {$\rm ph_{1}$}

$\rm
[ph_{1}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[ph_{1}
\mathrel {\ddot {=}}
\mathsf {a}
 _{Ph} 
]
\rceil 
)
]$

$\rm
[ph_{1}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ph
\_
\{1
\}
\mbox{''}
]$

$\rm
[ph_{1}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:55}{}\section* {$\rm ph_{2}$}

$\rm
[ph_{2}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[ph_{2}
\mathrel {\ddot {=}}
\mathsf {b}
 _{Ph} 
]
\rceil 
)
]$

$\rm
[ph_{2}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ph
\_
\{2
\}
\mbox{''}
]$

$\rm
[ph_{2}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:56}{}\section* {$\rm ph_{3}$}

$\rm
[ph_{3}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[ph_{3}
\mathrel {\ddot {=}}
\mathsf {c}
 _{Ph} 
]
\rceil 
)
]$

$\rm
[ph_{3}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ph
\_
\{3
\}
\mbox{''}
]$

$\rm
[ph_{3}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:57}{}\section* {$\rm \ast
 _{Ph} $}

$\rm
[
\ast 
 _{Ph} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\_
\{Ph
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[
\ast 
 _{Ph} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}placeholder
\mbox{-}var
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}var
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:58}{}\section* {$\rm \ast
 ^{Ph}$}

$\rm
[
\mathsf{x}
 ^{Ph}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{\char94}
\{Ph
\}
\mbox{''}
]$

$\rm
[
\ast 
 ^{Ph}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}placeholder
\mbox{-}var
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:59}{}\section* {$\rm \langle \ast
{\equiv} \ast
| \ast
{:==} \ast
\rangle_{Ph} $}

$\rm
[\langle 
\mathsf{x}
{\equiv} 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Ph} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Ph
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ph} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph
\mbox{-}sub
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:60}{}\section* {$\rm \langle \ast
{\equiv}^0 \ast
| \ast
{:==} \ast
\rangle_{Ph} $}

$\rm
[\langle 
\mathsf{x}
{\equiv}^0 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Ph} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}0
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Ph
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv}^0 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ph} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph
\mbox{-}sub0
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:61}{}\section* {$\rm \langle \ast
{\equiv}^1 \ast
| \ast
{:==} \ast
\rangle_{Ph} $}

$\rm
[\langle 
\mathsf{x}
{\equiv}^1 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Ph} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}1
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Ph
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ph} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph
\mbox{-}sub1
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:62}{}\section* {$\rm \langle \ast
{\equiv}^* \ast
| \ast
{:==} \ast
\rangle_{Ph} $}

$\rm
[\langle 
\mathsf{x}
{\equiv}^* 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Ph} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Ph
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Ph} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph
\mbox{-}sub
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:63}{}\section* {$\rm \langle \ast
{\equiv} \ast
| \ast
{:==} \ast
\rangle_{Me}$}

$\rm
[\langle 
\mathsf{x}
{\equiv} 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Me}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Me
\}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv} 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Me}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\mbox{-}sub
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:64}{}\section* {$\rm \langle \ast
{\equiv}^1 \ast
| \ast
{:==} \ast
\rangle_{Me} $}

$\rm
[\langle 
\mathsf{x}
{\equiv}^1 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Me} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}1
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Me
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv}^1 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Me} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\mbox{-}sub1
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:65}{}\section* {$\rm \langle \ast
{\equiv}^* \ast
| \ast
{:==} \ast
\rangle_{Me} $}

$\rm
[\langle 
\mathsf{x}
{\equiv}^* 
\mathsf{y}
| 
\mathsf{z}
{:==} 
\mathsf {u}
\rangle_{Me} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\{
\mbox {$\backslash $}equiv
\}
{\char94}
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline |
\linebreak [0]\ \hskip0em plus2.0em{}
\#3.
\newline 
\{
{:}
{=}
{=}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#4.
\newline 
\mbox {$\backslash $}rangle
\_
\{Me
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[\langle 
\ast 
{\equiv}^* 
\ast 
| 
\ast 
{:==} 
\ast 
\rangle_{Me} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\mbox{-}sub
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}where
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}sub
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:66}{}\section* {$\rm \mathsf {bs}$}

$\rm
[\mathsf {bs}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}mathsf
\linebreak [0]\ \hskip0em plus2.0em{}
\{bs
\}
\mbox{''}
]$

$\rm
[\mathsf {bs}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}big
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:67}{}\section* {$\rm  \mathsf {OBS}$}

$\rm
[ \mathsf {OBS}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[ \mathsf {OBS}
\mathrel {\ddot {=}}\overline{\mathsf {bs}}
]
\rceil 
)
]$

$\rm
[ \mathsf {OBS}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathsf
\linebreak [0]\ \hskip0em plus2.0em{}
\{OBS
\}
\mbox{''}
]$

$\rm
[ \mathsf {OBS}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}big
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:68}{}\section* {$\rm {\cal BS}$}

$\rm
[{\cal BS}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[{\cal BS}
\mathrel {\ddot {=}}\underline{\mathsf {bs}}
]
\rceil 
)
]$

$\rm
[{\cal BS}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\{
\mbox {$\backslash $}cal
\linebreak [0]\ \hskip0em plus2.0em{}BS
\}
\mbox{''}
]$

$\rm
[{\cal BS}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}big
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:69}{}\section* {$\rm \mathrm{\O}$}

$\rm
[\mathrm{\O}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}mathrm
\{
\mbox {$\backslash $}O
\}
\mbox{''}
]$

$\rm
[\mathrm{\O}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}zermelo
\linebreak [0]\ \hskip0em plus2.0em{}empty
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:70}{}\section* {$\rm SystemQ$}

$\rm
[SystemQ
\stackrel{
stmt
}{\rightarrow}
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon R(\underline{(fx)}
)
++R(\underline{(fy)}
)
 == R(\underline{(fy)}
)
++R(\underline{(fx)}
)
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon 
\forall \underline{(fz)}
\colon R(\underline{(fx)}
)
**R(\underline{(fy)}
)
**R(\underline{(fz)}
)
 == R(\underline{(fx)}
)
**R(\underline{(fy)}
)
**R(\underline{(fz)}
)
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(rx)}
\colon 
\forall \underline{(ry)}
\colon \underline{(rx)}
 == \underline{(ry)}
\vdash \underline{(fx)}
 \mathrel{\in} \underline{(rx)}
\vdash \underline{(fx)}
 \mathrel{\in} \underline{(ry)}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon UB(01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
, SetOfReals
)
\vdash xs
[(\underline{
\mathsf {m}}
+1
)
]
 == xs
[\underline{
\mathsf {m}}
]
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf{y}}
 <= \underline{
\mathsf{x}}
\Rightarrow \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {s}}
\colon 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} \{\underline{
\mathsf{x}}
,\underline{
\mathsf{y}}
\}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {s}}
\!\mathrel{==}\! \underline{
\mathsf{x}}
)n
\Rightarrow \underline{
\mathsf {s}}
\!\mathrel{==}\! \underline{
\mathsf{y}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {s}}
\!\mathrel{==}\! \underline{
\mathsf{x}}
)n
\Rightarrow \underline{
\mathsf {s}}
\!\mathrel{==}\! \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf {s}}
 \mathrel{\in} \{\underline{
\mathsf{x}}
,\underline{
\mathsf{y}}
\}
)n
)n
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon \underline{
\mathsf {n}}
 = 0
\vdash BS(\underline{
\mathsf {m}}
,\underline{
\mathsf {n}}
)
 =  rec(1
+1
)
 (exp) \underline{
\mathsf {m}}
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon (\underline{
\mathsf{x}}
+0
)
 = \underline{
\mathsf{x}}
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon R(\underline{(fx)}
)
 == R(\underline{(fy)}
)
\vdash SF(\underline{(fx)}
,\underline{(fy)}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\vdash \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon 
\forall \underline{(fz)}
\colon R(\underline{(fx)}
)
 = R(\underline{(fy)}
)
\vdash R(\underline{(fx)}
)
++R(\underline{(fz)}
)
 = R(\underline{(fy)}
)
++R(\underline{(fz)}
)
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon R(\underline{(fx)}
)
++R(0f
)
 == R(\underline{(fx)}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon (\underline{
\mathsf{x}}
*1
)
 = \underline{
\mathsf{x}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
\mathrel {\oplus} 
\forall \underline{(rx)}
\colon 
\forall \underline{(ry)}
\colon \underline{(rx)}
 == \underline{(ry)}
\vdash \underline{(ry)}
 == \underline{(rx)}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf{x}}
\colon \underline{
\mathsf {m}}
 = 0
\vdash  \underline{
\mathsf{x}}
 (exp) \underline{
\mathsf {m}}
 = 1
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon 0
 <= \underline{
\mathsf{z}}
\Rightarrow \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\Rightarrow (\underline{
\mathsf{x}}
*\underline{
\mathsf{z}}
)
 <= (\underline{
\mathsf{y}}
*\underline{
\mathsf{z}}
)
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon R(\underline{(fx)}
)
**R(
\mbox{1f}
)
 == R(\underline{(fx)}
)
\mathrel {\oplus} \dot{\neg}\,(0
 = 1
)n
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon Nat(\underline{
\mathsf {m}}
)
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} 0
 <= \underline{
\mathsf {m}}
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \dot{\neg}\,(\underline{
\mathsf{x}}
\!\mathrel{==}\! \underline{
\mathsf{y}}
\Rightarrow 
\forall_{obj} \overline{
\mathsf {s}}
\colon \dot{\neg}\,(\overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{y}}
\Rightarrow \dot{\neg}\,(\overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{y}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
)n
)n
\Rightarrow \dot{\neg}\,(
\forall_{obj} \overline{
\mathsf {s}}
\colon \dot{\neg}\,(\overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{y}}
\Rightarrow \dot{\neg}\,(\overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{y}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
)n
)n
\Rightarrow \underline{
\mathsf{x}}
\!\mathrel{==}\! \underline{
\mathsf{y}}
)n
)n
\mathrel {\oplus} 
\forall \underline{(rx)}
\colon 
\forall \underline{(ry)}
\colon 
\forall \underline{(rz)}
\colon \underline{(rx)}
 == \underline{(ry)}
\vdash \underline{(ry)}
 == \underline{(rz)}
\vdash \underline{(rx)}
 == \underline{(rz)}
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon (\underline{
\mathsf{x}}
+\underline{
\mathsf{y}}
)
 = (\underline{
\mathsf{y}}
+\underline{
\mathsf{x}}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon \underline{(fx)}
+_{f}\underline{(fy)}
[\underline{
\mathsf {m}}
]
 = (\underline{(fx)}
[\underline{
\mathsf {m}}
]
+\underline{(fy)}
[\underline{
\mathsf {m}}
]
)
\mathrel {\oplus} 
\forall \underline{(v1)}
\colon 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon \langle \underline{
\mathsf {b}}
{\equiv} \underline{
\mathsf {a}}
| \underline{(v1)}
{:==} 0
\rangle_{Me}
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \langle \underline{
\mathsf {c}}
{\equiv} \underline{
\mathsf {a}}
| \underline{(v1)}
{:==} (\underline{(v1)}
+1
)
\rangle_{Me}
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \underline{
\mathsf {b}}
\Rightarrow 
\forall_{obj} \underline{(v1)}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow 
\forall_{obj} \underline{(v1)}
\colon \underline{
\mathsf {a}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon \underline{
\mathsf {n}}
 = 0
\vdash UStelescope(\underline{
\mathsf {m}}
,\underline{
\mathsf {n}}
)
 = |(us
[\underline{
\mathsf {m}}
]
+(-uus
[(\underline{
\mathsf {m}}
+1
)
]
)
)
|
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon 
\forall \underline{(fz)}
\colon R(\underline{(fx)}
)
++R(\underline{(fy)}
)
++R(\underline{(fz)}
)
 = R(\underline{(fx)}
)
++R(\underline{(fy)}
)
++R(\underline{(fz)}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon (\underline{
\mathsf{x}}
*\underline{
\mathsf{y}}
)
 = (\underline{
\mathsf{y}}
*\underline{
\mathsf{x}}
)
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon \underline{(fx)}
 \mathrel{\in} R(\underline{(fy)}
)
\vdash SF(\underline{(fx)}
,\underline{(fy)}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\Rightarrow (\underline{
\mathsf{x}}
*\underline{
\mathsf{z}}
)
 = (\underline{
\mathsf{y}}
*\underline{
\mathsf{z}}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf {a}}
\colon \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {a}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon UB(01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
, SetOfReals
)
\vdash us
[(\underline{
\mathsf {m}}
+1
)
]
 == 01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \dot{\neg}\,(\underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
)n
\Rightarrow \underline{
\mathsf{y}}
 <= \underline{
\mathsf{x}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {s}}
\colon 
\forall \underline{
\mathsf{x}}
\colon \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} P(\underline{
\mathsf{x}}
)
\Rightarrow 
\forall_{obj} \overline{
\mathsf {s}}
\colon \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf {s}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \dot{\neg}\,(
\forall_{obj} \overline{
\mathsf {s}}
\colon \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf {s}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \underline{
\mathsf {s}}
 \mathrel{\in} P(\underline{
\mathsf{x}}
)
)n
)n
\mathrel {\oplus} us
[0
]
 == xs
[0
]
++R(
\mbox{1f}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon \underline{
\mathsf{x}}
 <= \underline{
\mathsf{x}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {s}}
\colon \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} \mathrm{\O}
)n
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon (\underline{
\mathsf{x}}
+(-u\underline{
\mathsf{x}}
)
)
 = 0
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf{x}}
 = \underline{
\mathsf{z}}
\Rightarrow \underline{
\mathsf{y}}
 = \underline{
\mathsf{z}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon \dot{\neg}\,(0
 <= \underline{
\mathsf {n}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(0
 = \underline{
\mathsf {n}}
)n
)n
)n
\vdash UStelescope(\underline{
\mathsf {m}}
,\underline{
\mathsf {n}}
)
 = (|(us
[(\underline{
\mathsf {m}}
+\underline{
\mathsf {n}}
)
]
+(-uus
[(\underline{
\mathsf {m}}
+(\underline{
\mathsf {n}}
+1
)
)
]
)
)
|
+UStelescope(\underline{
\mathsf {m}}
,(\underline{
\mathsf {n}}
+(-u1
)
)
)
)
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon 
\forall \underline{(fz)}
\colon R(\underline{(fx)}
+_{f}\underline{(fy)}
+_{f}\underline{(fz)}
)
 == R(\underline{(fx)}
+_{f}\underline{(fy)}
+_{f}\underline{(fz)}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon \dot{\neg}\,(\underline{
\mathsf{x}}
 = 0
)n
\Rightarrow (\underline{
\mathsf{x}}
*rec\underline{
\mathsf{x}}
)
 = 1
\mathrel {\oplus} 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {a}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash \underline{
\mathsf {b}}
\mathrel {\oplus} 
\forall \underline{(rx)}
\colon \underline{(rx)}
 == \underline{(rx)}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon \dot{\neg}\,(UB(01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
, SetOfReals
)
)n
\vdash us
[(\underline{
\mathsf {m}}
+1
)
]
 == us
[\underline{
\mathsf {m}}
]
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\Rightarrow (\underline{
\mathsf{x}}
+\underline{
\mathsf{z}}
)
 <= (\underline{
\mathsf{y}}
+\underline{
\mathsf{z}}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {p}}
\colon 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf {p}}
 ^{Ph}
\wedge \langle \underline{
\mathsf {b}}
{\equiv} \underline{
\mathsf {a}}
| \underline{
\mathsf {p}}
{:==} \underline{
\mathsf{z}}
\rangle_{Ph} 
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \dot{\neg}\,(\underline{
\mathsf{z}}
 \mathrel{\in}  \{ ph \mathrel{\in} \underline{
\mathsf{x}}
\mid \underline{
\mathsf {a}}
\}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf{z}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf{z}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\Rightarrow \underline{
\mathsf{z}}
 \mathrel{\in}  \{ ph \mathrel{\in} \underline{
\mathsf{x}}
\mid \underline{
\mathsf {a}}
\}
)n
)n
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{(fx)}
\colon R(\underline{(fx)}
)
++(--R(\underline{(fx)}
)
)
 == R(0f
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon (\underline{
\mathsf{x}}
*(\underline{
\mathsf{y}}
+\underline{
\mathsf{z}}
)
)
 = ((\underline{
\mathsf{x}}
*\underline{
\mathsf{y}}
)
+(\underline{
\mathsf{x}}
*\underline{
\mathsf{z}}
)
)
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon Nat(\underline{
\mathsf {m}}
)
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} Nat(\underline{
\mathsf {n}}
)
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \dot{\neg}\,(\underline{
\mathsf {m}}
 <= (\underline{
\mathsf {n}}
+1
)
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {m}}
 = (\underline{
\mathsf {n}}
+1
)
)n
)n
)n
\vdash \underline{
\mathsf {m}}
 <= \underline{
\mathsf {n}}
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf {t}}
\colon 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \langle 
\lceil \underline{
\mathsf {a}}
\rceil 
{\equiv}^0 
\lceil \underline{
\mathsf {b}}
\rceil 
| 
\lceil \underline{
\mathsf{x}}
\rceil 
{:==} 
\lceil \underline{
\mathsf {t}}
\rceil 
\rangle_{Ex} 
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf{x}}
\colon \dot{\neg}\,(0
 <= \underline{
\mathsf {m}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(0
 = \underline{
\mathsf {m}}
)n
)n
)n
\vdash  \underline{
\mathsf{x}}
 (exp) \underline{
\mathsf {m}}
 = (\underline{
\mathsf{x}}
* \underline{
\mathsf{x}}
 (exp) (\underline{
\mathsf {m}}
+(-u1
)
)
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon ((\underline{
\mathsf{x}}
+\underline{
\mathsf{y}}
)
+\underline{
\mathsf{z}}
)
 = (\underline{
\mathsf{x}}
+(\underline{
\mathsf{y}}
+\underline{
\mathsf{z}}
)
)
\mathrel {\oplus} 
\forall \underline{(v1)}
\colon 
\forall \underline{(v2)}
\colon 
\forall \underline{
\mathsf {n}}
\colon 
\forall \underline{(\epsilon)}
\colon 
\forall \underline{(fx)}
\colon 
\forall_{obj} \underline{(\epsilon)}
\colon \dot{\neg}\,(
\forall_{obj} \underline{
\mathsf {n}}
\colon \dot{\neg}\,(
\forall_{obj} \underline{(v1)}
\colon 
\forall_{obj} \underline{(v2)}
\colon \dot{\neg}\,(0
 <= \underline{(\epsilon)}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(0
 = \underline{(\epsilon)}
)n
)n
)n
\Rightarrow \underline{
\mathsf {n}}
 <= \underline{(v1)}
\Rightarrow \underline{
\mathsf {n}}
 <= \underline{(v2)}
\Rightarrow \dot{\neg}\,(|(\underline{(fx)}
[\underline{(v1)}
]
+(-u\underline{(fx)}
[\underline{(v2)}
]
)
)
|
 <= \underline{(\epsilon)}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(|(\underline{(fx)}
[\underline{(v1)}
]
+(-u\underline{(fx)}
[\underline{(v2)}
]
)
)
|
 = \underline{(\epsilon)}
)n
)n
)n
)n
)n
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{(v1)}
\colon 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \langle \underline{
\mathsf {a}}
{\equiv} \underline{
\mathsf {b}}
| \underline{(v1)}
{:==} \underline{
\mathsf{x}}
\rangle_{Me}
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} 
\forall_{obj} \underline{(v1)}
\colon \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {a}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon \dot{\neg}\,(0
 <= \underline{
\mathsf {n}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(0
 = \underline{
\mathsf {n}}
)n
)n
)n
\vdash BS(\underline{
\mathsf {m}}
,\underline{
\mathsf {n}}
)
 = ( rec(1
+1
)
 (exp) (\underline{
\mathsf {m}}
+\underline{
\mathsf {n}}
)
+BS(\underline{
\mathsf {m}}
,(\underline{
\mathsf {n}}
+(-u1
)
)
)
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon ((\underline{
\mathsf{x}}
*\underline{
\mathsf{y}}
)
*\underline{
\mathsf{z}}
)
 = (\underline{
\mathsf{x}}
*(\underline{
\mathsf{y}}
*\underline{
\mathsf{z}}
)
)
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon SF(\underline{(fx)}
,\underline{(fy)}
)
\vdash R(\underline{(fx)}
)
 == R(\underline{(fy)}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\Rightarrow (\underline{
\mathsf{x}}
+\underline{
\mathsf{z}}
)
 = (\underline{
\mathsf{y}}
+\underline{
\mathsf{z}}
)
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf {a}}
\colon \underline{
\mathsf {a}}
\vdash 
\forall_{obj} \underline{
\mathsf{x}}
\colon \underline{
\mathsf {a}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {m}}
\colon \dot{\neg}\,(UB(01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
, SetOfReals
)
)n
\vdash xs
[(\underline{
\mathsf {m}}
+1
)
]
 == 01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
\mathrel {\oplus} 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf{y}}
 <= \underline{
\mathsf{z}}
\Rightarrow \underline{
\mathsf{x}}
 <= \underline{
\mathsf{z}}
\mathrel {\oplus} 
\forall \underline{
\mathsf {s}}
\colon 
\forall \underline{
\mathsf{x}}
\colon \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} \cup \underline{
\mathsf{x}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} 
\mathsf {j}
 _{Ex}
\Rightarrow \dot{\neg}\,(
\mathsf {j}
 _{Ex}
 \mathrel{\in} \underline{
\mathsf{x}}
)n
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} 
\mathsf {j}
 _{Ex}
\Rightarrow \dot{\neg}\,(
\mathsf {j}
 _{Ex}
 \mathrel{\in} \underline{
\mathsf{x}}
)n
)n
\Rightarrow \underline{
\mathsf {s}}
 \mathrel{\in} \cup \underline{
\mathsf{x}}
)n
)n
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon R(\underline{(fx)}
)
**R(\underline{(fy)}
)
 == R(\underline{(fy)}
)
**R(\underline{(fx)}
)
\mathrel {\oplus} 
\forall \underline{(fx)}
\colon 
\forall \underline{(rx)}
\colon 
\forall \underline{(ry)}
\colon \underline{(rx)}
 == \underline{(ry)}
\vdash \underline{(fx)}
 \mathrel{\in} \underline{(ry)}
\vdash \underline{(fx)}
 \mathrel{\in} \underline{(rx)}
]$

$\rm
[SystemQ
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SystemQ
\mbox{''}
]$

$\rm
[SystemQ
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}system
\linebreak [0]\ \hskip0em plus2.0em{}Q
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:71}{}\section* {$\rm MP$}

$\rm
[MP
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[MP
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\vdash \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
]$

$\rm
[MP
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MP
\mbox{''}
]$

$\rm
[MP
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}mp
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:72}{}\section* {$\rm Gen$}

$\rm
[Gen
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Gen
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf {a}}
\colon \underline{
\mathsf {a}}
\vdash 
\forall_{obj} \underline{
\mathsf{x}}
\colon \underline{
\mathsf {a}}
]$

$\rm
[Gen
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Gen
\mbox{''}
]$

$\rm
[Gen
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}gen
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:73}{}\section* {$\rm Repetition$}

$\rm
[Repetition
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Repetition
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {a}}
]$

$\rm
[Repetition
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Repetition
\mbox{''}
]$

$\rm
[Repetition
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}repetition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:74}{}\section* {$\rm Neg$}

$\rm
[Neg
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Neg
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {a}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash \underline{
\mathsf {b}}
]$

$\rm
[Neg
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Neg
\mbox{''}
]$

$\rm
[Neg
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}ad
\linebreak [0]\ \hskip0em plus2.0em{}absurdum
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:75}{}\section* {$\rm Ded$}

$\rm
[Ded
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Ded
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
]$

$\rm
[Ded
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Ded
\mbox{''}
]$

$\rm
[Ded
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}deduction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:76}{}\section* {$\rm ExistIntro$}

$\rm
[ExistIntro
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[ExistIntro
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf {t}}
\colon 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \langle 
\lceil \underline{
\mathsf {a}}
\rceil 
{\equiv}^0 
\lceil \underline{
\mathsf {b}}
\rceil 
| 
\lceil \underline{
\mathsf{x}}
\rceil 
{:==} 
\lceil \underline{
\mathsf {t}}
\rceil 
\rangle_{Ex} 
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
]$

$\rm
[ExistIntro
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ExistIntro
\mbox{''}
]$

$\rm
[ExistIntro
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}exist
\linebreak [0]\ \hskip0em plus2.0em{}intro
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:77}{}\section* {$\rm Extensionality$}

$\rm
[Extensionality
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Extensionality
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \dot{\neg}\,(\underline{
\mathsf{x}}
\!\mathrel{==}\! \underline{
\mathsf{y}}
\Rightarrow 
\forall_{obj} \overline{
\mathsf {s}}
\colon \dot{\neg}\,(\overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{y}}
\Rightarrow \dot{\neg}\,(\overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{y}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
)n
)n
\Rightarrow \dot{\neg}\,(
\forall_{obj} \overline{
\mathsf {s}}
\colon \dot{\neg}\,(\overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{y}}
\Rightarrow \dot{\neg}\,(\overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{y}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
)n
)n
\Rightarrow \underline{
\mathsf{x}}
\!\mathrel{==}\! \underline{
\mathsf{y}}
)n
)n
]$

$\rm
[Extensionality
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Extensionality
\mbox{''}
]$

$\rm
[Extensionality
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}extensionality
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:78}{}\section* {$\rm \O{}def$}

$\rm
[\O{}def
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[\O{}def
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {s}}
\colon \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} \mathrm{\O}
)n
]$

$\rm
[\O{}def
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}O
\{
\}def
\mbox{''}
]$

$\rm
[\O{}def
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}empty
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:79}{}\section* {$\rm PairDef$}

$\rm
[PairDef
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[PairDef
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {s}}
\colon 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} \{\underline{
\mathsf{x}}
,\underline{
\mathsf{y}}
\}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {s}}
\!\mathrel{==}\! \underline{
\mathsf{x}}
)n
\Rightarrow \underline{
\mathsf {s}}
\!\mathrel{==}\! \underline{
\mathsf{y}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {s}}
\!\mathrel{==}\! \underline{
\mathsf{x}}
)n
\Rightarrow \underline{
\mathsf {s}}
\!\mathrel{==}\! \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf {s}}
 \mathrel{\in} \{\underline{
\mathsf{x}}
,\underline{
\mathsf{y}}
\}
)n
)n
]$

$\rm
[PairDef
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PairDef
\mbox{''}
]$

$\rm
[PairDef
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}pair
\linebreak [0]\ \hskip0em plus2.0em{}definition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:80}{}\section* {$\rm UnionDef$}

$\rm
[UnionDef
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[UnionDef
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {s}}
\colon 
\forall \underline{
\mathsf{x}}
\colon \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} \cup \underline{
\mathsf{x}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} 
\mathsf {j}
 _{Ex}
\Rightarrow \dot{\neg}\,(
\mathsf {j}
 _{Ex}
 \mathrel{\in} \underline{
\mathsf{x}}
)n
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} 
\mathsf {j}
 _{Ex}
\Rightarrow \dot{\neg}\,(
\mathsf {j}
 _{Ex}
 \mathrel{\in} \underline{
\mathsf{x}}
)n
)n
\Rightarrow \underline{
\mathsf {s}}
 \mathrel{\in} \cup \underline{
\mathsf{x}}
)n
)n
]$

$\rm
[UnionDef
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UnionDef
\mbox{''}
]$

$\rm
[UnionDef
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}union
\linebreak [0]\ \hskip0em plus2.0em{}definition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:81}{}\section* {$\rm PowerDef$}

$\rm
[PowerDef
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[PowerDef
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {s}}
\colon 
\forall \underline{
\mathsf{x}}
\colon \dot{\neg}\,(\underline{
\mathsf {s}}
 \mathrel{\in} P(\underline{
\mathsf{x}}
)
\Rightarrow 
\forall_{obj} \overline{
\mathsf {s}}
\colon \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf {s}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \dot{\neg}\,(
\forall_{obj} \overline{
\mathsf {s}}
\colon \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf {s}}
\Rightarrow \overline{
\mathsf {s}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \underline{
\mathsf {s}}
 \mathrel{\in} P(\underline{
\mathsf{x}}
)
)n
)n
]$

$\rm
[PowerDef
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PowerDef
\mbox{''}
]$

$\rm
[PowerDef
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}power
\linebreak [0]\ \hskip0em plus2.0em{}definition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:82}{}\section* {$\rm SeparationDef$}

$\rm
[SeparationDef
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[SeparationDef
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {p}}
\colon 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf {p}}
 ^{Ph}
\wedge \langle \underline{
\mathsf {b}}
{\equiv} \underline{
\mathsf {a}}
| \underline{
\mathsf {p}}
{:==} \underline{
\mathsf{z}}
\rangle_{Ph} 
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \dot{\neg}\,(\underline{
\mathsf{z}}
 \mathrel{\in}  \{ ph \mathrel{\in} \underline{
\mathsf{x}}
\mid \underline{
\mathsf {a}}
\}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf{z}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf{z}}
 \mathrel{\in} \underline{
\mathsf{x}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\Rightarrow \underline{
\mathsf{z}}
 \mathrel{\in}  \{ ph \mathrel{\in} \underline{
\mathsf{x}}
\mid \underline{
\mathsf {a}}
\}
)n
)n
]$

$\rm
[SeparationDef
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SeparationDef
\mbox{''}
]$

$\rm
[SeparationDef
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}separation
\linebreak [0]\ \hskip0em plus2.0em{}definition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:83}{}\section* {$\rm AddDoubleNeg$}

$\rm
[AddDoubleNeg
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}AddDoubleNeg
\mbox{''}
]$

$\rm
[AddDoubleNeg
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}add
\linebreak [0]\ \hskip0em plus2.0em{}double
\linebreak [0]\ \hskip0em plus2.0em{}neg
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:84}{}\section* {$\rm RemoveDoubleNeg$}

$\rm
[RemoveDoubleNeg
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}RemoveDoubleNeg
\mbox{''}
]$

$\rm
[RemoveDoubleNeg
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}remove
\linebreak [0]\ \hskip0em plus2.0em{}double
\linebreak [0]\ \hskip0em plus2.0em{}neg
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:85}{}\section* {$\rm AndCommutativity$}

$\rm
[AndCommutativity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}AndCommutativity
\mbox{''}
]$

$\rm
[AndCommutativity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}and
\linebreak [0]\ \hskip0em plus2.0em{}commutativity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:86}{}\section* {$\rm AutoImply$}

$\rm
[AutoImply
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}AutoImply
\mbox{''}
]$

$\rm
[AutoImply
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}auto
\linebreak [0]\ \hskip0em plus2.0em{}imply
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:87}{}\section* {$\rm Contrapositive$}

$\rm
[Contrapositive
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Contrapositive
\mbox{''}
]$

$\rm
[Contrapositive
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}contrapositive
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:88}{}\section* {$\rm FirstConjunct$}

$\rm
[FirstConjunct
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FirstConjunct
\mbox{''}
]$

$\rm
[FirstConjunct
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}first
\linebreak [0]\ \hskip0em plus2.0em{}conjunct
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:89}{}\section* {$\rm SecondConjunct$}

$\rm
[SecondConjunct
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SecondConjunct
\mbox{''}
]$

$\rm
[SecondConjunct
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}second
\linebreak [0]\ \hskip0em plus2.0em{}conjunct
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:90}{}\section* {$\rm FromContradiction$}

$\rm
[FromContradiction
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromContradiction
\mbox{''}
]$

$\rm
[FromContradiction
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}contradiction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:91}{}\section* {$\rm FromDisjuncts$}

$\rm
[FromDisjuncts
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromDisjuncts
\mbox{''}
]$

$\rm
[FromDisjuncts
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}disjuncts
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:92}{}\section* {$\rm IffCommutativity$}

$\rm
[IffCommutativity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IffCommutativity
\mbox{''}
]$

$\rm
[IffCommutativity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}iff
\linebreak [0]\ \hskip0em plus2.0em{}commutativity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:93}{}\section* {$\rm IffFirst$}

$\rm
[IffFirst
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IffFirst
\mbox{''}
]$

$\rm
[IffFirst
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}iff
\linebreak [0]\ \hskip0em plus2.0em{}first
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:94}{}\section* {$\rm IffSecond$}

$\rm
[IffSecond
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IffSecond
\mbox{''}
]$

$\rm
[IffSecond
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}iff
\linebreak [0]\ \hskip0em plus2.0em{}second
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:95}{}\section* {$\rm ImplyTransitivity$}

$\rm
[ImplyTransitivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ImplyTransitivity
\mbox{''}
]$

$\rm
[ImplyTransitivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}imply
\linebreak [0]\ \hskip0em plus2.0em{}transitivity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:96}{}\section* {$\rm JoinConjuncts$}

$\rm
[JoinConjuncts
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}JoinConjuncts
\mbox{''}
]$

$\rm
[JoinConjuncts
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}join
\linebreak [0]\ \hskip0em plus2.0em{}conjuncts
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:97}{}\section* {$\rm MP2$}

$\rm
[MP2
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MP2
\mbox{''}
]$

$\rm
[MP2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}mp2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:98}{}\section* {$\rm MP3$}

$\rm
[MP3
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MP3
\mbox{''}
]$

$\rm
[MP3
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}mp3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:99}{}\section* {$\rm MP4$}

$\rm
[MP4
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MP4
\mbox{''}
]$

$\rm
[MP4
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}mp4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:100}{}\section* {$\rm MP5$}

$\rm
[MP5
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MP5
\mbox{''}
]$

$\rm
[MP5
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}mp5
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:101}{}\section* {$\rm MT$}

$\rm
[MT
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MT
\mbox{''}
]$

$\rm
[MT
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}mt
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:102}{}\section* {$\rm NegativeMT$}

$\rm
[NegativeMT
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NegativeMT
\mbox{''}
]$

$\rm
[NegativeMT
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}negative
\linebreak [0]\ \hskip0em plus2.0em{}mt
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:103}{}\section* {$\rm Technicality$}

$\rm
[Technicality
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Technicality
\mbox{''}
]$

$\rm
[Technicality
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}technicality
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:104}{}\section* {$\rm Weakening$}

$\rm
[Weakening
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Weakening
\mbox{''}
]$

$\rm
[Weakening
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}weakening
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:105}{}\section* {$\rm WeakenOr1$}

$\rm
[WeakenOr1
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}WeakenOr1
\mbox{''}
]$

$\rm
[WeakenOr1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}weaken
\linebreak [0]\ \hskip0em plus2.0em{}or
\linebreak [0]\ \hskip0em plus2.0em{}first
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:106}{}\section* {$\rm WeakenOr2$}

$\rm
[WeakenOr2
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}WeakenOr2
\mbox{''}
]$

$\rm
[WeakenOr2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}weaken
\linebreak [0]\ \hskip0em plus2.0em{}or
\linebreak [0]\ \hskip0em plus2.0em{}second
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:107}{}\section* {$\rm Formula2Pair$}

$\rm
[Formula2Pair
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Formula2Pair
\mbox{''}
]$

$\rm
[Formula2Pair
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}formula2pair
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:108}{}\section* {$\rm Pair2Formula$}

$\rm
[Pair2Formula
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Pair2Formula
\mbox{''}
]$

$\rm
[Pair2Formula
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}pair2formula
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:109}{}\section* {$\rm Formula2Union$}

$\rm
[Formula2Union
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Formula2Union
\mbox{''}
]$

$\rm
[Formula2Union
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}formula2union
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:110}{}\section* {$\rm Union2Formula$}

$\rm
[Union2Formula
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Union2Formula
\mbox{''}
]$

$\rm
[Union2Formula
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}union2formula
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:111}{}\section* {$\rm Formula2Sep$}

$\rm
[Formula2Sep
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Formula2Sep
\mbox{''}
]$

$\rm
[Formula2Sep
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}formula2separation
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:112}{}\section* {$\rm Sep2Formula$}

$\rm
[Sep2Formula
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Sep2Formula
\mbox{''}
]$

$\rm
[Sep2Formula
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}separation2formula
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:113}{}\section* {$\rm Formula2Power$}

$\rm
[Formula2Power
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Formula2Power
\mbox{''}
]$

$\rm
[Formula2Power
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}formula2power
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:114}{}\section* {$\rm SubsetInPower$}

$\rm
[SubsetInPower
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SubsetInPower
\mbox{''}
]$

$\rm
[SubsetInPower
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}subset
\linebreak [0]\ \hskip0em plus2.0em{}in
\linebreak [0]\ \hskip0em plus2.0em{}power
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:115}{}\section* {$\rm HelperPowerIsSub$}

$\rm
[HelperPowerIsSub
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperPowerIsSub
\mbox{''}
]$

$\rm
[HelperPowerIsSub
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}power
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}subset0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:116}{}\section* {$\rm PowerIsSub$}

$\rm
[PowerIsSub
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PowerIsSub
\mbox{''}
]$

$\rm
[PowerIsSub
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}power
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:117}{}\section* {$\rm (Switch)HelperPowerIsSub$}

$\rm
[(Switch)HelperPowerIsSub
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(Switch)HelperPowerIsSub
\mbox{''}
]$

$\rm
[(Switch)HelperPowerIsSub
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}power
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}subset0
\mbox{-}switch
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:118}{}\section* {$\rm (Switch)PowerIsSub$}

$\rm
[(Switch)PowerIsSub
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(Switch)PowerIsSub
\mbox{''}
]$

$\rm
[(Switch)PowerIsSub
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}power
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{-}switch
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:119}{}\section* {$\rm ToSetEquality$}

$\rm
[ToSetEquality
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ToSetEquality
\mbox{''}
]$

$\rm
[ToSetEquality
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}equality
\linebreak [0]\ \hskip0em plus2.0em{}suff
\linebreak [0]\ \hskip0em plus2.0em{}condition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:120}{}\section* {$\rm HelperToSetEquality(t)$}

$\rm
[HelperToSetEquality(t)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperToSetEquality(t)
\mbox{''}
]$

$\rm
[HelperToSetEquality(t)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}equality
\linebreak [0]\ \hskip0em plus2.0em{}suff
\linebreak [0]\ \hskip0em plus2.0em{}condition(t)0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:121}{}\section* {$\rm ToSetEquality(t)$}

$\rm
[ToSetEquality(t)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ToSetEquality(t)
\mbox{''}
]$

$\rm
[ToSetEquality(t)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}equality
\linebreak [0]\ \hskip0em plus2.0em{}suff
\linebreak [0]\ \hskip0em plus2.0em{}condition(t)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:122}{}\section* {$\rm HelperFromSetEquality$}

$\rm
[HelperFromSetEquality
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperFromSetEquality
\mbox{''}
]$

$\rm
[HelperFromSetEquality
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}equality
\linebreak [0]\ \hskip0em plus2.0em{}skip
\linebreak [0]\ \hskip0em plus2.0em{}quantifier
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:123}{}\section* {$\rm FromSetEquality$}

$\rm
[FromSetEquality
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromSetEquality
\mbox{''}
]$

$\rm
[FromSetEquality
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}equality
\linebreak [0]\ \hskip0em plus2.0em{}nec
\linebreak [0]\ \hskip0em plus2.0em{}condition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:124}{}\section* {$\rm HelperReflexivity$}

$\rm
[HelperReflexivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperReflexivity
\mbox{''}
]$

$\rm
[HelperReflexivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}reflexivity0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:125}{}\section* {$\rm Reflexivity$}

$\rm
[Reflexivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Reflexivity
\mbox{''}
]$

$\rm
[Reflexivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}reflexivity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:126}{}\section* {$\rm HelperSymmetry$}

$\rm
[HelperSymmetry
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperSymmetry
\mbox{''}
]$

$\rm
[HelperSymmetry
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}symmetry0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:127}{}\section* {$\rm Symmetry$}

$\rm
[Symmetry
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Symmetry
\mbox{''}
]$

$\rm
[Symmetry
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}symmetry
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:128}{}\section* {$\rm HelperTransitivity$}

$\rm
[HelperTransitivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperTransitivity
\mbox{''}
]$

$\rm
[HelperTransitivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}transitivity0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:129}{}\section* {$\rm Transitivity$}

$\rm
[Transitivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Transitivity
\mbox{''}
]$

$\rm
[Transitivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}transitivity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:130}{}\section* {$\rm ERisReflexive$}

$\rm
[ERisReflexive
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ERisReflexive
\mbox{''}
]$

$\rm
[ERisReflexive
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}er
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}reflexive
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:131}{}\section* {$\rm ERisSymmetric$}

$\rm
[ERisSymmetric
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ERisSymmetric
\mbox{''}
]$

$\rm
[ERisSymmetric
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}er
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}symmetric
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:132}{}\section* {$\rm ERisTransitive$}

$\rm
[ERisTransitive
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ERisTransitive
\mbox{''}
]$

$\rm
[ERisTransitive
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}er
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}transitive
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:133}{}\section* {$\rm \O{}isSubset$}

$\rm
[\O{}isSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}O
\{
\}isSubset
\mbox{''}
]$

$\rm
[\O{}isSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}empty
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:134}{}\section* {$\rm HelperMemberNot\O{}$}

$\rm
[HelperMemberNot\O{}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperMemberNot
\mbox {$\backslash $}O
\{
\}
\mbox{''}
]$

$\rm
[HelperMemberNot\O{}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}member
\linebreak [0]\ \hskip0em plus2.0em{}not
\linebreak [0]\ \hskip0em plus2.0em{}empty0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:135}{}\section* {$\rm MemberNot\O{}$}

$\rm
[MemberNot\O{}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MemberNot
\mbox {$\backslash $}O
\{
\}
\mbox{''}
]$

$\rm
[MemberNot\O{}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}member
\linebreak [0]\ \hskip0em plus2.0em{}not
\linebreak [0]\ \hskip0em plus2.0em{}empty
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:136}{}\section* {$\rm HelperUnique\O{}$}

$\rm
[HelperUnique\O{}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperUnique
\mbox {$\backslash $}O
\{
\}
\mbox{''}
]$

$\rm
[HelperUnique\O{}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}unique
\linebreak [0]\ \hskip0em plus2.0em{}empty
\linebreak [0]\ \hskip0em plus2.0em{}set0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:137}{}\section* {$\rm Unique\O{}$}

$\rm
[Unique\O{}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Unique
\mbox {$\backslash $}O
\{
\}
\mbox{''}
]$

$\rm
[Unique\O{}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}unique
\linebreak [0]\ \hskip0em plus2.0em{}empty
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:138}{}\section* {$\rm ==\!{}Reflexivity$}

$\rm
[==\!{}Reflexivity
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[==\!{}Reflexivity
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(rx)}
\colon \underline{(rx)}
 == \underline{(rx)}
]$

$\rm
[==\!{}Reflexivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
{=}
{=}
\mbox {$\backslash $}!
\{
\}Reflexivity
\mbox{''}
]$

$\rm
[==\!{}Reflexivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}
{=}
{=}Reflexivity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:139}{}\section* {$\rm ==\!{}Symmetry$}

$\rm
[==\!{}Symmetry
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[==\!{}Symmetry
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(rx)}
\colon 
\forall \underline{(ry)}
\colon \underline{(rx)}
 == \underline{(ry)}
\vdash \underline{(ry)}
 == \underline{(rx)}
]$

$\rm
[==\!{}Symmetry
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
{=}
{=}
\mbox {$\backslash $}!
\{
\}Symmetry
\mbox{''}
]$

$\rm
[==\!{}Symmetry
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}
{=}
{=}Symmetry
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:140}{}\section* {$\rm Helper\!{}==\!{}Transitivity$}

$\rm
[Helper\!{}==\!{}Transitivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Helper
\mbox {$\backslash $}!
\{
\}
{=}
{=}
\mbox {$\backslash $}!
\{
\}Transitivity
\mbox{''}
]$

$\rm
[Helper\!{}==\!{}Transitivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}
{=}
{=}Transitivity0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:141}{}\section* {$\rm \!{}==\!{}Transitivity$}

$\rm
[\!{}==\!{}Transitivity
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[\!{}==\!{}Transitivity
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(rx)}
\colon 
\forall \underline{(ry)}
\colon 
\forall \underline{(rz)}
\colon \underline{(rx)}
 == \underline{(ry)}
\vdash \underline{(ry)}
 == \underline{(rz)}
\vdash \underline{(rx)}
 == \underline{(rz)}
]$

$\rm
[\!{}==\!{}Transitivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}!
\{
\}
{=}
{=}
\mbox {$\backslash $}!
\{
\}Transitivity
\mbox{''}
]$

$\rm
[\!{}==\!{}Transitivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}
{=}
{=}Transitivity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:142}{}\section* {$\rm HelperTransferNotEq$}

$\rm
[HelperTransferNotEq
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperTransferNotEq
\mbox{''}
]$

$\rm
[HelperTransferNotEq
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}transfer
\linebreak [0]\ \hskip0em plus2.0em{}
\char126 is0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:143}{}\section* {$\rm TransferNotEq$}

$\rm
[TransferNotEq
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TransferNotEq
\mbox{''}
]$

$\rm
[TransferNotEq
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}transfer
\linebreak [0]\ \hskip0em plus2.0em{}
\char126 is
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:144}{}\section* {$\rm HelperPairSubset$}

$\rm
[HelperPairSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperPairSubset
\mbox{''}
]$

$\rm
[HelperPairSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}pair
\linebreak [0]\ \hskip0em plus2.0em{}subset0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:145}{}\section* {$\rm Helper(2)PairSubset$}

$\rm
[Helper(2)PairSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Helper(2)PairSubset
\mbox{''}
]$

$\rm
[Helper(2)PairSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}pair
\linebreak [0]\ \hskip0em plus2.0em{}subset1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:146}{}\section* {$\rm PairSubset$}

$\rm
[PairSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PairSubset
\mbox{''}
]$

$\rm
[PairSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}pair
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:147}{}\section* {$\rm SamePair$}

$\rm
[SamePair
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SamePair
\mbox{''}
]$

$\rm
[SamePair
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}same
\linebreak [0]\ \hskip0em plus2.0em{}pair
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:148}{}\section* {$\rm SameSingleton$}

$\rm
[SameSingleton
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SameSingleton
\mbox{''}
]$

$\rm
[SameSingleton
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}same
\linebreak [0]\ \hskip0em plus2.0em{}singleton
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:149}{}\section* {$\rm UnionSubset$}

$\rm
[UnionSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UnionSubset
\mbox{''}
]$

$\rm
[UnionSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}union
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:150}{}\section* {$\rm SameUnion$}

$\rm
[SameUnion
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SameUnion
\mbox{''}
]$

$\rm
[SameUnion
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}same
\linebreak [0]\ \hskip0em plus2.0em{}union
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:151}{}\section* {$\rm SeparationSubset$}

$\rm
[SeparationSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SeparationSubset
\mbox{''}
]$

$\rm
[SeparationSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}separation
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:152}{}\section* {$\rm SameSeparation$}

$\rm
[SameSeparation
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SameSeparation
\mbox{''}
]$

$\rm
[SameSeparation
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}same
\linebreak [0]\ \hskip0em plus2.0em{}separation
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:153}{}\section* {$\rm SameBinaryUnion$}

$\rm
[SameBinaryUnion
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SameBinaryUnion
\mbox{''}
]$

$\rm
[SameBinaryUnion
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}same
\linebreak [0]\ \hskip0em plus2.0em{}binary
\linebreak [0]\ \hskip0em plus2.0em{}union
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:154}{}\section* {$\rm IntersectionSubset$}

$\rm
[IntersectionSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IntersectionSubset
\mbox{''}
]$

$\rm
[IntersectionSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}intersection
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:155}{}\section* {$\rm SameIntersection$}

$\rm
[SameIntersection
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SameIntersection
\mbox{''}
]$

$\rm
[SameIntersection
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}same
\linebreak [0]\ \hskip0em plus2.0em{}intersection
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:156}{}\section* {$\rm AutoMember$}

$\rm
[AutoMember
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}AutoMember
\mbox{''}
]$

$\rm
[AutoMember
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}auto
\linebreak [0]\ \hskip0em plus2.0em{}member
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:157}{}\section* {$\rm HelperEqSysNot\O{}$}

$\rm
[HelperEqSysNot\O{}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperEqSysNot
\mbox {$\backslash $}O
\{
\}
\mbox{''}
]$

$\rm
[HelperEqSysNot\O{}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}eq
\mbox{-}system
\linebreak [0]\ \hskip0em plus2.0em{}not
\linebreak [0]\ \hskip0em plus2.0em{}empty0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:158}{}\section* {$\rm EqSysNot\O{}$}

$\rm
[EqSysNot\O{}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqSysNot
\mbox {$\backslash $}O
\{
\}
\mbox{''}
]$

$\rm
[EqSysNot\O{}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}eq
\mbox{-}system
\linebreak [0]\ \hskip0em plus2.0em{}not
\linebreak [0]\ \hskip0em plus2.0em{}empty
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:159}{}\section* {$\rm HelperEqSubset$}

$\rm
[HelperEqSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperEqSubset
\mbox{''}
]$

$\rm
[HelperEqSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}eq
\linebreak [0]\ \hskip0em plus2.0em{}subset0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:160}{}\section* {$\rm EqSubset$}

$\rm
[EqSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqSubset
\mbox{''}
]$

$\rm
[EqSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}eq
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:161}{}\section* {$\rm HelperEqNecessary$}

$\rm
[HelperEqNecessary
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperEqNecessary
\mbox{''}
]$

$\rm
[HelperEqNecessary
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}nec
\linebreak [0]\ \hskip0em plus2.0em{}condition0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:162}{}\section* {$\rm EqNecessary$}

$\rm
[EqNecessary
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqNecessary
\mbox{''}
]$

$\rm
[EqNecessary
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}nec
\linebreak [0]\ \hskip0em plus2.0em{}condition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:163}{}\section* {$\rm HelperNoneEqNecessary$}

$\rm
[HelperNoneEqNecessary
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}HelperNoneEqNecessary
\mbox{''}
]$

$\rm
[HelperNoneEqNecessary
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}none
\mbox{-}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}nec
\linebreak [0]\ \hskip0em plus2.0em{}condition0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:164}{}\section* {$\rm Helper(2)NoneEqNecessary$}

$\rm
[Helper(2)NoneEqNecessary
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Helper(2)NoneEqNecessary
\mbox{''}
]$

$\rm
[Helper(2)NoneEqNecessary
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}none
\mbox{-}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}nec
\linebreak [0]\ \hskip0em plus2.0em{}condition1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:165}{}\section* {$\rm NoneEqNecessary$}

$\rm
[NoneEqNecessary
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NoneEqNecessary
\mbox{''}
]$

$\rm
[NoneEqNecessary
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}none
\mbox{-}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}nec
\linebreak [0]\ \hskip0em plus2.0em{}condition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:166}{}\section* {$\rm EqClassIsSubset$}

$\rm
[EqClassIsSubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqClassIsSubset
\mbox{''}
]$

$\rm
[EqClassIsSubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}class
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}subset
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:167}{}\section* {$\rm EqClassesAreDisjoint$}

$\rm
[EqClassesAreDisjoint
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqClassesAreDisjoint
\mbox{''}
]$

$\rm
[EqClassesAreDisjoint
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}classes
\linebreak [0]\ \hskip0em plus2.0em{}are
\linebreak [0]\ \hskip0em plus2.0em{}disjoint
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:168}{}\section* {$\rm AllDisjoint$}

$\rm
[AllDisjoint
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}AllDisjoint
\mbox{''}
]$

$\rm
[AllDisjoint
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}all
\linebreak [0]\ \hskip0em plus2.0em{}disjoint
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:169}{}\section* {$\rm AllDisjointImply$}

$\rm
[AllDisjointImply
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}AllDisjointImply
\mbox{''}
]$

$\rm
[AllDisjointImply
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}all
\linebreak [0]\ \hskip0em plus2.0em{}disjoint
\mbox{-}imply
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:170}{}\section* {$\rm BSsubset$}

$\rm
[BSsubset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}BSsubset
\mbox{''}
]$

$\rm
[BSsubset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}bs
\linebreak [0]\ \hskip0em plus2.0em{}subset
\linebreak [0]\ \hskip0em plus2.0em{}union(bs/r)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:171}{}\section* {$\rm Union(BS/R)subset$}

$\rm
[Union(BS/R)subset
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Union(BS/R)subset
\mbox{''}
]$

$\rm
[Union(BS/R)subset
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}union(bs/r)
\linebreak [0]\ \hskip0em plus2.0em{}subset
\linebreak [0]\ \hskip0em plus2.0em{}bs
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:172}{}\section* {$\rm UnionIdentity$}

$\rm
[UnionIdentity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UnionIdentity
\mbox{''}
]$

$\rm
[UnionIdentity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}union(bs/r)
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}bs
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:173}{}\section* {$\rm EqSysIsPartition$}

$\rm
[EqSysIsPartition
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqSysIsPartition
\mbox{''}
]$

$\rm
[EqSysIsPartition
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}theorem
\linebreak [0]\ \hskip0em plus2.0em{}eq
\mbox{-}system
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}partition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:174}{}\section* {$\rm (x1)$}

$\rm
[(x1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(x1)
\mbox{''}
]$

$\rm
[(x1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}x1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:175}{}\section* {$\rm (x2)$}

$\rm
[(x2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(x2)
\mbox{''}
]$

$\rm
[(x2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}x2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:176}{}\section* {$\rm (y1)$}

$\rm
[(y1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(y1)
\mbox{''}
]$

$\rm
[(y1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}y1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:177}{}\section* {$\rm (y2)$}

$\rm
[(y2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(y2)
\mbox{''}
]$

$\rm
[(y2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}y2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:178}{}\section* {$\rm (v1)$}

$\rm
[(v1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(v1)
\mbox{''}
]$

$\rm
[(v1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}v1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:179}{}\section* {$\rm (v2)$}

$\rm
[(v2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(v2)
\mbox{''}
]$

$\rm
[(v2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}v2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:180}{}\section* {$\rm (v3)$}

$\rm
[(v3)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(v3)
\mbox{''}
]$

$\rm
[(v3)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}v3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:181}{}\section* {$\rm (v4)$}

$\rm
[(v4)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(v4)
\mbox{''}
]$

$\rm
[(v4)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}v4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:182}{}\section* {$\rm (v2n)$}

$\rm
[(v2n)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(v2n)
\mbox{''}
]$

$\rm
[(v2n)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}v2n
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:183}{}\section* {$\rm (m1)$}

$\rm
[(m1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(m1)
\mbox{''}
]$

$\rm
[(m1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}m1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:184}{}\section* {$\rm (m2)$}

$\rm
[(m2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(m2)
\mbox{''}
]$

$\rm
[(m2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}m2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:185}{}\section* {$\rm (n1)$}

$\rm
[(n1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(n1)
\mbox{''}
]$

$\rm
[(n1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}n1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:186}{}\section* {$\rm (n2)$}

$\rm
[(n2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(n2)
\mbox{''}
]$

$\rm
[(n2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}n2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:187}{}\section* {$\rm (n3)$}

$\rm
[(n3)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(n3)
\mbox{''}
]$

$\rm
[(n3)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}n3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:188}{}\section* {$\rm (\epsilon)$}

$\rm
[(\epsilon)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\mbox {$\backslash $}epsilon)
\mbox{''}
]$

$\rm
[(\epsilon)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}ep
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:189}{}\section* {$\rm (\epsilon)_{1}$}

$\rm
[(\epsilon)_{1}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\mbox {$\backslash $}epsilon)
\_
\{1
\}
\mbox{''}
]$

$\rm
[(\epsilon)_{1}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}ep1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:190}{}\section* {$\rm (\epsilon 2)$}

$\rm
[(\epsilon 2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\mbox {$\backslash $}epsilon
\linebreak [0]\ \hskip0em plus2.0em{}2)
\mbox{''}
]$

$\rm
[(\epsilon 2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}ep2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:191}{}\section* {$\rm (fep)$}

$\rm
[(fep)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fep)
\mbox{''}
]$

$\rm
[(fep)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fep
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:192}{}\section* {$\rm (fx)$}

$\rm
[(fx)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fx)
\mbox{''}
]$

$\rm
[(fx)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fx
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:193}{}\section* {$\rm (fy)$}

$\rm
[(fy)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fy)
\mbox{''}
]$

$\rm
[(fy)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fy
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:194}{}\section* {$\rm (fz)$}

$\rm
[(fz)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fz)
\mbox{''}
]$

$\rm
[(fz)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fz
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:195}{}\section* {$\rm (fu)$}

$\rm
[(fu)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fu)
\mbox{''}
]$

$\rm
[(fu)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fu
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:196}{}\section* {$\rm (fv)$}

$\rm
[(fv)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fv)
\mbox{''}
]$

$\rm
[(fv)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fv
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:197}{}\section* {$\rm (fw)$}

$\rm
[(fw)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fw)
\mbox{''}
]$

$\rm
[(fw)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fw
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:198}{}\section* {$\rm (rx)$}

$\rm
[(rx)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(rx)
\mbox{''}
]$

$\rm
[(rx)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}rx
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:199}{}\section* {$\rm (ry)$}

$\rm
[(ry)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(ry)
\mbox{''}
]$

$\rm
[(ry)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}ry
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:200}{}\section* {$\rm (rz)$}

$\rm
[(rz)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(rz)
\mbox{''}
]$

$\rm
[(rz)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}rz
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:201}{}\section* {$\rm (ru)$}

$\rm
[(ru)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(ru)
\mbox{''}
]$

$\rm
[(ru)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}ru
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:202}{}\section* {$\rm (sx)$}

$\rm
[(sx)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(sx)
\mbox{''}
]$

$\rm
[(sx)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}sx
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:203}{}\section* {$\rm (sx1)$}

$\rm
[(sx1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(sx1)
\mbox{''}
]$

$\rm
[(sx1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}sx1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:204}{}\section* {$\rm (sy)$}

$\rm
[(sy)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(sy)
\mbox{''}
]$

$\rm
[(sy)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}sy
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:205}{}\section* {$\rm (sy1)$}

$\rm
[(sy1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(sy1)
\mbox{''}
]$

$\rm
[(sy1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}sy1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:206}{}\section* {$\rm (sz)$}

$\rm
[(sz)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(sz)
\mbox{''}
]$

$\rm
[(sz)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}sz
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:207}{}\section* {$\rm (sz1)$}

$\rm
[(sz1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(sz1)
\mbox{''}
]$

$\rm
[(sz1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}sz1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:208}{}\section* {$\rm (su)$}

$\rm
[(su)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(su)
\mbox{''}
]$

$\rm
[(su)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}su
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:209}{}\section* {$\rm (su1)$}

$\rm
[(su1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(su1)
\mbox{''}
]$

$\rm
[(su1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}su1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:210}{}\section* {$\rm (fxs)$}

$\rm
[(fxs)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fxs)
\mbox{''}
]$

$\rm
[(fxs)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fxs
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:211}{}\section* {$\rm (fys)$}

$\rm
[(fys)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(fys)
\mbox{''}
]$

$\rm
[(fys)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}fys
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:212}{}\section* {$\rm (crs1)$}

$\rm
[(crs1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(crs1)
\mbox{''}
]$

$\rm
[(crs1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}crs1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:213}{}\section* {$\rm (f1)$}

$\rm
[(f1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(f1)
\mbox{''}
]$

$\rm
[(f1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}f1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:214}{}\section* {$\rm (f2)$}

$\rm
[(f2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(f2)
\mbox{''}
]$

$\rm
[(f2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}f2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:215}{}\section* {$\rm (f3)$}

$\rm
[(f3)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(f3)
\mbox{''}
]$

$\rm
[(f3)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}f3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:216}{}\section* {$\rm (f4)$}

$\rm
[(f4)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(f4)
\mbox{''}
]$

$\rm
[(f4)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}f4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:217}{}\section* {$\rm (op1)$}

$\rm
[(op1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(op1)
\mbox{''}
]$

$\rm
[(op1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}op1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:218}{}\section* {$\rm (op2)$}

$\rm
[(op2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(op2)
\mbox{''}
]$

$\rm
[(op2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}op2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:219}{}\section* {$\rm (r1)$}

$\rm
[(r1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(r1)
\mbox{''}
]$

$\rm
[(r1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}r1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:220}{}\section* {$\rm (s1)$}

$\rm
[(s1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(s1)
\mbox{''}
]$

$\rm
[(s1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}s1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:221}{}\section* {$\rm (s2)$}

$\rm
[(s2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(s2)
\mbox{''}
]$

$\rm
[(s2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}var
\linebreak [0]\ \hskip0em plus2.0em{}s2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:222}{}\section* {$\rm X_{1}$}

$\rm
[X_{1}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[X_{1}
\mathrel {\ddot {=}}\underline{(x1)}
]
\rceil 
)
]$

$\rm
[X_{1}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}X
\_
\{1
\}
\mbox{''}
]$

$\rm
[X_{1}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}x1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:223}{}\section* {$\rm X_{2}$}

$\rm
[X_{2}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[X_{2}
\mathrel {\ddot {=}}\underline{(x2)}
]
\rceil 
)
]$

$\rm
[X_{2}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}X
\_
\{2
\}
\mbox{''}
]$

$\rm
[X_{2}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}x2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:224}{}\section* {$\rm Y_{1}$}

$\rm
[Y_{1}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[Y_{1}
\mathrel {\ddot {=}}\underline{(y1)}
]
\rceil 
)
]$

$\rm
[Y_{1}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Y
\_
\{1
\}
\mbox{''}
]$

$\rm
[Y_{1}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}y1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:225}{}\section* {$\rm Y_{2}$}

$\rm
[Y_{2}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[Y_{2}
\mathrel {\ddot {=}}\underline{(y2)}
]
\rceil 
)
]$

$\rm
[Y_{2}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Y
\_
\{2
\}
\mbox{''}
]$

$\rm
[Y_{2}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}y2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:226}{}\section* {$\rm V_{1}$}

$\rm
[V_{1}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[V_{1}
\mathrel {\ddot {=}}\underline{(v1)}
]
\rceil 
)
]$

$\rm
[V_{1}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}V
\_
\{1
\}
\mbox{''}
]$

$\rm
[V_{1}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}v1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:227}{}\section* {$\rm V_{2}$}

$\rm
[V_{2}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[V_{2}
\mathrel {\ddot {=}}\underline{(v2)}
]
\rceil 
)
]$

$\rm
[V_{2}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}V
\_
\{2
\}
\mbox{''}
]$

$\rm
[V_{2}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}v2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:228}{}\section* {$\rm V_{3}$}

$\rm
[V_{3}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[V_{3}
\mathrel {\ddot {=}}\underline{(v3)}
]
\rceil 
)
]$

$\rm
[V_{3}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}V
\_
\{3
\}
\mbox{''}
]$

$\rm
[V_{3}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}v3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:229}{}\section* {$\rm V_{4}$}

$\rm
[V_{4}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[V_{4}
\mathrel {\ddot {=}}\underline{(v4)}
]
\rceil 
)
]$

$\rm
[V_{4}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}V
\_
\{4
\}
\mbox{''}
]$

$\rm
[V_{4}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}v4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:230}{}\section* {$\rm V_{2n}$}

$\rm
[V_{2n}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[V_{2n}
\mathrel {\ddot {=}}\underline{(v2n)}
]
\rceil 
)
]$

$\rm
[V_{2n}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}V
\_
\{2n
\}
\mbox{''}
]$

$\rm
[V_{2n}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}v2n
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:231}{}\section* {$\rm M_{1}$}

$\rm
[M_{1}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[M_{1}
\mathrel {\ddot {=}}\underline{(m1)}
]
\rceil 
)
]$

$\rm
[M_{1}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}M
\_
\{1
\}
\mbox{''}
]$

$\rm
[M_{1}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}m1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:232}{}\section* {$\rm M_{2}$}

$\rm
[M_{2}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[M_{2}
\mathrel {\ddot {=}}\underline{(m2)}
]
\rceil 
)
]$

$\rm
[M_{2}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}M
\_
\{2
\}
\mbox{''}
]$

$\rm
[M_{2}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}m2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:233}{}\section* {$\rm N_{1} $}

$\rm
[N_{1} 
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[N_{1} 
\mathrel {\ddot {=}}\underline{(n1)}
]
\rceil 
)
]$

$\rm
[N_{1} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}N
\_
\{1
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[N_{1} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}n1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:234}{}\section* {$\rm N_{2} $}

$\rm
[N_{2} 
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[N_{2} 
\mathrel {\ddot {=}}\underline{(n2)}
]
\rceil 
)
]$

$\rm
[N_{2} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}N
\_
\{2
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[N_{2} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}n2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:235}{}\section* {$\rm N_{3} $}

$\rm
[N_{3} 
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[N_{3} 
\mathrel {\ddot {=}}\underline{(n3)}
]
\rceil 
)
]$

$\rm
[N_{3} 
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}N
\_
\{3
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{''}
]$

$\rm
[N_{3} 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}n3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:236}{}\section* {$\rm \epsilon$}

$\rm
[\epsilon
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[\epsilon
\mathrel {\ddot {=}}\underline{(\epsilon)}
]
\rceil 
)
]$

$\rm
[\epsilon
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}epsilon
\mbox{''}
]$

$\rm
[\epsilon
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}ep
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:237}{}\section* {$\rm \epsilon 1$}

$\rm
[\epsilon 1
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[\epsilon 1
\mathrel {\ddot {=}}\underline{(\epsilon)_{1}}
]
\rceil 
)
]$

$\rm
[\epsilon 1
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}epsilon
\linebreak [0]\ \hskip0em plus2.0em{}1
\mbox{''}
]$

$\rm
[\epsilon 1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}ep1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:238}{}\section* {$\rm \epsilon 2$}

$\rm
[\epsilon 2
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[\epsilon 2
\mathrel {\ddot {=}}\underline{(\epsilon 2)}
]
\rceil 
)
]$

$\rm
[\epsilon 2
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}epsilon
\linebreak [0]\ \hskip0em plus2.0em{}2
\mbox{''}
]$

$\rm
[\epsilon 2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}ep2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:239}{}\section* {$\rm FX$}

$\rm
[FX
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FX
\mathrel {\ddot {=}}\underline{(fx)}
]
\rceil 
)
]$

$\rm
[FX
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FX
\mbox{''}
]$

$\rm
[FX
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fx
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:240}{}\section* {$\rm FY$}

$\rm
[FY
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FY
\mathrel {\ddot {=}}\underline{(fy)}
]
\rceil 
)
]$

$\rm
[FY
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FY
\mbox{''}
]$

$\rm
[FY
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fy
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:241}{}\section* {$\rm FZ$}

$\rm
[FZ
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FZ
\mathrel {\ddot {=}}\underline{(fz)}
]
\rceil 
)
]$

$\rm
[FZ
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FZ
\mbox{''}
]$

$\rm
[FZ
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fz
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:242}{}\section* {$\rm FU$}

$\rm
[FU
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FU
\mathrel {\ddot {=}}\underline{(fu)}
]
\rceil 
)
]$

$\rm
[FU
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FU
\mbox{''}
]$

$\rm
[FU
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fu
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:243}{}\section* {$\rm FV$}

$\rm
[FV
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FV
\mathrel {\ddot {=}}\underline{(fv)}
]
\rceil 
)
]$

$\rm
[FV
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FV
\mbox{''}
]$

$\rm
[FV
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fv
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:244}{}\section* {$\rm FW$}

$\rm
[FW
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FW
\mathrel {\ddot {=}}\underline{(fw)}
]
\rceil 
)
]$

$\rm
[FW
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FW
\mbox{''}
]$

$\rm
[FW
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fw
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:245}{}\section* {$\rm FEP$}

$\rm
[FEP
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FEP
\mathrel {\ddot {=}}\underline{(fep)}
]
\rceil 
)
]$

$\rm
[FEP
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FEP
\mbox{''}
]$

$\rm
[FEP
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fep
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:246}{}\section* {$\rm RX$}

$\rm
[RX
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[RX
\mathrel {\ddot {=}}\underline{(rx)}
]
\rceil 
)
]$

$\rm
[RX
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}RX
\mbox{''}
]$

$\rm
[RX
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}rx
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:247}{}\section* {$\rm RY$}

$\rm
[RY
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[RY
\mathrel {\ddot {=}}\underline{(ry)}
]
\rceil 
)
]$

$\rm
[RY
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}RY
\mbox{''}
]$

$\rm
[RY
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}ry
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:248}{}\section* {$\rm RZ$}

$\rm
[RZ
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[RZ
\mathrel {\ddot {=}}\underline{(rz)}
]
\rceil 
)
]$

$\rm
[RZ
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}RZ
\mbox{''}
]$

$\rm
[RZ
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}rz
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:249}{}\section* {$\rm RU$}

$\rm
[RU
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[RU
\mathrel {\ddot {=}}\underline{(ru)}
]
\rceil 
)
]$

$\rm
[RU
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}RU
\mbox{''}
]$

$\rm
[RU
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}ru
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:250}{}\section* {$\rm (SX)$}

$\rm
[(SX)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(SX)
\mathrel {\ddot {=}}\underline{(sx)}
]
\rceil 
)
]$

$\rm
[(SX)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(SX)
\mbox{''}
]$

$\rm
[(SX)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}sx
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:251}{}\section* {$\rm (SX1)$}

$\rm
[(SX1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(SX1)
\mathrel {\ddot {=}}\underline{(sx1)}
]
\rceil 
)
]$

$\rm
[(SX1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(SX1)
\mbox{''}
]$

$\rm
[(SX1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}sx1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:252}{}\section* {$\rm (SY)$}

$\rm
[(SY)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(SY)
\mathrel {\ddot {=}}\underline{(sy)}
]
\rceil 
)
]$

$\rm
[(SY)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(SY)
\mbox{''}
]$

$\rm
[(SY)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}sy
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:253}{}\section* {$\rm (SY1)$}

$\rm
[(SY1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(SY1)
\mathrel {\ddot {=}}\underline{(sy1)}
]
\rceil 
)
]$

$\rm
[(SY1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(SY1)
\mbox{''}
]$

$\rm
[(SY1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}sy1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:254}{}\section* {$\rm (SZ)$}

$\rm
[(SZ)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(SZ)
\mathrel {\ddot {=}}\underline{(sz)}
]
\rceil 
)
]$

$\rm
[(SZ)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(SZ)
\mbox{''}
]$

$\rm
[(SZ)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}sz
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:255}{}\section* {$\rm (SZ1)$}

$\rm
[(SZ1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(SZ1)
\mathrel {\ddot {=}}\underline{(sz1)}
]
\rceil 
)
]$

$\rm
[(SZ1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(SZ1)
\mbox{''}
]$

$\rm
[(SZ1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}sz1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:256}{}\section* {$\rm (SU)$}

$\rm
[(SU)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(SU)
\mathrel {\ddot {=}}\underline{(su)}
]
\rceil 
)
]$

$\rm
[(SU)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(SU)
\mbox{''}
]$

$\rm
[(SU)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}su
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:257}{}\section* {$\rm (SU1)$}

$\rm
[(SU1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(SU1)
\mathrel {\ddot {=}}\underline{(su1)}
]
\rceil 
)
]$

$\rm
[(SU1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(SU1)
\mbox{''}
]$

$\rm
[(SU1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}su1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:258}{}\section* {$\rm FXS$}

$\rm
[FXS
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FXS
\mathrel {\ddot {=}}\underline{(fxs)}
]
\rceil 
)
]$

$\rm
[FXS
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FXS
\mbox{''}
]$

$\rm
[FXS
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fxs
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:259}{}\section* {$\rm FYS$}

$\rm
[FYS
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[FYS
\mathrel {\ddot {=}}\underline{(fys)}
]
\rceil 
)
]$

$\rm
[FYS
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FYS
\mbox{''}
]$

$\rm
[FYS
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}fys
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:260}{}\section* {$\rm (F1)$}

$\rm
[(F1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(F1)
\mathrel {\ddot {=}}\underline{(f1)}
]
\rceil 
)
]$

$\rm
[(F1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(F1)
\mbox{''}
]$

$\rm
[(F1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}f1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:261}{}\section* {$\rm (F2)$}

$\rm
[(F2)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(F2)
\mathrel {\ddot {=}}\underline{(f2)}
]
\rceil 
)
]$

$\rm
[(F2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(F2)
\mbox{''}
]$

$\rm
[(F2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}f2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:262}{}\section* {$\rm (F3)$}

$\rm
[(F3)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(F3)
\mathrel {\ddot {=}}\underline{(f3)}
]
\rceil 
)
]$

$\rm
[(F3)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(F3)
\mbox{''}
]$

$\rm
[(F3)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}f3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:263}{}\section* {$\rm (F4)$}

$\rm
[(F4)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(F4)
\mathrel {\ddot {=}}\underline{(f4)}
]
\rceil 
)
]$

$\rm
[(F4)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(F4)
\mbox{''}
]$

$\rm
[(F4)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}f4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:264}{}\section* {$\rm (OP1)$}

$\rm
[(OP1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(OP1)
\mathrel {\ddot {=}}\underline{(op1)}
]
\rceil 
)
]$

$\rm
[(OP1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(OP1)
\mbox{''}
]$

$\rm
[(OP1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}op1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:265}{}\section* {$\rm (OP2)$}

$\rm
[(OP2)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(OP2)
\mathrel {\ddot {=}}\underline{(op2)}
]
\rceil 
)
]$

$\rm
[(OP2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(OP2)
\mbox{''}
]$

$\rm
[(OP2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}op2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:266}{}\section* {$\rm (R1)$}

$\rm
[(R1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(R1)
\mathrel {\ddot {=}}\underline{(r1)}
]
\rceil 
)
]$

$\rm
[(R1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(R1)
\mbox{''}
]$

$\rm
[(R1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}r1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:267}{}\section* {$\rm (S1)$}

$\rm
[(S1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(S1)
\mathrel {\ddot {=}}\underline{(s1)}
]
\rceil 
)
]$

$\rm
[(S1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(S1)
\mbox{''}
]$

$\rm
[(S1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}s1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:268}{}\section* {$\rm (S2)$}

$\rm
[(S2)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(S2)
\mathrel {\ddot {=}}\underline{(s2)}
]
\rceil 
)
]$

$\rm
[(S2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(S2)
\mbox{''}
]$

$\rm
[(S2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}meta
\linebreak [0]\ \hskip0em plus2.0em{}s2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:269}{}\section* {$\rm (EPob)$}

$\rm
[(EPob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(EPob)
\mathrel {\ddot {=}}\overline{(\epsilon)}
]
\rceil 
)
]$

$\rm
[(EPob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(EPob)
\mbox{''}
]$

$\rm
[(EPob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}ep
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:270}{}\section* {$\rm (CRS1ob)$}

$\rm
[(CRS1ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(CRS1ob)
\mathrel {\ddot {=}}\overline{(crs1)}
]
\rceil 
)
]$

$\rm
[(CRS1ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(CRS1ob)
\mbox{''}
]$

$\rm
[(CRS1ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}crs1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:271}{}\section* {$\rm (F1ob)$}

$\rm
[(F1ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(F1ob)
\mathrel {\ddot {=}}\overline{(f1)}
]
\rceil 
)
]$

$\rm
[(F1ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(F1ob)
\mbox{''}
]$

$\rm
[(F1ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}f1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:272}{}\section* {$\rm (F2ob)$}

$\rm
[(F2ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(F2ob)
\mathrel {\ddot {=}}\overline{(f2)}
]
\rceil 
)
]$

$\rm
[(F2ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(F2ob)
\mbox{''}
]$

$\rm
[(F2ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}f2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:273}{}\section* {$\rm (F3ob)$}

$\rm
[(F3ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(F3ob)
\mathrel {\ddot {=}}\overline{(f3)}
]
\rceil 
)
]$

$\rm
[(F3ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(F3ob)
\mbox{''}
]$

$\rm
[(F3ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}f3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:274}{}\section* {$\rm (F4ob)$}

$\rm
[(F4ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(F4ob)
\mathrel {\ddot {=}}\overline{(f4)}
]
\rceil 
)
]$

$\rm
[(F4ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(F4ob)
\mbox{''}
]$

$\rm
[(F4ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}f4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:275}{}\section* {$\rm (N1ob)$}

$\rm
[(N1ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(N1ob)
\mathrel {\ddot {=}}\overline{(n1)}
]
\rceil 
)
]$

$\rm
[(N1ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(N1ob)
\mbox{''}
]$

$\rm
[(N1ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}n1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:276}{}\section* {$\rm (N2ob)$}

$\rm
[(N2ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(N2ob)
\mathrel {\ddot {=}}\overline{(n2)}
]
\rceil 
)
]$

$\rm
[(N2ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(N2ob)
\mbox{''}
]$

$\rm
[(N2ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}n2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:277}{}\section* {$\rm (OP1ob)$}

$\rm
[(OP1ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(OP1ob)
\mathrel {\ddot {=}}\overline{(op1)}
]
\rceil 
)
]$

$\rm
[(OP1ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(OP1ob)
\mbox{''}
]$

$\rm
[(OP1ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}op1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:278}{}\section* {$\rm (OP2ob)$}

$\rm
[(OP2ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(OP2ob)
\mathrel {\ddot {=}}\overline{(op2)}
]
\rceil 
)
]$

$\rm
[(OP2ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(OP2ob)
\mbox{''}
]$

$\rm
[(OP2ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}op2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:279}{}\section* {$\rm (R1ob)$}

$\rm
[(R1ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(R1ob)
\mathrel {\ddot {=}}\overline{(r1)}
]
\rceil 
)
]$

$\rm
[(R1ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(R1ob)
\mbox{''}
]$

$\rm
[(R1ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}r1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:280}{}\section* {$\rm (S1ob)$}

$\rm
[(S1ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(S1ob)
\mathrel {\ddot {=}}\overline{(s1)}
]
\rceil 
)
]$

$\rm
[(S1ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(S1ob)
\mbox{''}
]$

$\rm
[(S1ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}s1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:281}{}\section* {$\rm (S2ob)$}

$\rm
[(S2ob)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(S2ob)
\mathrel {\ddot {=}}\overline{(s2)}
]
\rceil 
)
]$

$\rm
[(S2ob)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(S2ob)
\mbox{''}
]$

$\rm
[(S2ob)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}object
\linebreak [0]\ \hskip0em plus2.0em{}s2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:282}{}\section* {$\rm ph_{4}$}

$\rm
[ph_{4}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[ph_{4}
\mathrel {\ddot {=}}
\mathsf {d}
 _{Ph} 
]
\rceil 
)
]$

$\rm
[ph_{4}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ph
\_
\{4
\}
\mbox{''}
]$

$\rm
[ph_{4}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:283}{}\section* {$\rm ph_{5}$}

$\rm
[ph_{5}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[ph_{5}
\mathrel {\ddot {=}}
\mathsf {e}
 _{Ph} 
]
\rceil 
)
]$

$\rm
[ph_{5}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ph
\_
\{5
\}
\mbox{''}
]$

$\rm
[ph_{5}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph5
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:284}{}\section* {$\rm ph_{6}$}

$\rm
[ph_{6}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[ph_{6}
\mathrel {\ddot {=}}
\mathsf {f}
 _{Ph} 
]
\rceil 
)
]$

$\rm
[ph_{6}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ph
\_
\{6
\}
\mbox{''}
]$

$\rm
[ph_{6}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ph6
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:285}{}\section* {$\rm NAT$}

$\rm
[NAT
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NAT
\mbox{''}
]$

$\rm
[NAT
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}NAT
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:286}{}\section* {$\rm RATIONAL_SERIES$}

$\rm
[RATIONAL_SERIES
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}RATIONAL
\_SERIES
\mbox{''}
]$

$\rm
[RATIONAL_SERIES
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}RATIONAL
\_SERIES
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:287}{}\section* {$\rm SERIES$}

$\rm
[SERIES
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SERIES
\mbox{''}
]$

$\rm
[SERIES
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}SERIES
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:288}{}\section* {$\rm SetOfReals$}

$\rm
[SetOfReals
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SetOfReals
\mbox{''}
]$

$\rm
[SetOfReals
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}setOfReals
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:289}{}\section* {$\rm SetOfFxs$}

$\rm
[SetOfFxs
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SetOfFxs
\mbox{''}
]$

$\rm
[SetOfFxs
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}setOfFxs
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:290}{}\section* {$\rm N$}

$\rm
[N
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}N
\mbox{''}
]$

$\rm
[N
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}N
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:291}{}\section* {$\rm Q$}

$\rm
[Q
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Q
\mbox{''}
]$

$\rm
[Q
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}Q
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:292}{}\section* {$\rm X$}

$\rm
[X
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}X
\mbox{''}
]$

$\rm
[X
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}X
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:293}{}\section* {$\rm xs$}

$\rm
[xs
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}xs
\mbox{''}
]$

$\rm
[xs
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}xs
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:294}{}\section* {$\rm xaF$}

$\rm
[xaF
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}xaF
\mbox{''}
]$

$\rm
[xaF
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}xsF
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:295}{}\section* {$\rm ysF$}

$\rm
[ysF
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ysF
\mbox{''}
]$

$\rm
[ysF
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}ysF
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:296}{}\section* {$\rm us$}

$\rm
[us
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}us
\mbox{''}
]$

$\rm
[us
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}us
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:297}{}\section* {$\rm usFoelge$}

$\rm
[usFoelge
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}usFoelge
\mbox{''}
]$

$\rm
[usFoelge
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}usF
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:298}{}\section* {$\rm 0$}

$\rm
[0
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}0
\mbox{''}
]$

$\rm
[0
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:299}{}\section* {$\rm 1$}

$\rm
[1
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}1
\mbox{''}
]$

$\rm
[1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:300}{}\section* {$\rm (-1)$}

$\rm
[(-1)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(-1)
\mathrel {\ddot {=}}(-u1
)
]
\rceil 
)
]$

$\rm
[(-1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\mbox{-}1)
\mbox{''}
]$

$\rm
[(-1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}(
\mbox{-}1)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:301}{}\section* {$\rm 2$}

$\rm
[2
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[2
\mathrel {\ddot {=}}(1
+1
)
]
\rceil 
)
]$

$\rm
[2
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}2
\mbox{''}
]$

$\rm
[2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:302}{}\section* {$\rm 3$}

$\rm
[3
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[3
\mathrel {\ddot {=}}(2
+1
)
]
\rceil 
)
]$

$\rm
[3
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}3
\mbox{''}
]$

$\rm
[3
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:303}{}\section* {$\rm 1/2$}

$\rm
[1/2
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[1/2
\mathrel {\ddot {=}}rec2
]
\rceil 
)
]$

$\rm
[1/2
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}1/2
\mbox{''}
]$

$\rm
[1/2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1/2
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:304}{}\section* {$\rm 1/3$}

$\rm
[1/3
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[1/3
\mathrel {\ddot {=}}rec3
]
\rceil 
)
]$

$\rm
[1/3
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}1/3
\mbox{''}
]$

$\rm
[1/3
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1/3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:305}{}\section* {$\rm 2/3$}

$\rm
[2/3
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[2/3
\mathrel {\ddot {=}}(2
*1/3
)
]
\rceil 
)
]$

$\rm
[2/3
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}2/3
\mbox{''}
]$

$\rm
[2/3
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}2/3
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:306}{}\section* {$\rm 0f$}

$\rm
[0f
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}0f
\mbox{''}
]$

$\rm
[0f
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}0f
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:307}{}\section* {$\rm 
\mbox{1f}$}

$\rm
[
\mbox{1f}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1f
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:308}{}\section* {$\rm 00$}

$\rm
[00
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[00
\mathrel {\ddot {=}}R(0f
)
]
\rceil 
)
]$

$\rm
[00
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}00
\mbox{''}
]$

$\rm
[00
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}00
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:309}{}\section* {$\rm 
\mbox{01}$}

$\rm
[
\mbox{01}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mbox{01}
\mathrel {\ddot {=}}R(
\mbox{1f}
)
]
\rceil 
)
]$

$\rm
[
\mbox{01}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}01
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:310}{}\section* {$\rm (--01)$}

$\rm
[(--01)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\mbox{-}
\mbox{-}01)
\mbox{''}
]$

$\rm
[(--01)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}(
\mbox{-}
\mbox{-}01)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:311}{}\section* {$\rm 02$}

$\rm
[02
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}02
\mbox{''}
]$

$\rm
[02
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}02
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:312}{}\section* {$\rm 01//02$}

$\rm
[01//02
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}01//02
\mbox{''}
]$

$\rm
[01//02
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}01//02
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:313}{}\section* {$\rm PlusAssociativity(R)$}

$\rm
[PlusAssociativity(R)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[PlusAssociativity(R)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon 
\forall \underline{(fz)}
\colon R(\underline{(fx)}
)
++R(\underline{(fy)}
)
++R(\underline{(fz)}
)
 = R(\underline{(fx)}
)
++R(\underline{(fy)}
)
++R(\underline{(fz)}
)
]$

$\rm
[PlusAssociativity(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PlusAssociativity(R)
\mbox{''}
]$

$\rm
[PlusAssociativity(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}plusAssociativity(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:314}{}\section* {$\rm PlusAssociativity(R)XX$}

$\rm
[PlusAssociativity(R)XX
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[PlusAssociativity(R)XX
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon 
\forall \underline{(fz)}
\colon R(\underline{(fx)}
+_{f}\underline{(fy)}
+_{f}\underline{(fz)}
)
 == R(\underline{(fx)}
+_{f}\underline{(fy)}
+_{f}\underline{(fz)}
)
]$

$\rm
[PlusAssociativity(R)XX
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PlusAssociativity(R)XX
\mbox{''}
]$

$\rm
[PlusAssociativity(R)XX
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}plusAssociativity(R)XX
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:315}{}\section* {$\rm Plus0(R)$}

$\rm
[Plus0(R)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Plus0(R)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon R(\underline{(fx)}
)
++R(0f
)
 == R(\underline{(fx)}
)
]$

$\rm
[Plus0(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Plus0(R)
\mbox{''}
]$

$\rm
[Plus0(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}plus0(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:316}{}\section* {$\rm Negative(R)$}

$\rm
[Negative(R)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Negative(R)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{(fx)}
\colon R(\underline{(fx)}
)
++(--R(\underline{(fx)}
)
)
 == R(0f
)
]$

$\rm
[Negative(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Negative(R)
\mbox{''}
]$

$\rm
[Negative(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}negative(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:317}{}\section* {$\rm Times1(R)$}

$\rm
[Times1(R)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Times1(R)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon R(\underline{(fx)}
)
**R(
\mbox{1f}
)
 == R(\underline{(fx)}
)
]$

$\rm
[Times1(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Times1(R)
\mbox{''}
]$

$\rm
[Times1(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}times1(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:318}{}\section* {$\rm lessAddition(R)$}

$\rm
[lessAddition(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}lessAddition(R)
\mbox{''}
]$

$\rm
[lessAddition(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}lessAddition(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:319}{}\section* {$\rm PlusCommutativity(R)$}

$\rm
[PlusCommutativity(R)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[PlusCommutativity(R)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon R(\underline{(fx)}
)
++R(\underline{(fy)}
)
 == R(\underline{(fy)}
)
++R(\underline{(fx)}
)
]$

$\rm
[PlusCommutativity(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PlusCommutativity(R)
\mbox{''}
]$

$\rm
[PlusCommutativity(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}plusCommutativity(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:320}{}\section* {$\rm LeqAntisymmetry(R)$}

$\rm
[LeqAntisymmetry(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}LeqAntisymmetry(R)
\mbox{''}
]$

$\rm
[LeqAntisymmetry(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}leqAntisymmetry(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:321}{}\section* {$\rm LeqTransitivity(R)$}

$\rm
[LeqTransitivity(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}LeqTransitivity(R)
\mbox{''}
]$

$\rm
[LeqTransitivity(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}leqTransitivity(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:322}{}\section* {$\rm leqAddition(R)$}

$\rm
[leqAddition(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}leqAddition(R)
\mbox{''}
]$

$\rm
[leqAddition(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}leqAddition(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:323}{}\section* {$\rm Distribution(R)$}

$\rm
[Distribution(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Distribution(R)
\mbox{''}
]$

$\rm
[Distribution(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}distribution(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:324}{}\section* {$\rm A4(Axiom)$}

$\rm
[A4(Axiom)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[A4(Axiom)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{(v1)}
\colon 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \langle \underline{
\mathsf {a}}
{\equiv} \underline{
\mathsf {b}}
| \underline{(v1)}
{:==} \underline{
\mathsf{x}}
\rangle_{Me}
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} 
\forall_{obj} \underline{(v1)}
\colon \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {a}}
]$

$\rm
[A4(Axiom)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}A4(Axiom)
\mbox{''}
]$

$\rm
[A4(Axiom)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}a4
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:325}{}\section* {$\rm InductionAxiom$}

$\rm
[InductionAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[InductionAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(v1)}
\colon 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon \langle \underline{
\mathsf {b}}
{\equiv} \underline{
\mathsf {a}}
| \underline{(v1)}
{:==} 0
\rangle_{Me}
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \langle \underline{
\mathsf {c}}
{\equiv} \underline{
\mathsf {a}}
| \underline{(v1)}
{:==} (\underline{(v1)}
+1
)
\rangle_{Me}
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \underline{
\mathsf {b}}
\Rightarrow 
\forall_{obj} \underline{(v1)}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow 
\forall_{obj} \underline{(v1)}
\colon \underline{
\mathsf {a}}
]$

$\rm
[InductionAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}InductionAxiom
\mbox{''}
]$

$\rm
[InductionAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}induction
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:326}{}\section* {$\rm EqualityAxiom$}

$\rm
[EqualityAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[EqualityAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf{x}}
 = \underline{
\mathsf{z}}
\Rightarrow \underline{
\mathsf{y}}
 = \underline{
\mathsf{z}}
]$

$\rm
[EqualityAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqualityAxiom
\mbox{''}
]$

$\rm
[EqualityAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}equality
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:327}{}\section* {$\rm EqLeqAxiom$}

$\rm
[EqLeqAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[EqLeqAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
]$

$\rm
[EqLeqAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqLeqAxiom
\mbox{''}
]$

$\rm
[EqLeqAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}eqLeq
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:328}{}\section* {$\rm EqAdditionAxiom$}

$\rm
[EqAdditionAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[EqAdditionAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\Rightarrow (\underline{
\mathsf{x}}
+\underline{
\mathsf{z}}
)
 = (\underline{
\mathsf{y}}
+\underline{
\mathsf{z}}
)
]$

$\rm
[EqAdditionAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqAdditionAxiom
\mbox{''}
]$

$\rm
[EqAdditionAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}eqAddition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:329}{}\section* {$\rm EqMultiplicationAxiom$}

$\rm
[EqMultiplicationAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[EqMultiplicationAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
\Rightarrow (\underline{
\mathsf{x}}
*\underline{
\mathsf{z}}
)
 = (\underline{
\mathsf{y}}
*\underline{
\mathsf{z}}
)
]$

$\rm
[EqMultiplicationAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqMultiplicationAxiom
\mbox{''}
]$

$\rm
[EqMultiplicationAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}eqMultiplication
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:330}{}\section* {$\rm QisClosed(Reciprocal)(Imply)$}

$\rm
[QisClosed(Reciprocal)(Imply)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}QisClosed(Reciprocal)(Imply)
\mbox{''}
]$

$\rm
[QisClosed(Reciprocal)(Imply)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}QisClosed(reciprocal)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:331}{}\section* {$\rm QisClosed(Reciprocal)$}

$\rm
[QisClosed(Reciprocal)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}QisClosed(Reciprocal)
\mbox{''}
]$

$\rm
[QisClosed(Reciprocal)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}QisClosed(reciprocal)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:332}{}\section* {$\rm QisClosed(Negative)(Imply)$}

$\rm
[QisClosed(Negative)(Imply)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}QisClosed(Negative)(Imply)
\mbox{''}
]$

$\rm
[QisClosed(Negative)(Imply)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}QisClosed(negative)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:333}{}\section* {$\rm QisClosed(Negative)$}

$\rm
[QisClosed(Negative)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}QisClosed(Negative)
\mbox{''}
]$

$\rm
[QisClosed(Negative)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}QisClosed(negative)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:334}{}\section* {$\rm leqReflexivity$}

$\rm
[leqReflexivity
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[leqReflexivity
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon \underline{
\mathsf{x}}
 <= \underline{
\mathsf{x}}
]$

$\rm
[leqReflexivity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}leqReflexivity
\mbox{''}
]$

$\rm
[leqReflexivity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}leqReflexivity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:335}{}\section* {$\rm leqAntisymmetryAxiom$}

$\rm
[leqAntisymmetryAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[leqAntisymmetryAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf{y}}
 <= \underline{
\mathsf{x}}
\Rightarrow \underline{
\mathsf{x}}
 = \underline{
\mathsf{y}}
]$

$\rm
[leqAntisymmetryAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}leqAntisymmetryAxiom
\mbox{''}
]$

$\rm
[leqAntisymmetryAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}leqAntisymmetry
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:336}{}\section* {$\rm leqTransitivityAxiom$}

$\rm
[leqTransitivityAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[leqTransitivityAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\Rightarrow \underline{
\mathsf{y}}
 <= \underline{
\mathsf{z}}
\Rightarrow \underline{
\mathsf{x}}
 <= \underline{
\mathsf{z}}
]$

$\rm
[leqTransitivityAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}leqTransitivityAxiom
\mbox{''}
]$

$\rm
[leqTransitivityAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}leqTransitivity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:337}{}\section* {$\rm leqTotality$}

$\rm
[leqTotality
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[leqTotality
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon \dot{\neg}\,(\underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
)n
\Rightarrow \underline{
\mathsf{y}}
 <= \underline{
\mathsf{x}}
]$

$\rm
[leqTotality
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}leqTotality
\mbox{''}
]$

$\rm
[leqTotality
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}leqTotality
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:338}{}\section* {$\rm leqAdditionAxiom$}

$\rm
[leqAdditionAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[leqAdditionAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\Rightarrow (\underline{
\mathsf{x}}
+\underline{
\mathsf{z}}
)
 <= (\underline{
\mathsf{y}}
+\underline{
\mathsf{z}}
)
]$

$\rm
[leqAdditionAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}leqAdditionAxiom
\mbox{''}
]$

$\rm
[leqAdditionAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}leqAddition
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:339}{}\section* {$\rm leqMultiplicationAxiom$}

$\rm
[leqMultiplicationAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[leqMultiplicationAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon 0
 <= \underline{
\mathsf{z}}
\Rightarrow \underline{
\mathsf{x}}
 <= \underline{
\mathsf{y}}
\Rightarrow (\underline{
\mathsf{x}}
*\underline{
\mathsf{z}}
)
 <= (\underline{
\mathsf{y}}
*\underline{
\mathsf{z}}
)
]$

$\rm
[leqMultiplicationAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}leqMultiplicationAxiom
\mbox{''}
]$

$\rm
[leqMultiplicationAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}leqMultiplication
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:340}{}\section* {$\rm plusAssociativity$}

$\rm
[plusAssociativity
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[plusAssociativity
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon ((\underline{
\mathsf{x}}
+\underline{
\mathsf{y}}
)
+\underline{
\mathsf{z}}
)
 = (\underline{
\mathsf{x}}
+(\underline{
\mathsf{y}}
+\underline{
\mathsf{z}}
)
)
]$

$\rm
[plusAssociativity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}plusAssociativity
\mbox{''}
]$

$\rm
[plusAssociativity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}plusAssociativity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:341}{}\section* {$\rm plusCommutativity$}

$\rm
[plusCommutativity
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[plusCommutativity
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon (\underline{
\mathsf{x}}
+\underline{
\mathsf{y}}
)
 = (\underline{
\mathsf{y}}
+\underline{
\mathsf{x}}
)
]$

$\rm
[plusCommutativity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}plusCommutativity
\mbox{''}
]$

$\rm
[plusCommutativity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}plusCommutativity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:342}{}\section* {$\rm Negative$}

$\rm
[Negative
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Negative
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon (\underline{
\mathsf{x}}
+(-u\underline{
\mathsf{x}}
)
)
 = 0
]$

$\rm
[Negative
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Negative
\mbox{''}
]$

$\rm
[Negative
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}negative
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:343}{}\section* {$\rm plus0$}

$\rm
[plus0
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[plus0
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon (\underline{
\mathsf{x}}
+0
)
 = \underline{
\mathsf{x}}
]$

$\rm
[plus0
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}plus0
\mbox{''}
]$

$\rm
[plus0
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}plus0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:344}{}\section* {$\rm timesAssociativity$}

$\rm
[timesAssociativity
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[timesAssociativity
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon ((\underline{
\mathsf{x}}
*\underline{
\mathsf{y}}
)
*\underline{
\mathsf{z}}
)
 = (\underline{
\mathsf{x}}
*(\underline{
\mathsf{y}}
*\underline{
\mathsf{z}}
)
)
]$

$\rm
[timesAssociativity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}timesAssociativity
\mbox{''}
]$

$\rm
[timesAssociativity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}timesAssociativity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:345}{}\section* {$\rm timesCommutativity$}

$\rm
[timesCommutativity
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[timesCommutativity
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon (\underline{
\mathsf{x}}
*\underline{
\mathsf{y}}
)
 = (\underline{
\mathsf{y}}
*\underline{
\mathsf{x}}
)
]$

$\rm
[timesCommutativity
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}timesCommutativity
\mbox{''}
]$

$\rm
[timesCommutativity
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}timesCommutativity
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:346}{}\section* {$\rm ReciprocalAxiom$}

$\rm
[ReciprocalAxiom
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[ReciprocalAxiom
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon \dot{\neg}\,(\underline{
\mathsf{x}}
 = 0
)n
\Rightarrow (\underline{
\mathsf{x}}
*rec\underline{
\mathsf{x}}
)
 = 1
]$

$\rm
[ReciprocalAxiom
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ReciprocalAxiom
\mbox{''}
]$

$\rm
[ReciprocalAxiom
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}reciprocal
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:347}{}\section* {$\rm times1$}

$\rm
[times1
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[times1
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon (\underline{
\mathsf{x}}
*1
)
 = \underline{
\mathsf{x}}
]$

$\rm
[times1
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}times1
\mbox{''}
]$

$\rm
[times1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}times1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:348}{}\section* {$\rm Distribution$}

$\rm
[Distribution
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Distribution
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf{x}}
\colon 
\forall \underline{
\mathsf{y}}
\colon 
\forall \underline{
\mathsf{z}}
\colon (\underline{
\mathsf{x}}
*(\underline{
\mathsf{y}}
+\underline{
\mathsf{z}}
)
)
 = ((\underline{
\mathsf{x}}
*\underline{
\mathsf{y}}
)
+(\underline{
\mathsf{x}}
*\underline{
\mathsf{z}}
)
)
]$

$\rm
[Distribution
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Distribution
\mbox{''}
]$

$\rm
[Distribution
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}distribution
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:349}{}\section* {$\rm 0not1$}

$\rm
[0not1
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[0not1
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash \dot{\neg}\,(0
 = 1
)n
]$

$\rm
[0not1
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}0not1
\mbox{''}
]$

$\rm
[0not1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}0not1
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:350}{}\section* {$\rm 
\mbox{lemma eqLeq(R)}$}

$\rm
[
\mbox{lemma eqLeq(R)}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}eqLeq(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:351}{}\section* {$\rm TimesAssociativity(R)$}

$\rm
[TimesAssociativity(R)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[TimesAssociativity(R)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon 
\forall \underline{(fz)}
\colon R(\underline{(fx)}
)
**R(\underline{(fy)}
)
**R(\underline{(fz)}
)
 == R(\underline{(fx)}
)
**R(\underline{(fy)}
)
**R(\underline{(fz)}
)
]$

$\rm
[TimesAssociativity(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TimesAssociativity(R)
\mbox{''}
]$

$\rm
[TimesAssociativity(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}timesAssociativity(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:352}{}\section* {$\rm TimesCommutativity(R)$}

$\rm
[TimesCommutativity(R)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[TimesCommutativity(R)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon R(\underline{(fx)}
)
**R(\underline{(fy)}
)
 == R(\underline{(fy)}
)
**R(\underline{(fx)}
)
]$

$\rm
[TimesCommutativity(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TimesCommutativity(R)
\mbox{''}
]$

$\rm
[TimesCommutativity(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}timesCommutativity(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:353}{}\section* {$\rm (Adgic)SameR$}

$\rm
[(Adgic)SameR
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(Adgic)SameR
\mbox{''}
]$

$\rm
[(Adgic)SameR
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}adhoc
\linebreak [0]\ \hskip0em plus2.0em{}sameR
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:354}{}\section* {$\rm Separation2formula(1)$}

$\rm
[Separation2formula(1)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Separation2formula(1)
\mbox{''}
]$

$\rm
[Separation2formula(1)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}separation2formula(1)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:355}{}\section* {$\rm Separation2formula(2)$}

$\rm
[Separation2formula(2)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Separation2formula(2)
\mbox{''}
]$

$\rm
[Separation2formula(2)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}separation2formula(2)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:356}{}\section* {$\rm Cauchy$}

$\rm
[Cauchy
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Cauchy
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(v1)}
\colon 
\forall \underline{(v2)}
\colon 
\forall \underline{
\mathsf {n}}
\colon 
\forall \underline{(\epsilon)}
\colon 
\forall \underline{(fx)}
\colon 
\forall_{obj} \underline{(\epsilon)}
\colon \dot{\neg}\,(
\forall_{obj} \underline{
\mathsf {n}}
\colon \dot{\neg}\,(
\forall_{obj} \underline{(v1)}
\colon 
\forall_{obj} \underline{(v2)}
\colon \dot{\neg}\,(0
 <= \underline{(\epsilon)}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(0
 = \underline{(\epsilon)}
)n
)n
)n
\Rightarrow \underline{
\mathsf {n}}
 <= \underline{(v1)}
\Rightarrow \underline{
\mathsf {n}}
 <= \underline{(v2)}
\Rightarrow \dot{\neg}\,(|(\underline{(fx)}
[\underline{(v1)}
]
+(-u\underline{(fx)}
[\underline{(v2)}
]
)
)
|
 <= \underline{(\epsilon)}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(|(\underline{(fx)}
[\underline{(v1)}
]
+(-u\underline{(fx)}
[\underline{(v2)}
]
)
)
|
 = \underline{(\epsilon)}
)n
)n
)n
)n
)n
]$

$\rm
[Cauchy
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Cauchy
\mbox{''}
]$

$\rm
[Cauchy
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}cauchy
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:357}{}\section* {$\rm PlusF$}

$\rm
[PlusF
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[PlusF
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon \underline{(fx)}
+_{f}\underline{(fy)}
[\underline{
\mathsf {m}}
]
 = (\underline{(fx)}
[\underline{
\mathsf {m}}
]
+\underline{(fy)}
[\underline{
\mathsf {m}}
]
)
]$

$\rm
[PlusF
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PlusF
\mbox{''}
]$

$\rm
[PlusF
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}plusF
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:358}{}\section* {$\rm ReciprocalF$}

$\rm
[ReciprocalF
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ReciprocalF
\mbox{''}
]$

$\rm
[ReciprocalF
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}reciprocalF
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:359}{}\section* {$\rm From==$}

$\rm
[From==
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[From==
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon R(\underline{(fx)}
)
 == R(\underline{(fy)}
)
\vdash SF(\underline{(fx)}
,\underline{(fy)}
)
]$

$\rm
[From==
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}From
{=}
{=}
\mbox{''}
]$

$\rm
[From==
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}from
{=}
{=}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:360}{}\section* {$\rm To==$}

$\rm
[To==
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[To==
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon SF(\underline{(fx)}
,\underline{(fy)}
)
\vdash R(\underline{(fx)}
)
 == R(\underline{(fy)}
)
]$

$\rm
[To==
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}To
{=}
{=}
\mbox{''}
]$

$\rm
[To==
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}to
{=}
{=}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:361}{}\section* {$\rm FromInR$}

$\rm
[FromInR
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[FromInR
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon \underline{(fx)}
 \mathrel{\in} R(\underline{(fy)}
)
\vdash SF(\underline{(fx)}
,\underline{(fy)}
)
]$

$\rm
[FromInR
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromInR
\mbox{''}
]$

$\rm
[FromInR
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}fromInR
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:362}{}\section* {$\rm PlusR(Sym)$}

$\rm
[PlusR(Sym)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}PlusR(Sym)
\mbox{''}
]$

$\rm
[PlusR(Sym)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}plusR(Sym)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:363}{}\section* {$\rm ReciprocalR(Axiom)$}

$\rm
[ReciprocalR(Axiom)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ReciprocalR(Axiom)
\mbox{''}
]$

$\rm
[ReciprocalR(Axiom)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}reciprocalR
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:364}{}\section* {$\rm LessMinus1(N)$}

$\rm
[LessMinus1(N)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[LessMinus1(N)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon Nat(\underline{
\mathsf {m}}
)
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} Nat(\underline{
\mathsf {n}}
)
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} \dot{\neg}\,(\underline{
\mathsf {m}}
 <= (\underline{
\mathsf {n}}
+1
)
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {m}}
 = (\underline{
\mathsf {n}}
+1
)
)n
)n
)n
\vdash \underline{
\mathsf {m}}
 <= \underline{
\mathsf {n}}
]$

$\rm
[LessMinus1(N)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}LessMinus1(N)
\mbox{''}
]$

$\rm
[LessMinus1(N)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}lessMinus1(N)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:365}{}\section* {$\rm Nonnegative(N)$}

$\rm
[Nonnegative(N)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[Nonnegative(N)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon Nat(\underline{
\mathsf {m}}
)
\mathrel {\makebox [0mm][l]{$\vdash $}\,{\vdash }} 0
 <= \underline{
\mathsf {m}}
]$

$\rm
[Nonnegative(N)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Nonnegative(N)
\mbox{''}
]$

$\rm
[Nonnegative(N)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}nonnegative(N)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:366}{}\section* {$\rm US0$}

$\rm
[US0
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[US0
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash us
[0
]
 == xs
[0
]
++R(
\mbox{1f}
)
]$

$\rm
[US0
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}US0
\mbox{''}
]$

$\rm
[US0
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}US0
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:367}{}\section* {$\rm NextXS(UpperBound)$}

$\rm
[NextXS(UpperBound)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[NextXS(UpperBound)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon UB(01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
, SetOfReals
)
\vdash xs
[(\underline{
\mathsf {m}}
+1
)
]
 == xs
[\underline{
\mathsf {m}}
]
]$

$\rm
[NextXS(UpperBound)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NextXS(UpperBound)
\mbox{''}
]$

$\rm
[NextXS(UpperBound)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}nextXS(upperBound)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:368}{}\section* {$\rm NextXS(NoUpperBound)$}

$\rm
[NextXS(NoUpperBound)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[NextXS(NoUpperBound)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon \dot{\neg}\,(UB(01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
, SetOfReals
)
)n
\vdash xs
[(\underline{
\mathsf {m}}
+1
)
]
 == 01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
]$

$\rm
[NextXS(NoUpperBound)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NextXS(NoUpperBound)
\mbox{''}
]$

$\rm
[NextXS(NoUpperBound)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}nextXS(noUpperBound)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:369}{}\section* {$\rm NextUS(UpperBound)$}

$\rm
[NextUS(UpperBound)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[NextUS(UpperBound)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon UB(01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
, SetOfReals
)
\vdash us
[(\underline{
\mathsf {m}}
+1
)
]
 == 01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
]$

$\rm
[NextUS(UpperBound)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NextUS(UpperBound)
\mbox{''}
]$

$\rm
[NextUS(UpperBound)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}nextUS(upperBound)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:370}{}\section* {$\rm NextUS(NoUpperBound)$}

$\rm
[NextUS(NoUpperBound)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[NextUS(NoUpperBound)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon \dot{\neg}\,(UB(01//02
**xs
[\underline{
\mathsf {m}}
]
++us
[\underline{
\mathsf {m}}
]
, SetOfReals
)
)n
\vdash us
[(\underline{
\mathsf {m}}
+1
)
]
 == us
[\underline{
\mathsf {m}}
]
]$

$\rm
[NextUS(NoUpperBound)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NextUS(NoUpperBound)
\mbox{''}
]$

$\rm
[NextUS(NoUpperBound)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}nextUS(noUpperBound)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:371}{}\section* {$\rm ExpZero$}

$\rm
[ExpZero
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[ExpZero
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf{x}}
\colon \underline{
\mathsf {m}}
 = 0
\vdash  \underline{
\mathsf{x}}
 (exp) \underline{
\mathsf {m}}
 = 1
]$

$\rm
[ExpZero
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ExpZero
\mbox{''}
]$

$\rm
[ExpZero
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}expZero
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:372}{}\section* {$\rm ExpPositive$}

$\rm
[ExpPositive
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[ExpPositive
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf{x}}
\colon \dot{\neg}\,(0
 <= \underline{
\mathsf {m}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(0
 = \underline{
\mathsf {m}}
)n
)n
)n
\vdash  \underline{
\mathsf{x}}
 (exp) \underline{
\mathsf {m}}
 = (\underline{
\mathsf{x}}
* \underline{
\mathsf{x}}
 (exp) (\underline{
\mathsf {m}}
+(-u1
)
)
)
]$

$\rm
[ExpPositive
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ExpPositive
\mbox{''}
]$

$\rm
[ExpPositive
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}expPositive
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:373}{}\section* {$\rm ExpZero(R)$}

$\rm
[ExpZero(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ExpZero(R)
\mbox{''}
]$

$\rm
[ExpZero(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}expZero(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:374}{}\section* {$\rm ExpPositive(R)$}

$\rm
[ExpPositive(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ExpPositive(R)
\mbox{''}
]$

$\rm
[ExpPositive(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}expPositive(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:375}{}\section* {$\rm BSzero$}

$\rm
[BSzero
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[BSzero
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon \underline{
\mathsf {n}}
 = 0
\vdash BS(\underline{
\mathsf {m}}
,\underline{
\mathsf {n}}
)
 =  rec(1
+1
)
 (exp) \underline{
\mathsf {m}}
]$

$\rm
[BSzero
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}BSzero
\mbox{''}
]$

$\rm
[BSzero
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}base(1/2)Sum
\linebreak [0]\ \hskip0em plus2.0em{}zero
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:376}{}\section* {$\rm BSpositive$}

$\rm
[BSpositive
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[BSpositive
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon \dot{\neg}\,(0
 <= \underline{
\mathsf {n}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(0
 = \underline{
\mathsf {n}}
)n
)n
)n
\vdash BS(\underline{
\mathsf {m}}
,\underline{
\mathsf {n}}
)
 = ( rec(1
+1
)
 (exp) (\underline{
\mathsf {m}}
+\underline{
\mathsf {n}}
)
+BS(\underline{
\mathsf {m}}
,(\underline{
\mathsf {n}}
+(-u1
)
)
)
)
]$

$\rm
[BSpositive
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}BSpositive
\mbox{''}
]$

$\rm
[BSpositive
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}base(1/2)Sum
\linebreak [0]\ \hskip0em plus2.0em{}positive
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:377}{}\section* {$\rm UStelescope(Zero)$}

$\rm
[UStelescope(Zero)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[UStelescope(Zero)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon \underline{
\mathsf {n}}
 = 0
\vdash UStelescope(\underline{
\mathsf {m}}
,\underline{
\mathsf {n}}
)
 = |(us
[\underline{
\mathsf {m}}
]
+(-uus
[(\underline{
\mathsf {m}}
+1
)
]
)
)
|
]$

$\rm
[UStelescope(Zero)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UStelescope(Zero)
\mbox{''}
]$

$\rm
[UStelescope(Zero)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}UStelescope
\linebreak [0]\ \hskip0em plus2.0em{}zero
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:378}{}\section* {$\rm UStelescope(Positive)$}

$\rm
[UStelescope(Positive)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[UStelescope(Positive)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {m}}
\colon 
\forall \underline{
\mathsf {n}}
\colon \dot{\neg}\,(0
 <= \underline{
\mathsf {n}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(0
 = \underline{
\mathsf {n}}
)n
)n
)n
\vdash UStelescope(\underline{
\mathsf {m}}
,\underline{
\mathsf {n}}
)
 = (|(us
[(\underline{
\mathsf {m}}
+\underline{
\mathsf {n}}
)
]
+(-uus
[(\underline{
\mathsf {m}}
+(\underline{
\mathsf {n}}
+1
)
)
]
)
)
|
+UStelescope(\underline{
\mathsf {m}}
,(\underline{
\mathsf {n}}
+(-u1
)
)
)
)
]$

$\rm
[UStelescope(Positive)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UStelescope(Positive)
\mbox{''}
]$

$\rm
[UStelescope(Positive)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}UStelescope
\linebreak [0]\ \hskip0em plus2.0em{}positive
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:379}{}\section* {$\rm EqAddition(R)$}

$\rm
[EqAddition(R)
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[EqAddition(R)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(fy)}
\colon 
\forall \underline{(fz)}
\colon R(\underline{(fx)}
)
 = R(\underline{(fy)}
)
\vdash R(\underline{(fx)}
)
++R(\underline{(fz)}
)
 = R(\underline{(fy)}
)
++R(\underline{(fz)}
)
]$

$\rm
[EqAddition(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqAddition(R)
\mbox{''}
]$

$\rm
[EqAddition(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}adhoc
\linebreak [0]\ \hskip0em plus2.0em{}eqAddition(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:380}{}\section* {$\rm FromLimit$}

$\rm
[FromLimit
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromLimit
\mbox{''}
]$

$\rm
[FromLimit
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}fromLimit
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:381}{}\section* {$\rm ToUpperBound$}

$\rm
[ToUpperBound
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ToUpperBound
\mbox{''}
]$

$\rm
[ToUpperBound
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}toUpperBound
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:382}{}\section* {$\rm FromUpperBound$}

$\rm
[FromUpperBound
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromUpperBound
\mbox{''}
]$

$\rm
[FromUpperBound
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}fromUpperBound
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:383}{}\section* {$\rm USisUpperBound$}

$\rm
[USisUpperBound
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}USisUpperBound
\mbox{''}
]$

$\rm
[USisUpperBound
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}USisUpperBound
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:384}{}\section* {$\rm 0not1(R)$}

$\rm
[0not1(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}0not1(R)
\mbox{''}
]$

$\rm
[0not1(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}0not1(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:385}{}\section* {$\rm ExpUnbounded(R)$}

$\rm
[ExpUnbounded(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ExpUnbounded(R)
\mbox{''}
]$

$\rm
[ExpUnbounded(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}expUnbounded
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:386}{}\section* {$\rm FromLeq(Advanced)(N)$}

$\rm
[FromLeq(Advanced)(N)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromLeq(Advanced)(N)
\mbox{''}
]$

$\rm
[FromLeq(Advanced)(N)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}fromLeq(Advanced)(N)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:387}{}\section* {$\rm FromLeastUpperBound$}

$\rm
[FromLeastUpperBound
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromLeastUpperBound
\mbox{''}
]$

$\rm
[FromLeastUpperBound
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}fromLeastUpperBound
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:388}{}\section* {$\rm ToLeastUpperBound$}

$\rm
[ToLeastUpperBound
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ToLeastUpperBound
\mbox{''}
]$

$\rm
[ToLeastUpperBound
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}toLeastUpperBound
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:389}{}\section* {$\rm XSisNotUpperBound$}

$\rm
[XSisNotUpperBound
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}XSisNotUpperBound
\mbox{''}
]$

$\rm
[XSisNotUpperBound
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}XSisNotUpperBound
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:390}{}\section* {$\rm ysFGreater$}

$\rm
[ysFGreater
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ysFGreater
\mbox{''}
]$

$\rm
[ysFGreater
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}ysFGreater
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:391}{}\section* {$\rm ysFLess$}

$\rm
[ysFLess
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ysFLess
\mbox{''}
]$

$\rm
[ysFLess
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}ysFLess
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:392}{}\section* {$\rm SmallInverse$}

$\rm
[SmallInverse
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SmallInverse
\mbox{''}
]$

$\rm
[SmallInverse
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1rule
\linebreak [0]\ \hskip0em plus2.0em{}smallInverse
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:393}{}\section* {$\rm NatType$}

$\rm
[NatType
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NatType
\mbox{''}
]$

$\rm
[NatType
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}natType
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:394}{}\section* {$\rm RationalType$}

$\rm
[RationalType
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}RationalType
\mbox{''}
]$

$\rm
[RationalType
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}rationalType
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:395}{}\section* {$\rm SeriesType$}

$\rm
[SeriesType
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SeriesType
\mbox{''}
]$

$\rm
[SeriesType
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}seriesType
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:396}{}\section* {$\rm Max$}

$\rm
[Max
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Max
\mbox{''}
]$

$\rm
[Max
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}max
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:397}{}\section* {$\rm Numerical$}

$\rm
[Numerical
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Numerical
\mbox{''}
]$

$\rm
[Numerical
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}numerical
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:398}{}\section* {$\rm NumericalF$}

$\rm
[NumericalF
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NumericalF
\mbox{''}
]$

$\rm
[NumericalF
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}numericalF
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:399}{}\section* {$\rm MemberOfSeries(Imply)$}

$\rm
[MemberOfSeries(Imply)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MemberOfSeries(Imply)
\mbox{''}
]$

$\rm
[MemberOfSeries(Imply)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}axiom
\linebreak [0]\ \hskip0em plus2.0em{}memberOfSeries
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:400}{}\section* {$\rm JoinConjuncts(2conditions)$}

$\rm
[JoinConjuncts(2conditions)
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
\vdash MP2
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\rhd \underline{
\mathsf {a}}
\rhd \underline{
\mathsf {b}}
\gg \underline{
\mathsf {c}}
; MP2
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\rhd \underline{
\mathsf {a}}
\rhd \underline{
\mathsf {b}}
\gg \underline{
\mathsf {d}}
; JoinConjuncts
\rhd \underline{
\mathsf {c}}
\rhd \underline{
\mathsf {d}}
\gg \dot{\neg}\,(\underline{
\mathsf {c}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
)n
; 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon Ded
\rhd 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
)n
\gg \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
)n
; \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\vdash MP2
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
)n
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\gg \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[JoinConjuncts(2conditions)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
)n
]$

$\rm
[JoinConjuncts(2conditions)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}JoinConjuncts(2conditions)
\mbox{''}
]$

$\rm
[JoinConjuncts(2conditions)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}doubly
\linebreak [0]\ \hskip0em plus2.0em{}conditioned
\linebreak [0]\ \hskip0em plus2.0em{}join
\linebreak [0]\ \hskip0em plus2.0em{}conjuncts
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:401}{}\section* {$\rm 
\mbox{prop lemma imply negation}$}

$\rm
[
\mbox{prop lemma imply negation}
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash AutoImply
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
; TND
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
; FromDisjuncts
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\rhd \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[
\mbox{prop lemma imply negation}
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
]$

$\rm
[
\mbox{prop lemma imply negation}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}imply
\linebreak [0]\ \hskip0em plus2.0em{}negation
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:402}{}\section* {$\rm TND$}

$\rm
[TND
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon AutoImply
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
; Repetition
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[TND
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
]$

$\rm
[TND
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TND
\mbox{''}
]$

$\rm
[TND
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}tertium
\linebreak [0]\ \hskip0em plus2.0em{}non
\linebreak [0]\ \hskip0em plus2.0em{}datur
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:403}{}\section* {$\rm FromNegatedImply$}

$\rm
[FromNegatedImply
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\vdash \underline{
\mathsf {a}}
\vdash MP
\rhd \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\rhd \underline{
\mathsf {a}}
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
; RemoveDoubleNeg
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\gg \underline{
\mathsf {b}}
; 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon Ded
\rhd 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\vdash \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {b}}
\gg \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
; \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
\vdash MT
\rhd \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
; Repetition
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[FromNegatedImply
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
]$

$\rm
[FromNegatedImply
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromNegatedImply
\mbox{''}
]$

$\rm
[FromNegatedImply
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}negated
\linebreak [0]\ \hskip0em plus2.0em{}imply
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:404}{}\section* {$\rm ToNegatedImply$}

$\rm
[ToNegatedImply
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\vdash \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\vdash RemoveDoubleNeg
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\gg \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
; MP
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\rhd \underline{
\mathsf {a}}
\gg \underline{
\mathsf {b}}
; FromContradiction
\rhd \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
; 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon Ded
\rhd 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\vdash \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
\gg \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
; \underline{
\mathsf {a}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\vdash MP2
\rhd \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
\rhd \underline{
\mathsf {a}}
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
; AutoImply
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
; Neg
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[ToNegatedImply
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
)n
]$

$\rm
[ToNegatedImply
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ToNegatedImply
\mbox{''}
]$

$\rm
[ToNegatedImply
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}to
\linebreak [0]\ \hskip0em plus2.0em{}negated
\linebreak [0]\ \hskip0em plus2.0em{}imply
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:405}{}\section* {$\rm FromNegated(2*Imply)$}

$\rm
[FromNegated(2*Imply)
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
)n
\vdash FromNegatedImply
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
)n
)n
)n
; FirstConjunct
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
)n
)n
)n
\gg \underline{
\mathsf {a}}
; SecondConjunct
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
)n
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
)n
; FromNegatedImply
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
)n
\gg \dot{\neg}\,(\underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
)n
; FirstConjunct
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
)n
\gg \underline{
\mathsf {b}}
; SecondConjunct
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {c}}
)n
; JoinConjuncts
\rhd \underline{
\mathsf {a}}
\rhd \underline{
\mathsf {b}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
; JoinConjuncts
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\rhd \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[FromNegated(2*Imply)
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
)n
\vdash \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
)n
]$

$\rm
[FromNegated(2*Imply)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromNegated(2
{*}Imply)
\mbox{''}
]$

$\rm
[FromNegated(2*Imply)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}negated
\linebreak [0]\ \hskip0em plus2.0em{}double
\linebreak [0]\ \hskip0em plus2.0em{}imply
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:406}{}\section* {$\rm FromNegatedAnd$}

$\rm
[FromNegatedAnd
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\vdash \underline{
\mathsf {a}}
\vdash Repetition
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
; RemoveDoubleNeg
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\gg \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
; MP
\rhd \underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\rhd \underline{
\mathsf {a}}
\gg \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[FromNegatedAnd
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\vdash \underline{
\mathsf {a}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
]$

$\rm
[FromNegatedAnd
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromNegatedAnd
\mbox{''}
]$

$\rm
[FromNegatedAnd
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}negated
\linebreak [0]\ \hskip0em plus2.0em{}and
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:407}{}\section* {$\rm FromNegatedOr$}

$\rm
[FromNegatedOr
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
\vdash Repetition
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
; FromNegatedImply
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[FromNegatedOr
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
\vdash \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
]$

$\rm
[FromNegatedOr
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromNegatedOr
\mbox{''}
]$

$\rm
[FromNegatedOr
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}negated
\linebreak [0]\ \hskip0em plus2.0em{}or
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:408}{}\section* {$\rm ToNegatedOr$}

$\rm
[ToNegatedOr
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash FirstConjunct
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
; SecondConjunct
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {b}}
)n
; NegateDisjunct1
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\gg \underline{
\mathsf {b}}
; FromContradiction
\rhd \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
; 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon Ded
\rhd 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
; \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\vdash MP
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
\rhd \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
; 
\mbox{prop lemma imply negation}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
\gg \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[ToNegatedOr
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {b}}
)n
)n
)n
\vdash \dot{\neg}\,(\dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
)n
]$

$\rm
[ToNegatedOr
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ToNegatedOr
\mbox{''}
]$

$\rm
[ToNegatedOr
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}to
\linebreak [0]\ \hskip0em plus2.0em{}negated
\linebreak [0]\ \hskip0em plus2.0em{}or
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:409}{}\section* {$\rm FromNegations$}

$\rm
[FromNegations
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash TND
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
; FromDisjuncts
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\gg \underline{
\mathsf {b}}
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[FromNegations
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \underline{
\mathsf {b}}
]$

$\rm
[FromNegations
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}FromNegations
\mbox{''}
]$

$\rm
[FromNegations
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}negations
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:410}{}\section* {$\rm From3Disjuncts$}

$\rm
[From3Disjuncts
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash Repetition
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
; MP
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\gg \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
; FromDisjuncts
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\rhd \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\rhd \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {d}}
\gg \underline{
\mathsf {d}}
; 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon Ded
\rhd 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash \underline{
\mathsf {d}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {d}}
; AutoImply
\gg \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
; \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {d}}
\vdash MP3
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {d}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\rhd \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\rhd \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {d}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {d}}
; MP
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\gg \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
; FromNegations
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {d}}
\gg \underline{
\mathsf {d}}
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[From3Disjuncts
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \underline{
\mathsf {c}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {d}}
]$

$\rm
[From3Disjuncts
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}From3Disjuncts
\mbox{''}
]$

$\rm
[From3Disjuncts
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}three
\linebreak [0]\ \hskip0em plus2.0em{}disjuncts
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:411}{}\section* {$\rm From2*2Disjuncts$}

$\rm
[From2*2Disjuncts
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon 
\forall \underline{
\mathsf {e}}
\colon \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {a}}
\vdash MP
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \underline{
\mathsf {a}}
\gg \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
; MP
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \underline{
\mathsf {a}}
\gg \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
; FromDisjuncts
\rhd \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\rhd \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\gg \underline{
\mathsf {e}}
; 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon 
\forall \underline{
\mathsf {e}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash NegateDisjunct1
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\gg \underline{
\mathsf {b}}
; MP
\rhd \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \underline{
\mathsf {b}}
\gg \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
; MP
\rhd \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \underline{
\mathsf {b}}
\gg \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
; FromDisjuncts
\rhd \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\rhd \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\gg \underline{
\mathsf {e}}
; 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon 
\forall \underline{
\mathsf {e}}
\colon Ded
\rhd 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon 
\forall \underline{
\mathsf {e}}
\colon \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {a}}
\vdash \underline{
\mathsf {e}}
\gg \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {e}}
; Ded
\rhd 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon 
\forall \underline{
\mathsf {e}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash \underline{
\mathsf {e}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {e}}
; \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\vdash MP3
\rhd \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\Rightarrow \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\gg \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {e}}
; MP4
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {e}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\rhd \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {e}}
; FromNegations
\rhd \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {e}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {e}}
\gg \underline{
\mathsf {e}}
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[From2*2Disjuncts
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon 
\forall \underline{
\mathsf {e}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {a}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {c}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {b}}
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \underline{
\mathsf {e}}
\vdash \underline{
\mathsf {e}}
]$

$\rm
[From2*2Disjuncts
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}From2
{*}2Disjuncts
\mbox{''}
]$

$\rm
[From2*2Disjuncts
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}from
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}times
\linebreak [0]\ \hskip0em plus2.0em{}two
\linebreak [0]\ \hskip0em plus2.0em{}disjuncts
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:412}{}\section* {$\rm NegateDisjunct1$}

$\rm
[NegateDisjunct1
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash Repetition
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
; MP
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\gg \underline{
\mathsf {b}}
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[NegateDisjunct1
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\vdash \underline{
\mathsf {b}}
]$

$\rm
[NegateDisjunct1
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NegateDisjunct1
\mbox{''}
]$

$\rm
[NegateDisjunct1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}negate
\linebreak [0]\ \hskip0em plus2.0em{}first
\linebreak [0]\ \hskip0em plus2.0em{}disjunct
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:413}{}\section* {$\rm NegateDisjunct2$}

$\rm
[NegateDisjunct2
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\vdash Repetition
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
; NegativeMT
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\gg \underline{
\mathsf {a}}
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[NegateDisjunct2
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\vdash \underline{
\mathsf {a}}
]$

$\rm
[NegateDisjunct2
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}NegateDisjunct2
\mbox{''}
]$

$\rm
[NegateDisjunct2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}negate
\linebreak [0]\ \hskip0em plus2.0em{}second
\linebreak [0]\ \hskip0em plus2.0em{}disjunct
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:414}{}\section* {$\rm ExpandDisjuncts$}

$\rm
[ExpandDisjuncts
\stackrel{
proof
}{\rightarrow}
\lambda 
\mathsf {c}
.
\lambda 
\mathsf{x}
.
{\cal P}( 
\lceil SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\vdash NegateDisjunct2
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\gg \underline{
\mathsf {a}}
; NegateDisjunct2
\rhd \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\rhd \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\gg \underline{
\mathsf {c}}
; JoinConjuncts
\rhd \underline{
\mathsf {a}}
\rhd \underline{
\mathsf {c}}
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
; 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon Ded
\rhd 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\vdash \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
; \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash MP2
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
\rhd \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\rhd \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\gg \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
; Repetition
\rhd \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
\gg \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
\rceil 
, 
p_0
, 
\mathsf {c}
)
]$

$\rm
[ExpandDisjuncts
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{
\mathsf {a}}
\colon 
\forall \underline{
\mathsf {b}}
\colon 
\forall \underline{
\mathsf {c}}
\colon 
\forall \underline{
\mathsf {d}}
\colon \dot{\neg}\,(\underline{
\mathsf {a}}
)n
\Rightarrow \underline{
\mathsf {b}}
\vdash \dot{\neg}\,(\underline{
\mathsf {c}}
)n
\Rightarrow \underline{
\mathsf {d}}
\vdash \dot{\neg}\,(\underline{
\mathsf {b}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {d}}
)n
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {a}}
\Rightarrow \dot{\neg}\,(\underline{
\mathsf {c}}
)n
)n
]$

$\rm
[ExpandDisjuncts
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ExpandDisjuncts
\mbox{''}
]$

$\rm
[ExpandDisjuncts
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}prop
\linebreak [0]\ \hskip0em plus2.0em{}lemma
\linebreak [0]\ \hskip0em plus2.0em{}expand
\linebreak [0]\ \hskip0em plus2.0em{}disjuncts
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:415}{}\section* {$\rm SENC1$}

$\rm
[SENC1
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[SENC1
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(rx)}
\colon 
\forall \underline{(ry)}
\colon \underline{(rx)}
 == \underline{(ry)}
\vdash \underline{(fx)}
 \mathrel{\in} \underline{(rx)}
\vdash \underline{(fx)}
 \mathrel{\in} \underline{(ry)}
]$

$\rm
[SENC1
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SENC1
\mbox{''}
]$

$\rm
[SENC1
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}equality
\linebreak [0]\ \hskip0em plus2.0em{}nec
\linebreak [0]\ \hskip0em plus2.0em{}condition(1)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:416}{}\section* {$\rm SENC2$}

$\rm
[SENC2
\stackrel{
proof
}{\rightarrow}
Rule\ tactic
]$

$\rm
[SENC2
\stackrel{
stmt
}{\rightarrow}SystemQ
\vdash 
\forall \underline{(fx)}
\colon 
\forall \underline{(rx)}
\colon 
\forall \underline{(ry)}
\colon \underline{(rx)}
 == \underline{(ry)}
\vdash \underline{(fx)}
 \mathrel{\in} \underline{(ry)}
\vdash \underline{(fx)}
 \mathrel{\in} \underline{(rx)}
]$

$\rm
[SENC2
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SENC2
\mbox{''}
]$

$\rm
[SENC2
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}equality
\linebreak [0]\ \hskip0em plus2.0em{}nec
\linebreak [0]\ \hskip0em plus2.0em{}condition(2)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:417}{}\section* {$\rm LessLeq(R)$}

$\rm
[LessLeq(R)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}LessLeq(R)
\mbox{''}
]$

$\rm
[LessLeq(R)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}lessLeq(R)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:418}{}\section* {$\rm MemberOfSeries$}

$\rm
[MemberOfSeries
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}MemberOfSeries
\mbox{''}
]$

$\rm
[MemberOfSeries
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}memberOfSeries
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:419}{}\section* {$\rm memberOfSeries(Type)$}

$\rm
[memberOfSeries(Type)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}memberOfSeries(Type)
\mbox{''}
]$

$\rm
[memberOfSeries(Type)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}lemma
\linebreak [0]\ \hskip0em plus2.0em{}memberOfSeries(Type)
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:420}{}\section* {$\rm  \ast
 (exp) \ast$}

$\rm
[ 
\mathsf{x}
 (exp) 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}(exp)
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[ 
\ast 
 (exp) 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{\char94}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:421}{}\section* {$\rm R(\ast
)$}

$\rm
[R(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}R(
\#1.
\newline )
\mbox{''}
]$

$\rm
[R(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}R(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:422}{}\section* {$\rm --R(\ast
)$}

$\rm
[--R(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox{-}
\mbox{-}R(
\#1.
\newline )
\mbox{''}
]$

$\rm
[--R(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox{-}
\mbox{-}R(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:423}{}\section* {$\rm rec\ast$}

$\rm
[rec
\mathsf{x}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}rec
\#1.
\mbox{''}
]$

$\rm
[rec
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1/
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:424}{}\section* {$\rm \ast
 / \ast$}

$\rm
[\mathsf {bs}
 / 
\mathsf {r}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[\mathsf {bs}
 / 
\mathsf {r}
\mathrel {\ddot {=}} \{ ph \mathrel{\in} P(\mathsf {bs}
)
\mid Ex_{20}
 \mathrel{\in} \mathsf {bs}
\mathrel{\dot{\wedge}} [Ex_{20}
 \mathrel{\in} \mathsf {bs}
]_{
\mathsf {r}
}
\!\mathrel{==}\! ph_{2}
\}
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 / 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}/
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 / 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}eq
\mbox{-}system
\linebreak [0]\ \hskip0em plus2.0em{}of
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}modulo
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:425}{}\section* {$\rm \ast
 \cap \ast$}

$\rm
[
\mathsf{x}
 \cap 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 \cap 
\mathsf{y}
\mathrel {\ddot {=}} \{ ph \mathrel{\in} 
\mathsf{x}
 \mathrel{\cup} 
\mathsf{y}
\mid ph_{3}
 \mathrel{\in} 
\mathsf{x}
\mathrel{\dot{\wedge}} ph_{3}
 \mathrel{\in} 
\mathsf{y}
\}
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 \cap 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}cap
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \cap 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}intersection
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}comma
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}intersection
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:426}{}\section* {$\rm \ast
[\ast
]$}

$\rm
[
\mathsf{x}
[
\mathsf{y}
]
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline [
\#2.
\newline ]
\mbox{''}
]$

$\rm
[
\ast 
[
\ast 
]
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}[
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{};
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}]
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:427}{}\section* {$\rm \cup \ast$}

$\rm
[\cup 
\mathsf{x}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}cup
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\mbox{''}
]$

$\rm
[\cup 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}union
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}union
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:428}{}\section* {$\rm \ast
 \mathrel{\cup} \ast$}

$\rm
[
\mathsf{x}
 \mathrel{\cup} 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 \mathrel{\cup} 
\mathsf{y}
\mathrel {\ddot {=}}\cup \{\{
\mathsf{x}
\}
,\{
\mathsf{y}
\}
\}
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 \mathrel{\cup} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}cup
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \mathrel{\cup} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}binary
\mbox{-}union
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}comma
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}union
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:429}{}\section* {$\rm P(\ast
)$}

$\rm
[P(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}P(
\#1.
\newline )
\mbox{''}
]$

$\rm
[P(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}power
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}power
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:430}{}\section* {$\rm \{\ast
\}$}

$\rm
[\{
\mathsf{x}
\}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[\{
\mathsf{x}
\}
\mathrel {\ddot {=}}\{
\mathsf{x}
,
\mathsf{x}
\}
]
\rceil 
)
]$

$\rm
[\{
\mathsf{x}
\}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}
\{
\#1.
\newline 
\mbox {$\backslash $}
\}
\mbox{''}
]$

$\rm
[\{
\ast 
\}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}zermelo
\linebreak [0]\ \hskip0em plus2.0em{}singleton
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}singleton
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:431}{}\section* {$\rm StateExpand(\ast
,\ast
,\ast
)$}

$\rm
[StateExpand(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}StateExpand(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[StateExpand(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}stateExpand(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:432}{}\section* {$\rm extractSeries(\ast
)$}

$\rm
[extractSeries(
\mathsf {t}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}extractSeries(
\#1.
\newline )
\mbox{''}
]$

$\rm
[extractSeries(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}extractSeries(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:433}{}\section* {$\rm SetOfSeries(\ast
)$}

$\rm
[SetOfSeries(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SetOfSeries(
\#1.
\newline )
\mbox{''}
]$

$\rm
[SetOfSeries(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}setOfSeries(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:434}{}\section* {$\rm --Macro(\ast
)$}

$\rm
[--Macro(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox{-}
\mbox{-}Macro(
\#1.
\newline )
\mbox{''}
]$

$\rm
[--Macro(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox{-}
\mbox{-}Macro(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:435}{}\section* {$\rm ExpandList(\ast
,\ast
,\ast
)$}

$\rm
[ExpandList(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ExpandList(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[ExpandList(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}expandList(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:436}{}\section* {$\rm **Macro(\ast
)$}

$\rm
[**Macro(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
{*}
{*}Macro(
\#1.
\newline )
\mbox{''}
]$

$\rm
[**Macro(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
{*}
{*}Macro(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:437}{}\section* {$\rm ++Macro(\ast
)$}

$\rm
[++Macro(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
{+}
{+}Macro(
\#1.
\newline )
\mbox{''}
]$

$\rm
[++Macro(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
{+}
{+}Macro(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:438}{}\section* {$\rm <<Macro(\ast
)$}

$\rm
[<<Macro(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
{<}
{<}Macro(
\#1.
\newline )
\mbox{''}
]$

$\rm
[<<Macro(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
{<}
{<}Macro(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:439}{}\section* {$\rm ||Macro(\ast
)$}

$\rm
[||Macro(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}||Macro(
\#1.
\newline )
\mbox{''}
]$

$\rm
[||Macro(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}||Macro(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:440}{}\section* {$\rm 01//Macro(\ast
)$}

$\rm
[01//Macro(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}01//Macro(
\#1.
\newline )
\mbox{''}
]$

$\rm
[01//Macro(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}01//Macro(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:441}{}\section* {$\rm UB(\ast
, \ast
)$}

$\rm
[UB(
\mathsf{x}
, 
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UB(
\#1.
\newline ,
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline )
\mbox{''}
]$

$\rm
[UB(
\ast 
, 
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}upperBound(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:442}{}\section* {$\rm LUB(\ast
, \ast
)$}

$\rm
[LUB(
\mathsf{x}
, 
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}LUB(
\#1.
\newline ,
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline )
\mbox{''}
]$

$\rm
[LUB(
\ast 
, 
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}leastUpperBound(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:443}{}\section* {$\rm BS(\ast
,\ast
)$}

$\rm
[BS(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}BS(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[BS(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}base(1/2)Sum(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:444}{}\section* {$\rm UStelescope(\ast
,\ast
)$}

$\rm
[UStelescope(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}UStelescope(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[UStelescope(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}UStelescope(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:445}{}\section* {$\rm (\ast
)$}

$\rm
[(
\mathsf{x}
)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(
\mathsf{x}
)
\mathrel {\ddot {=}}
(
\mathsf{x}
)
]
\rceil 
)
]$

$\rm
[(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\#1.
\newline )
\mbox{''}
]$

$\rm
[(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:446}{}\section* {$\rm |f\ast
|$}

$\rm
[|f
\mathsf{x}
|
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}|f
\#1.
\newline |
\mbox{''}
]$

$\rm
[|f
\ast 
|
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}|f
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}|
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:447}{}\section* {$\rm |r\ast
|$}

$\rm
[|r
\mathsf{x}
|
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}|r
\#1.
\newline |
\mbox{''}
]$

$\rm
[|r
\ast 
|
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}|r
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}|
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:448}{}\section* {$\rm Limit(\ast
,\ast
)$}

$\rm
[Limit(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Limit(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[Limit(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}limit(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:449}{}\section* {$\rm Union(\ast
)$}

$\rm
[Union(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Union(
\#1.
\newline )
\mbox{''}
]$

$\rm
[Union(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}U(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:450}{}\section* {$\rm IsOrderedPair(\ast
,\ast
,\ast
)$}

$\rm
[IsOrderedPair(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IsOrderedPair(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[IsOrderedPair(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}isOrderedPair(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:451}{}\section* {$\rm IsRelation(\ast
,\ast
,\ast
)$}

$\rm
[IsRelation(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IsRelation(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[IsRelation(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}isRelation(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:452}{}\section* {$\rm isFunction(\ast
,\ast
,\ast
)$}

$\rm
[isFunction(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}isFunction(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[isFunction(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}isFunction(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:453}{}\section* {$\rm IsSeries(\ast
,\ast
)$}

$\rm
[IsSeries(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IsSeries(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[IsSeries(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}isSeries(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:454}{}\section* {$\rm IsNatural(\ast
,\ast
)$}

$\rm
[IsNatural(
\mathsf{x}
\mathsf{y}
,\ast
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}IsNatural(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[IsNatural(
\ast 
,\ast
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}isNatural(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:455}{}\section* {$\rm OrderedPair(\ast
,\ast
)$}

$\rm
[OrderedPair(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}OrderedPair(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[OrderedPair(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}(o
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:456}{}\section* {$\rm TypeNat(\ast
)$}

$\rm
[TypeNat(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TypeNat(
\#1.
\newline )
\mbox{''}
]$

$\rm
[TypeNat(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}typeNat(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:457}{}\section* {$\rm TypeNat0(\ast
)$}

$\rm
[TypeNat0(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TypeNat0(
\#1.
\newline )
\mbox{''}
]$

$\rm
[TypeNat0(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}typeNat0(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:458}{}\section* {$\rm TypeRational(\ast
)$}

$\rm
[TypeRational(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TypeRational(
\#1.
\newline )
\mbox{''}
]$

$\rm
[TypeRational(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}typeRational(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:459}{}\section* {$\rm TypeRational0(\ast
)$}

$\rm
[TypeRational0(
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TypeRational0(
\#1.
\newline )
\mbox{''}
]$

$\rm
[TypeRational0(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}typeRational0(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:460}{}\section* {$\rm TypeSeries(\ast
,\ast
)$}

$\rm
[TypeSeries(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TypeSeries(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[TypeSeries(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}typeSeries(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:461}{}\section* {$\rm Typeseries0(\ast
,\ast
)$}

$\rm
[Typeseries0(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Typeseries0(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[Typeseries0(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}typeSeries0(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:462}{}\section* {$\rm \{\ast
,\ast
\}$}

$\rm
[\{
\mathsf{x}
,
\mathsf{y}
\}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}
\{
\#1.
\newline ,
\#2.
\newline 
\mbox {$\backslash $}
\}
\mbox{''}
]$

$\rm
[\{
\ast 
,
\ast 
\}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}zermelo
\linebreak [0]\ \hskip0em plus2.0em{}pair
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}comma
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}pair
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:463}{}\section* {$\rm \langle \ast
,\ast
\rangle$}

$\rm
[\langle 
\mathsf{x}
,
\mathsf{y}
\rangle
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[\langle 
\mathsf{x}
,
\mathsf{y}
\rangle
\mathrel {\ddot {=}}\{\{
\mathsf{x}
\}
,\{
\mathsf{x}
,
\mathsf{y}
\}
\}
]
\rceil 
)
]$

$\rm
[\langle 
\mathsf{x}
,
\mathsf{y}
\rangle
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}langle
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline ,
\#2.
\newline 
\mbox {$\backslash $}rangle
\mbox{''}
]$

$\rm
[\langle 
\ast 
,
\ast 
\rangle
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}zermelo
\linebreak [0]\ \hskip0em plus2.0em{}ordered
\linebreak [0]\ \hskip0em plus2.0em{}pair
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}comma
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}pair
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:464}{}\section* {$\rm (-u\ast
)$}

$\rm
[(-u
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\mbox{-}u
\#1.
\newline )
\mbox{''}
]$

$\rm
[(-u
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox{-}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:465}{}\section* {$\rm -_{f}\ast$}

$\rm
[-_{f}
\mathsf{x}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox{-}
\_
\{f
\}
\#1.
\mbox{''}
]$

$\rm
[-_{f}
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox{-}f
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:466}{}\section* {$\rm (--\ast
)$}

$\rm
[(--
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\mbox{-}
\mbox{-}
\#1.
\newline )
\mbox{''}
]$

$\rm
[(--
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox{-}
\mbox{-}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:467}{}\section* {$\rm 1f/\ast$}

$\rm
[1f/
\mathsf{x}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}1f/
\#1.
\mbox{''}
]$

$\rm
[1f/
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}1f/
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:468}{}\section* {$\rm 01//temp\ast$}

$\rm
[01//temp
\mathsf{x}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}01//temp
\#1.
\mbox{''}
]$

$\rm
[01//temp
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}01//
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:469}{}\section* {$\rm \ast
(\ast
,\ast
)$}

$\rm
[
\mathsf {r}
(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf {r}
(
\mathsf{x}
,
\mathsf{y}
)
\mathrel {\ddot {=}}\langle 
\mathsf{x}
,
\mathsf{y}
\rangle
 \mathrel{\in} 
\mathsf {r}
]
\rceil 
)
]$

$\rm
[
\mathsf{z}
(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#3.
\newline (
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[
\ast 
(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}related
\linebreak [0]\ \hskip0em plus2.0em{}to
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}under
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:470}{}\section* {$\rm ReflRel(\ast
,\ast
)$}

$\rm
[ReflRel(
\mathsf {r}
,
\mathsf{x}
)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[ReflRel(
\mathsf {r}
,
\mathsf{x}
)
\mathrel {\ddot {=}}
\forall 
\mathit{s}
\colon 
(
\mathit{s}
 \mathrel{\in} 
\mathsf{x}
\Rightarrow 
\mathsf {r}
(
\mathit{s}
,
\mathit{s}
)
)
]
\rceil 
)
]$

$\rm
[ReflRel(
\mathsf {r}
,
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}ReflRel(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[ReflRel(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}reflexive
\linebreak [0]\ \hskip0em plus2.0em{}relation
\linebreak [0]\ \hskip0em plus2.0em{}in
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:471}{}\section* {$\rm SymRel(\ast
,\ast
)$}

$\rm
[SymRel(
\mathsf {r}
,
\mathsf{x}
)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[SymRel(
\mathsf {r}
,
\mathsf{x}
)
\mathrel {\ddot {=}}
\forall 
\mathit{s}
,\linebreak [0] 
\mathit{t}
\colon 
(
\mathit{s}
 \mathrel{\in} 
\mathsf{x}
\Rightarrow 
\mathit{t}
 \mathrel{\in} 
\mathsf{x}
\Rightarrow 
\mathsf {r}
(
\mathit{s}
,
\mathit{t}
)
\Rightarrow 
\mathsf {r}
(
\mathit{t}
,
\mathit{s}
)
)
]
\rceil 
)
]$

$\rm
[SymRel(
\mathsf {r}
,
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SymRel(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[SymRel(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}symmetric
\linebreak [0]\ \hskip0em plus2.0em{}relation
\linebreak [0]\ \hskip0em plus2.0em{}in
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:472}{}\section* {$\rm TransRel(\ast
,\ast
)$}

$\rm
[TransRel(
\mathsf {r}
,
\mathsf{x}
)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[TransRel(
\mathsf {r}
,
\mathsf{x}
)
\mathrel {\ddot {=}}
\newline 
\forall 
\mathit{s}
,\linebreak [0] 
\mathit{t}
,\linebreak [0] 
\mathit{u}
\colon 
(
\mathit{s}
 \mathrel{\in} 
\mathsf{x}
\Rightarrow 
\mathit{t}
 \mathrel{\in} 
\mathsf{x}
\Rightarrow 
\mathit{u}
 \mathrel{\in} 
\mathsf{x}
\Rightarrow 
\mathsf {r}
(
\mathit{s}
,
\mathit{t}
)
\Rightarrow 
\mathsf {r}
(
\mathit{t}
,
\mathit{u}
)
\Rightarrow 
\mathsf {r}
(
\mathit{s}
,
\mathit{u}
)
)
]
\rceil 
)
]$

$\rm
[TransRel(
\mathsf {r}
,
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}TransRel(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[TransRel(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}transitive
\linebreak [0]\ \hskip0em plus2.0em{}relation
\linebreak [0]\ \hskip0em plus2.0em{}in
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:473}{}\section* {$\rm EqRel(\ast
,\ast
)$}

$\rm
[EqRel(
\mathsf {r}
,
\mathsf{x}
)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[EqRel(
\mathsf {r}
,
\mathsf{x}
)
\mathrel {\ddot {=}}ReflRel(
\mathsf {r}
,
\mathsf{x}
)
\mathrel{\dot{\wedge}} SymRel(
\mathsf {r}
,
\mathsf{x}
)
\mathrel{\dot{\wedge}} TransRel(
\mathsf {r}
,
\mathsf{x}
)
]
\rceil 
)
]$

$\rm
[EqRel(
\mathsf {r}
,
\mathsf{x}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}EqRel(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[EqRel(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}relation
\linebreak [0]\ \hskip0em plus2.0em{}in
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:474}{}\section* {$\rm [\ast
 \mathrel{\in} \ast
]_{\ast
}$}

$\rm
[[
\mathsf{x}
 \mathrel{\in} \mathsf {bs}
]_{
\mathsf {r}
}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[[
\mathsf{x}
 \mathrel{\in} \mathsf {bs}
]_{
\mathsf {r}
}
\mathrel {\ddot {=}} \{ ph \mathrel{\in} \mathsf {bs}
\mid 
\mathsf {r}
(ph_{1}
,
\mathsf{x}
)
\}
]
\rceil 
)
]$

$\rm
[[
\mathsf{x}
 \mathrel{\in} \mathsf {bs}
]_{
\mathsf {r}
}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}[
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}in
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline ]
\_
\{
\#3.
\newline 
\}
\mbox{''}
]$

$\rm
[[
\ast 
 \mathrel{\in} 
\ast 
]_{
\ast 
}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}equivalence
\linebreak [0]\ \hskip0em plus2.0em{}class
\linebreak [0]\ \hskip0em plus2.0em{}of
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}in
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}modulo
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:475}{}\section* {$\rm Partition(\ast
,\ast
)$}

$\rm
[Partition(
\mathsf {p}
,\mathsf {bs}
)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[Partition(
\mathsf {p}
,\mathsf {bs}
)
\mathrel {\ddot {=}}
(
\forall 
\mathit{s}
\colon 
(
\mathit{s}
 \mathrel{\in} 
\mathsf {p}
\Rightarrow 
\mathit{s}
 \mathrel{\neq} \mathrm{\O}
)
)
\mathrel{\dot{\wedge}} 
\newline 
(
\forall 
\mathit{s}
,\linebreak [0] 
\mathit{t}
\colon 
(
\mathit{s}
 \mathrel{\in} 
\mathsf {p}
\Rightarrow 
\mathit{t}
 \mathrel{\in} 
\mathsf {p}
\Rightarrow 
\mathit{s}
 \mathrel{\neq} 
\mathit{t}
\Rightarrow 
\mathit{s}
 \cap 
\mathit{t}
\!\mathrel{==}\! \mathrm{\O}
)
)
\mathrel{\dot{\wedge}} 
\newline \cup 
\mathsf {p}
\!\mathrel{==}\! \mathsf {bs}
]
\rceil 
)
]$

$\rm
[Partition(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Partition(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[Partition(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}partition
\linebreak [0]\ \hskip0em plus2.0em{}of
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:476}{}\section* {$\rm (\ast
*\ast
)$}

$\rm
[(
\mathsf{x}
*
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\#1.
\newline 
{*}
\#2.
\newline )
\mbox{''}
]$

$\rm
[(
\ast 
*
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:477}{}\section* {$\rm \ast
*_{f}\ast$}

$\rm
[(fx)
*_{f}(fy)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
{*}
\_
\{f
\}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
*_{f}
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{*}f
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:478}{}\section* {$\rm \ast
**\ast$}

$\rm
[
\mathsf{x}
**
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
{*}
{*}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
**
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{*}
{*}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:479}{}\section* {$\rm (\ast
+\ast
)$}

$\rm
[(
\mathsf{x}
+
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\#1.
\newline 
{+}
\#2.
\newline )
\mbox{''}
]$

$\rm
[(
\ast 
+
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{+}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:480}{}\section* {$\rm (\ast
-\ast
)$}

$\rm
[(
\mathsf{x}
-
\mathsf{y}
)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(
\mathsf{x}
-
\mathsf{y}
)
\mathrel {\ddot {=}}(
\mathsf{x}
+(-u
\mathsf{y}
)
)
]
\rceil 
)
]$

$\rm
[(
\mathsf{x}
-
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}(
\#1.
\newline 
\mbox{-}
\#2.
\newline )
\mbox{''}
]$

$\rm
[(
\ast 
-
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{-}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:481}{}\section* {$\rm \ast
+_{f}\ast$}

$\rm
[(fx)
+_{f}(fy)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
{+}
\_
\{f
\}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
+_{f}
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{+}f
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:482}{}\section* {$\rm \ast
-_{f}\ast$}

$\rm
[(fx)
-_{f}(fy)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\mbox{-}
\_
\{f
\}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
-_{f}
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{-}f
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:483}{}\section* {$\rm \ast
++\ast$}

$\rm
[
\mathsf{x}
++
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
{+}
{+}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
++
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{+}
{+}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:484}{}\section* {$\rm R(\ast
) -- R(\ast
)$}

$\rm
[R((fx)
) -- R((fy)
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}R(
\#1.
\newline )
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{-}
\mbox{-}
\linebreak [0]\ \hskip0em plus2.0em{}R(
\#2.
\newline )
\mbox{''}
]$

$\rm
[R(
\ast 
) -- R(
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}R(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox{-}
\mbox{-}
\linebreak [0]\ \hskip0em plus2.0em{}R(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:485}{}\section* {$\rm \ast
 \mathrel{\in} \ast$}

$\rm
[
\mathsf{x}
 \mathrel{\in} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}in
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \mathrel{\in} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}in0
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:486}{}\section* {$\rm |\ast
|$}

$\rm
[|
\mathsf{x}
|
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}|
\#1.
\newline |
\mbox{''}
]$

$\rm
[|
\ast 
|
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}|
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}|
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:487}{}\section* {$\rm if(\ast
,\ast
,\ast
)$}

$\rm
[if(
\mathsf{x}
,
\mathsf{y}
,
\mathsf{z}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}if(
\#1.
\newline ,
\#2.
\newline ,
\#3.
\newline )
\mbox{''}
]$

$\rm
[if(
\ast 
,
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}if(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:488}{}\section* {$\rm Max(\ast
,\ast
)$}

$\rm
[Max(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Max(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[Max(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}max(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:489}{}\section* {$\rm Max(\ast
,\ast
)$}

$\rm
[Max(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}Max(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[Max(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}maxR(
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{},
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{})
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:490}{}\section* {$\rm \ast
 = \ast$}

$\rm
[
\mathsf{x}
 = 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 = 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:491}{}\section* {$\rm \ast
 \neq \ast$}

$\rm
[
\mathsf{x}
 \neq 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 \neq 
\mathsf{y}
\mathrel {\ddot {=}}\dot{\neg}\,(
\mathsf{x}
 = 
\mathsf{y}
)n
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 \neq 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}neq
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \neq 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}!
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:492}{}\section* {$\rm \ast
 <= \ast$}

$\rm
[
\mathsf{x}
 <= 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 <= 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:493}{}\section* {$\rm \ast
 < \ast$}

$\rm
[
\mathsf{x}
 < 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 < 
\mathsf{y}
\mathrel {\ddot {=}}
\mathsf{x}
 <= 
\mathsf{y}
\mathrel{\dot{\wedge}} 
\mathsf{x}
 \neq 
\mathsf{y}
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 < 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 < 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:494}{}\section* {$\rm \ast
<_{f}\ast$}

$\rm
[
\mathsf{x}
<_{f}
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
{<}
\_
\{f
\}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
<_{f}
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{<}f
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:495}{}\section* {$\rm \ast
\leq_{f}\ast$}

$\rm
[(fx)
\leq_{f}(fy)
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[(fx)
\leq_{f}(fy)
\mathrel {\ddot {=}}(fx)
<_{f}(fy)
 \mathrel{\dot{\vee}} SF((fx)
,(fy)
)
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
\leq_{f}
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}leq
\_
\{f
\}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
\leq_{f}
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
{=}f
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:496}{}\section* {$\rm SF(\ast
,\ast
)$}

$\rm
[SF(
\mathsf{x}
,
\mathsf{y}
)
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}SF(
\#1.
\newline ,
\#2.
\newline )
\mbox{''}
]$

$\rm
[SF(
\ast 
,
\ast 
)
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}sameF
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:497}{}\section* {$\rm \ast
 == \ast$}

$\rm
[
\mathsf{x}
 == 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{=}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 == 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{=}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:498}{}\section* {$\rm \ast
 !!== \ast$}

$\rm
[
\mathsf{x}
 !!== 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 !!== 
\mathsf{y}
\mathrel {\ddot {=}}\dot{\neg}\,(
\mathsf{x}
 == 
\mathsf{y}
)n
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 !!== 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}!!
{=}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 !!== 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}!!
{=}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:499}{}\section* {$\rm \ast
 << \ast$}

$\rm
[
\mathsf{x}
 << 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
{<}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 << 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
{<}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:500}{}\section* {$\rm \ast
 <<== \ast$}

$\rm
[
\mathsf{x}
 <<== 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 <<== 
\mathsf{y}
\mathrel {\ddot {=}}
\mathsf{x}
 << 
\mathsf{y}
 \mathrel{\dot{\vee}} 
\mathsf{x}
 == 
\mathsf{y}
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 <<== 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
{<}
{=}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 <<== 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}
{<}
{<}
{=}
{=}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:501}{}\section* {$\rm \ast
\!\mathrel{==}\! \ast$}

$\rm
[
\mathsf{x}
\!\mathrel{==}\! 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}!
\mbox {$\backslash $}mathrel
\{
{=}
{=}
\}
\mbox {$\backslash $}!
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
\!\mathrel{==}\! 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}zermelo
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:502}{}\section* {$\rm \ast
 \mathrel{\subseteq} \ast$}

$\rm
[
\mathsf{x}
 \mathrel{\subseteq} 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 \mathrel{\subseteq} 
\mathsf{y}
\mathrel {\ddot {=}}
\forall (S1ob)
\colon ((S1ob)
 \mathrel{\in} 
\mathsf{x}
\Rightarrow (S1ob)
 \mathrel{\in} 
\mathsf{y}
)
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 \mathrel{\subseteq} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}subseteq
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \mathrel{\subseteq} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}is
\linebreak [0]\ \hskip0em plus2.0em{}subset
\linebreak [0]\ \hskip0em plus2.0em{}of
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:503}{}\section* {$\rm \dot{\neg}\,(\ast
)n$}

$\rm
[\dot{\neg}\,(
\mathsf{x}
)n
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\mbox {$\backslash $}dot
\{
\mbox {$\backslash $}neg
\}
\mbox {$\backslash $},(
\#1.
\newline )n
\mbox{''}
]$

$\rm
[\dot{\neg}\,(
\ast 
)n
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}not0
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:504}{}\section* {$\rm \ast
 \mathrel{\notin} \ast$}

$\rm
[
\mathsf{x}
 \mathrel{\notin} 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 \mathrel{\notin} 
\mathsf{y}
\mathrel {\ddot {=}}\dot{\neg}\,(
\mathsf{x}
 \mathrel{\in} 
\mathsf{y}
)n
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 \mathrel{\notin} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}notin
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \mathrel{\notin} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}zermelo
\linebreak [0]\ \hskip0em plus2.0em{}
\char126 in
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:505}{}\section* {$\rm \ast
 \mathrel{\neq} \ast$}

$\rm
[
\mathsf{x}
 \mathrel{\neq} 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 \mathrel{\neq} 
\mathsf{y}
\mathrel {\ddot {=}}\dot{\neg}\,(
\mathsf{x}
\!\mathrel{==}\! 
\mathsf{y}
)n
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 \mathrel{\neq} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}neq
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \mathrel{\neq} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}zermelo
\linebreak [0]\ \hskip0em plus2.0em{}
\char126 is
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:506}{}\section* {$\rm \ast
\mathrel{\dot{\wedge}} \ast$}

$\rm
[
\mathsf{x}
\mathrel{\dot{\wedge}} 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
\mathrel{\dot{\wedge}} 
\mathsf{y}
\mathrel {\ddot {=}}\dot{\neg}\,(
(
\mathsf{x}
\Rightarrow \dot{\neg}\,(
\mathsf{y}
)n
)
)n
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
\mathrel{\dot{\wedge}} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}dot
\{
\mbox {$\backslash $}wedge
\}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
\mathrel{\dot{\wedge}} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}and0
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:507}{}\section* {$\rm \ast
 \mathrel{\dot{\vee}} \ast$}

$\rm
[
\mathsf{x}
 \mathrel{\dot{\vee}} 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
 \mathrel{\dot{\vee}} 
\mathsf{y}
\mathrel {\ddot {=}}\dot{\neg}\,(
\mathsf{x}
)n
\Rightarrow 
\mathsf{y}
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
 \mathrel{\dot{\vee}} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}dot
\{
\mbox {$\backslash $}vee
\}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
 \mathrel{\dot{\vee}} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}or0
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:508}{}\section* {$\rm 
\exists \ast
\colon \ast$}

$\rm
[
\exists (v1)
\colon 
\mathsf {a}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\exists (v1)
\colon 
\mathsf {a}
\mathrel {\ddot {=}}\dot{\neg}\,(
\forall (v1)
\colon \dot{\neg}\,(
\mathsf {a}
)n
)n
]
\rceil 
)
]$

$\rm
[
\exists 
\mathsf{x}
\colon 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\newline 
\mbox {$\backslash $}exists
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\mbox {$\backslash $}colon
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\exists 
\ast 
\colon 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}exist0
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}indeed
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:509}{}\section* {$\rm \ast
\mathrel{\dot{\Leftrightarrow}} \ast$}

$\rm
[
\mathsf{x}
\mathrel{\dot{\Leftrightarrow}} 
\mathsf{y}
\stackrel{
\mathrm {macro}
}{\rightarrow}
\lambda 
\mathsf {t}
.
\lambda 
\mathsf {s}
.
\lambda 
\mathsf {c}
.
\tilde {{\cal M}}_4(
\mathsf {t}
,
\mathsf {s}
,
\mathsf {c}
,
\lceil 
[
\mathsf{x}
\mathrel{\dot{\Leftrightarrow}} 
\mathsf{y}
\mathrel {\ddot {=}}
(
\mathsf{x}
\Rightarrow 
\mathsf{y}
)
\mathrel{\dot{\wedge}} 
(
\mathsf{y}
\Rightarrow 
\mathsf{x}
)
]
\rceil 
)
]$

$\rm
[
\mathsf{x}
\mathrel{\dot{\Leftrightarrow}} 
\mathsf{y}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\#1.
\newline 
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}dot
\{
\mbox {$\backslash $}Leftrightarrow
\}
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\mbox{''}
]$

$\rm
[
\ast 
\mathrel{\dot{\Leftrightarrow}} 
\ast 
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}iff
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\mbox{''}
]$

\hypertarget {url:1808490782658911215215844543754112306433607076424339373311695870409267457:510}{}\section* {$\rm  \{ ph \mathrel{\in} \ast
\mid \ast
\}$}

$\rm
[ \{ ph \mathrel{\in} 
\mathsf{x}
\mid 
\mathsf {a}
\}
\stackrel{
\mathrm{tex}
}{\rightarrow}
\mbox{``}
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}
\{
\linebreak [0]\ \hskip0em plus2.0em{}ph
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {$\backslash $}mathrel
\{
\mbox {$\backslash $}in
\}
\linebreak [0]\ \hskip0em plus2.0em{}
\#1.
\newline 
\mbox {$\backslash $}mid
\linebreak [0]\ \hskip0em plus2.0em{}
\#2.
\newline 
\mbox {$\backslash $}
\}
\mbox{''}
]$

$\rm
[ \{ ph \mathrel{\in} 
\ast 
\mid 
\ast 
\}
\stackrel{
\mathrm{pyk}
}{\rightarrow}
\mbox{``}the
\linebreak [0]\ \hskip0em plus2.0em{}set
\linebreak [0]\ \hskip0em plus2.0em{}of
\linebreak [0]\ \hskip0em plus2.0em{}ph
\linebreak [0]\ \hskip0em plus2.0em{}in
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}such
\linebreak [0]\ \hskip0em plus2.0em{}that
\linebreak [0]\ \hskip0em plus2.0em{}
\mbox {\tt \char34}
\linebreak [0]\ \hskip0em plus2.0em{}end
\linebreak [0]\ \hskip0em plus2.0em{}set
\mbox{''}
]$

\vspace{2ex}

{\em \href {http://www.diku.dk/~grue/logiweb/20060417/logiweb/doc/compiler/index.html}{The pyk compiler},
version 0.grue.20060417+
by
\href {http://www.diku.dk/~grue/index.html}{Klaus Grue}\\
\href {http://www.diku.dk/~grue/logiweb/20060417/logiweb/doc/misc/time.html}{GRD-2006-12-15.UTC:00:19:10.164930} = 
\href {http://www.diku.dk/~grue/logiweb/20060417/logiweb/doc/misc/time.html}{MJD-54084.TAI:00:19:43.164930} = 
\href {http://www.diku.dk/~grue/logiweb/20060417/logiweb/doc/misc/time.html}{LGT-4672858783164930e-6}
}

\end{document}

