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File page.tex
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\begin{document}
\title{Propositional Calculus}
\author {Allan Hvam Petersen}
\maketitle
"
begin math define pyk of propositional calculus as text "propositional calculus" end text end define end math
end "
\tex{"
begin math define tex of propositional theory as text "
T_{Prop}" end text end define end math
end "}
Define theory:
"
begin math define statement of propositional theory as all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar infer metavar var a end metavar imply metavar var b end metavar infer metavar var b end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply metavar var b end metavar imply metavar var a end metavar imply metavar var c end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed metavar var c end metavar free for metavar var b end metavar in metavar var a end metavar endorse all metavar var b end metavar indeed metavar var a end metavar imply sub metavar var a end metavar set metavar var b end metavar to metavar var c end metavar end sub rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed not metavar var c end metavar free in metavar var a end metavar endorse all metavar var c end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var a end metavar imply all metavar var c end metavar indeed metavar var b end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var a end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed not metavar var a end metavar imply not metavar var b end metavar imply not metavar var a end metavar imply metavar var b end metavar imply metavar var a end metavar rule plus all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar infer all metavar var b end metavar indeed metavar var a end metavar end define end math
end "\footnote{"
begin math define pyk of propositional theory as text "propositional theory" end text end define end math
end "}
\subsection*{Implication}
\tex{"
begin math define tex of var x imply var y as text "#1.
\Rightarrow{}#2." end text end define end math
end "}
"
begin math define value of var x imply var y as not var x or var y end define end math
end "
\footnote{"
begin math define pyk of var x imply var y as text "* imply *" end text end define end math
end "}
\test{"
begin math test true imply true end test end math
end "}
\test{"
begin math false test true imply false end test end math
end "}
\test{"
begin math test false imply true end test end math
end "}
\test{"
begin math test false imply false end test end math
end "}
\subsection*{Axioms}
\tex{"
begin math define tex of axiom one as text "A1" end text end define end math
end "}
"
begin math define statement of axiom one as propositional theory infer all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var a end metavar end define
then define proof of axiom one as rule tactic end define end math
end "
\footnote{"
begin math define pyk of axiom one as text "axiom one" end text end define end math
end "}
\tex{"
begin math define tex of axiom two as text "A2" end text end define end math
end "}
"
begin math define statement of axiom two as propositional theory infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply metavar var b end metavar imply metavar var a end metavar imply metavar var c end metavar end define
then define proof of axiom two as rule tactic end define end math
end "
\footnote{"
begin math define pyk of axiom two as text "axiom two" end text end define end math
end "}
\tex{"
begin math define tex of axiom three as text "A3" end text end define end math
end "}
"
begin math define statement of axiom three as propositional theory infer all metavar var a end metavar indeed all metavar var b end metavar indeed not metavar var a end metavar imply not metavar var b end metavar imply not metavar var a end metavar imply metavar var b end metavar imply metavar var a end metavar end define
then define proof of axiom three as rule tactic end define end math
end "
\footnote{"
begin math define pyk of axiom three as text "axiom three" end text end define end math
end "}
\tex{"
begin math define tex of axiom four as text "A4" end text end define end math
end "}
"
begin math define statement of axiom four as propositional theory infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed metavar var c end metavar free for metavar var b end metavar in metavar var a end metavar endorse all metavar var b end metavar indeed metavar var a end metavar imply sub metavar var a end metavar set metavar var b end metavar to metavar var c end metavar end sub end define
then define proof of axiom four as rule tactic end define end math
end "
\footnote{"
begin math define pyk of axiom four as text "axiom four" end text end define end math
end "}
\tex{"
begin math define tex of axiom five as text "A5" end text end define end math
end "}
"
begin math define statement of axiom five as propositional theory infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed not metavar var c end metavar free in metavar var a end metavar endorse all metavar var c end metavar indeed metavar var a end metavar imply metavar var b end metavar imply metavar var a end metavar imply all metavar var c end metavar indeed metavar var b end metavar end define
then define proof of axiom five as rule tactic end define end math
end "
\footnote{"
begin math define pyk of axiom five as text "axiom five" end text end define end math
end "}
\tex{"
begin math define tex of axiom mp as text "MP" end text end define end math
end "}
"
begin math define statement of axiom mp as propositional theory infer all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar infer metavar var a end metavar imply metavar var b end metavar infer metavar var b end metavar end define
then define proof of axiom mp as rule tactic end define end math
end "
\footnote{"
begin math define pyk of axiom mp as text "axiom mp" end text end define end math
end "}
\tex{"
begin math define tex of axiom gen as text "Gen" end text end define end math
end "}
"
begin math define statement of axiom gen as propositional theory infer all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar infer all metavar var b end metavar indeed metavar var a end metavar end define
then define proof of axiom gen as rule tactic end define end math
end "
\footnote{"
begin math define pyk of axiom gen as text "axiom gen" end text end define end math
end "}
\subsection*{Proof}
\tex{"
begin math define tex of mendelson lemma one eight as text "Mendelson\ \textbf{1.8}" end text end define end math
end "}
"
begin math define statement of mendelson lemma one eight as propositional theory infer all metavar var a end metavar indeed metavar var a end metavar imply metavar var a end metavar end define end math
end "
\footnote{"
begin math define pyk of mendelson lemma one eight as text "mendelson lemma one eight" end text end define end math
end "}
"
begin math define proof of mendelson lemma one eight as lambda var c dot lambda var x dot proof expand quote propositional theory infer all metavar var a end metavar indeed axiom two conclude metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar cut axiom one conclude metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar cut axiom mp modus ponens metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar modus ponens metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar conclude metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar cut axiom one conclude metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar cut axiom mp modus ponens metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar modus ponens metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar imply metavar var a end metavar conclude metavar var a end metavar imply metavar var a end metavar end quote state proof state cache var c end expand end define end math
end "
\subsection*{Experimental}
\tex{"
begin math define tex of mendelson corollary one ten a as text "Mendelson\ \textbf{1.10} a" end text end define end math
end "}
"
begin math define statement of mendelson corollary one ten a as propositional theory infer all metavar var e end metavar indeed all metavar var d end metavar indeed all metavar var f end metavar indeed metavar var d end metavar imply metavar var e end metavar infer metavar var e end metavar imply metavar var f end metavar infer metavar var d end metavar imply metavar var f end metavar end define end math
end "
\footnote{"
begin math define pyk of mendelson corollary one ten a as text "mendelson corollary one ten a" end text end define end math
end "}
"
begin math define proof of mendelson corollary one ten a as lambda var c dot lambda var x dot proof expand quote propositional theory infer all metavar var e end metavar indeed all metavar var d end metavar indeed all metavar var f end metavar indeed metavar var d end metavar imply metavar var e end metavar infer metavar var e end metavar imply metavar var f end metavar infer axiom two conclude metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar imply metavar var d end metavar imply metavar var e end metavar imply metavar var d end metavar imply metavar var f end metavar cut axiom one conclude metavar var e end metavar imply metavar var f end metavar imply metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar cut axiom mp modus ponens metavar var e end metavar imply metavar var f end metavar modus ponens metavar var e end metavar imply metavar var f end metavar imply metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar conclude metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar cut axiom mp modus ponens metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar modus ponens metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar imply metavar var d end metavar imply metavar var e end metavar imply metavar var d end metavar imply metavar var f end metavar conclude metavar var d end metavar imply metavar var e end metavar imply metavar var d end metavar imply metavar var f end metavar cut axiom mp modus ponens metavar var d end metavar imply metavar var e end metavar modus ponens metavar var d end metavar imply metavar var e end metavar imply metavar var d end metavar imply metavar var f end metavar conclude metavar var d end metavar imply metavar var f end metavar end quote state proof state cache var c end expand end define end math
end "
\tex{"
begin math define tex of mendelson corollary one ten b as text "Mendelson\ \textbf{1.10} b" end text end define end math
end "}
"
begin math define statement of mendelson corollary one ten b as propositional theory infer all metavar var d end metavar indeed all metavar var e end metavar indeed all metavar var f end metavar indeed metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar infer metavar var e end metavar infer metavar var d end metavar imply metavar var f end metavar end define end math
end "
\footnote{"
begin math define pyk of mendelson corollary one ten b as text "mendelson corollary one ten b" end text end define end math
end "}
"
begin math define proof of mendelson corollary one ten b as lambda var c dot lambda var x dot proof expand quote propositional theory infer all metavar var d end metavar indeed all metavar var e end metavar indeed all metavar var f end metavar indeed metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar infer metavar var e end metavar infer axiom two conclude metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar imply metavar var d end metavar imply metavar var e end metavar imply metavar var d end metavar imply metavar var f end metavar cut axiom one conclude metavar var e end metavar imply metavar var d end metavar imply metavar var e end metavar cut axiom mp modus ponens metavar var e end metavar modus ponens metavar var e end metavar imply metavar var d end metavar imply metavar var e end metavar conclude metavar var d end metavar imply metavar var e end metavar cut axiom mp modus ponens metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar modus ponens metavar var d end metavar imply metavar var e end metavar imply metavar var f end metavar imply metavar var d end metavar imply metavar var e end metavar imply metavar var d end metavar imply metavar var f end metavar conclude metavar var d end metavar imply metavar var e end metavar imply metavar var d end metavar imply metavar var f end metavar cut axiom mp modus ponens metavar var d end metavar imply metavar var e end metavar modus ponens metavar var d end metavar imply metavar var e end metavar imply metavar var d end metavar imply metavar var f end metavar conclude metavar var d end metavar imply metavar var f end metavar end quote state proof state cache var c end expand end define end math
end "
\tex{"
begin math define tex of mendelson lemma one eleven a as text "Mendelson\ \textbf{1.11} a" end text end define end math
end "}
"
begin math define statement of mendelson lemma one eleven a as propositional theory infer all metavar var g end metavar indeed not not metavar var g end metavar imply metavar var g end metavar end define end math
end "
\footnote{"
begin math define pyk of mendelson lemma one eleven a as text "mendelson lemma one eleven a" end text end define end math
end "}
"
begin math define proof of mendelson lemma one eleven a as lambda var c dot lambda var x dot proof expand quote propositional theory infer all metavar var g end metavar indeed axiom three conclude not metavar var g end metavar imply not not metavar var g end metavar imply not metavar var g end metavar imply not metavar var g end metavar imply metavar var g end metavar cut mendelson lemma one eight conclude not metavar var g end metavar imply not metavar var g end metavar cut axiom one conclude not not metavar var g end metavar imply not metavar var g end metavar imply not not metavar var g end metavar cut mendelson corollary one ten b modus ponens not metavar var g end metavar imply not not metavar var g end metavar imply not metavar var g end metavar imply not metavar var g end metavar imply metavar var g end metavar modus ponens not metavar var g end metavar imply not metavar var g end metavar conclude not metavar var g end metavar imply not not metavar var g end metavar imply metavar var g end metavar cut mendelson corollary one ten a modus ponens not not metavar var g end metavar imply not metavar var g end metavar imply not not metavar var g end metavar modus ponens not metavar var g end metavar imply not not metavar var g end metavar imply metavar var g end metavar conclude not not metavar var g end metavar imply metavar var g end metavar end quote state proof state cache var c end expand end define end math
end "
\appendix
\section{\TeX\ definitions}
\begin{list}{}{
\setlength{\leftmargin}{5em}
\setlength{\itemindent}{-5em}}
\immediate\closeout\outex
\input{./page.otx}
\end{list}
\section{Test}
\begin{list}{}{
\setlength{\leftmargin}{5em}
\setlength{\itemindent}{-5em}}
\immediate\closeout\outest
\input{./page.tst}
\end{list}
\section{Priority table}
"
begin flush left math define priority of propositional calculus as preassociative priority propositional calculus equal priority base equal priority bracket x end bracket equal priority big bracket x end bracket equal priority math x end math equal priority flush left x end left equal priority var x equal priority var y equal priority var z equal priority proclaim x as x end proclaim equal priority define x of x as x end define equal priority pyk equal priority tex equal priority tex name equal priority priority equal priority x equal priority true equal priority if x then x else x end if equal priority introduce x of x as x end introduce equal priority value equal priority claim equal priority bottom equal priority function f of x end function equal priority identity x end identity equal priority false equal priority untagged zero equal priority untagged one equal priority untagged two equal priority untagged three equal priority untagged four equal priority untagged five equal priority untagged six equal priority untagged seven equal priority untagged eight equal priority untagged nine equal priority zero equal priority one equal priority two equal priority three equal priority four equal priority five equal priority six equal priority seven equal priority eight equal priority nine equal priority var a equal priority var b equal priority var c equal priority var d equal priority var e equal priority var f equal priority var g equal priority var h equal priority var i equal priority var j equal priority var k equal priority var l equal priority var m equal priority var n equal priority var o equal priority var p equal priority var q equal priority var r equal priority var s equal priority var t equal priority var u equal priority var v equal priority var w equal priority tagged parenthesis x end tagged equal priority tagged if x then x else x end if equal priority array x is x end array equal priority left equal priority center equal priority right equal priority empty equal priority substitute x set x to x end substitute equal priority map tag x end tag equal priority raw map untag x end untag equal priority map untag x end untag equal priority normalizing untag x end untag equal priority apply x to x end apply equal priority apply one x to x end apply equal priority identifier x end identifier equal priority identifier one x plus id x end identifier equal priority array plus x and x end plus equal priority array remove x array x level x end remove equal priority array put x value x array x level x end put equal priority array add x value x index x value x level x end add equal priority bit x of x end bit equal priority bit one x of x end bit equal priority example rack equal priority vector hook equal priority bibliography hook equal priority dictionary hook equal priority body hook equal priority codex hook equal priority expansion hook equal priority code hook equal priority cache hook equal priority diagnose hook equal priority pyk aspect equal priority tex aspect equal priority texname aspect equal priority value aspect equal priority message aspect equal priority macro aspect equal priority definition aspect equal priority unpack aspect equal priority claim aspect equal priority priority aspect equal priority lambda identifier equal priority apply identifier equal priority true identifier equal priority if identifier equal priority quote identifier equal priority proclaim identifier equal priority define identifier equal priority introduce identifier equal priority hide identifier equal priority pre identifier equal priority post identifier equal priority eval x stack x cache x end eval equal priority eval two x ref x id x stack x cache x end eval equal priority eval three x function x stack x cache x end eval equal priority eval four x arguments x stack x cache x end eval equal priority lookup x stack x default x end lookup equal priority abstract x term x stack x cache x end abstract equal priority quote x end quote equal priority expand x state x cache x end expand equal priority expand two x definition x state x cache x end expand equal priority expand list x state x cache x end expand equal priority macro equal priority macro state equal priority zip x with x end zip equal priority assoc one x address x index x end assoc equal priority protect x end protect equal priority self equal priority macro define x as x end define equal priority value define x as x end define equal priority intro define x as x end define equal priority pyk define x as x end define equal priority tex define x as x end define equal priority tex name define x as x end define equal priority priority table x end table equal priority macro define one equal priority macro define two x end define equal priority macro define three x end define equal priority macro define four x state x cache x definition x end define equal priority state expand x state x cache x end expand equal priority quote expand x term x stack x end expand equal priority quote expand two x term x stack x end expand equal priority quote expand three x term x stack x value x end expand equal priority quote expand star x term x stack x end expand equal priority parenthesis x end parenthesis equal priority aspect x subcodex x end aspect equal priority aspect x term x cache x end aspect equal priority tuple x end tuple equal priority tuple one x end tuple equal priority tuple two x end tuple equal priority let two x apply x end let equal priority let one x apply x end let equal priority claim define x as x end define equal priority checker equal priority check x cache x end check equal priority check two x cache x def x end check equal priority check three x cache x def x end check equal priority check list x cache x end check equal priority check list two x cache x value x end check equal priority test x end test equal priority false test x end test equal priority raw test x end test equal priority message equal priority message define x as x end define equal priority the statement aspect equal priority statement equal priority statement define x as x end define equal priority example axiom equal priority example scheme equal priority example rule equal priority absurdity equal priority contraexample equal priority example theory primed equal priority example lemma equal priority metavar x end metavar equal priority meta a equal priority meta b equal priority meta c equal priority meta d equal priority meta e equal priority meta f equal priority meta g equal priority meta h equal priority meta i equal priority meta j equal priority meta k equal priority meta l equal priority meta m equal priority meta n equal priority meta o equal priority meta p equal priority meta q equal priority meta r equal priority meta s equal priority meta t equal priority meta u equal priority meta v equal priority meta w equal priority meta x equal priority meta y equal priority meta z equal priority sub x set x to x end sub equal priority sub star x set x to x end sub equal priority the empty set equal priority example remainder equal priority make visible x end visible equal priority error x term x end error equal priority error two x term x end error equal priority proof x term x cache x end proof equal priority proof two x term x end proof equal priority sequent eval x term x end eval equal priority seqeval init x term x end eval equal priority seqeval modus x term x end eval equal priority seqeval modus one x term x sequent x end eval equal priority seqeval verify x term x end eval equal priority seqeval verify one x term x sequent x end eval equal priority sequent eval plus x term x end eval equal priority seqeval plus one x term x sequent x end eval equal priority seqeval minus x term x end eval equal priority seqeval minus one x term x sequent x end eval equal priority seqeval deref x term x end eval equal priority seqeval deref one x term x sequent x end eval equal priority seqeval deref two x term x sequent x def x end eval equal priority seqeval at x term x end eval equal priority seqeval at one x term x sequent x end eval equal priority seqeval infer x term x end eval equal priority seqeval infer one x term x premise x sequent x end eval equal priority seqeval endorse x term x end eval equal priority seqeval endorse one x term x side x sequent x end eval equal priority seqeval est x term x end eval equal priority seqeval est one x term x name x sequent x end eval equal priority seqeval est two x term x name x sequent x def x end eval equal priority seqeval all x term x end eval equal priority seqeval all one x term x variable x sequent x end eval equal priority seqeval cut x term x end eval equal priority seqeval cut one x term x forerunner x end eval equal priority seqeval cut two x term x forerunner x sequent x end eval equal priority computably true x end true equal priority claims x cache x ref x end claims equal priority claims two x cache x ref x end claims equal priority the proof aspect equal priority proof equal priority lemma x says x end lemma equal priority proof of x reads x end proof equal priority in theory x lemma x says x end lemma equal priority in theory x antilemma x says x end antilemma equal priority in theory x rule x says x end rule equal priority in theory x antirule x says x end antirule equal priority verifier equal priority verify one x end verify equal priority verify two x proofs x end verify equal priority verify three x ref x sequents x diagnose x end verify equal priority verify four x premises x end verify equal priority verify five x ref x array x sequents x end verify equal priority verify six x ref x list x sequents x end verify equal priority verify seven x ref x id x sequents x end verify equal priority cut x and x end cut equal priority head x end head equal priority tail x end tail equal priority rule one x theory x end rule equal priority rule x subcodex x end rule equal priority rule tactic equal priority plus x and x end plus equal priority theory x end theory equal priority theory two x cache x end theory equal priority theory three x name x end theory equal priority theory four x name x sum x end theory equal priority example axiom lemma primed equal priority example scheme lemma primed equal priority example rule lemma primed equal priority contraexample lemma primed equal priority example axiom lemma equal priority example scheme lemma equal priority example rule lemma equal priority contraexample lemma equal priority example theory equal priority ragged right equal priority ragged right expansion equal priority color x term x end color equal priority color star x term x end color equal priority vars x end vars equal priority vars star x end vars equal priority instantiate x color x term x end instantiate equal priority instantiate star x color x term x end instantiate equal priority unify x term x with x term x plus x end unify equal priority unify star x term x with x term x plus x end unify equal priority unify one x term x with x term x plus x end unify equal priority unify two x plus x end unify equal priority unify three x vars x plus x end unify equal priority check equal priority parameter term x stack x seed x end parameter equal priority parameter term star x stack x seed x end parameter equal priority instantiate x with x end instantiate equal priority instantiate star x with x end instantiate equal priority occur x in x end occur equal priority occur star x in x end occur equal priority circular x term x substitution x end circular equal priority circular star x term x substitution x end circular equal priority unify x with x substitution x end unify equal priority unify star x with x substitution x end unify equal priority unify two x with x substitution x end unify equal priority ell a equal priority ell b equal priority ell c equal priority ell d equal priority ell e equal priority ell f equal priority ell g equal priority ell h equal priority ell i equal priority ell j equal priority ell k equal priority ell l equal priority ell m equal priority ell n equal priority ell o equal priority ell p equal priority ell q equal priority ell r equal priority ell s equal priority ell t equal priority ell u equal priority ell v equal priority ell w equal priority ell x equal priority ell y equal priority ell z equal priority ell big a equal priority ell big b equal priority ell big c equal priority ell big d equal priority ell big e equal priority ell big f equal priority ell big g equal priority ell big h equal priority ell big i equal priority ell big j equal priority ell big k equal priority ell big l equal priority ell big m equal priority ell big n equal priority ell big o equal priority ell big p equal priority ell big q equal priority ell big r equal priority ell big s equal priority ell big t equal priority ell big u equal priority ell big v equal priority ell big w equal priority ell big x equal priority ell big y equal priority ell big z equal priority ell dummy equal priority reflexivity lemma equal priority reflexivity lemma one equal priority commutativity lemma equal priority the tactic aspect equal priority tactic equal priority tactic define x as x end define equal priority proof expand x state x cache x end expand equal priority proof expand list x state x cache x end expand equal priority proof state equal priority conclude one x cache x end conclude equal priority conclude two x proves x cache x end conclude equal priority conclude three x proves x lemma x substitution x end conclude equal priority propositional theory equal priority axiom one equal priority axiom two equal priority axiom three equal priority axiom four equal priority axiom five equal priority axiom mp equal priority axiom gen equal priority mendelson lemma one eight equal priority mendelson corollary one ten a equal priority mendelson corollary one ten b equal priority mendelson lemma one eleven a equal priority nani teta saka...:13 end priority greater than preassociative priority x sub x end sub equal priority x prime equal priority x assoc x end assoc equal priority x set x to x end set equal priority x set multi x to x end set end priority greater than preassociative priority unicode start of text x end unicode text equal priority unicode end of text equal priority text x end text equal priority text x plus x equal priority text x plus indent x equal priority
unicode newline x equal priority unicode space x equal priority unicode exclamation mark x equal priority unicode quotation mark x equal priority unicode number sign x equal priority unicode dollar sign x equal priority unicode percent x equal priority unicode ampersand x equal priority unicode apostrophe x equal priority unicode left parenthesis x equal priority unicode right parenthesis x equal priority unicode asterisk x equal priority unicode plus sign x equal priority unicode comma x equal priority unicode hyphen x equal priority unicode period x equal priority unicode slash x equal priority unicode zero x equal priority unicode one x equal priority unicode two x equal priority unicode three x equal priority unicode four x equal priority unicode five x equal priority unicode six x equal priority unicode seven x equal priority unicode eight x equal priority unicode nine x equal priority unicode colon x equal priority unicode semicolon x equal priority unicode less than x equal priority unicode equal sign x equal priority unicode greater than x equal priority unicode question mark x equal priority unicode commercial at x equal priority unicode capital a x equal priority unicode capital b x equal priority unicode capital c x equal priority unicode capital d x equal priority unicode capital e x equal priority unicode capital f x equal priority unicode capital g x equal priority unicode capital h x equal priority unicode capital i x equal priority unicode capital j x equal priority unicode capital k x equal priority unicode capital l x equal priority unicode capital m x equal priority unicode capital n x equal priority unicode capital o x equal priority unicode capital p x equal priority unicode capital q x equal priority unicode capital r x equal priority unicode capital s x equal priority unicode capital t x equal priority unicode capital u x equal priority unicode capital v x equal priority unicode capital w x equal priority unicode capital x x equal priority unicode capital y x equal priority unicode capital z x equal priority unicode left bracket x equal priority unicode backslash x equal priority unicode right bracket x equal priority unicode circumflex x equal priority unicode underscore x equal priority unicode grave accent x equal priority unicode small a x equal priority unicode small b x equal priority unicode small c x equal priority unicode small d x equal priority unicode small e x equal priority unicode small f x equal priority unicode small g x equal priority unicode small h x equal priority unicode small i x equal priority unicode small j x equal priority unicode small k x equal priority unicode small l x equal priority unicode small m x equal priority unicode small n x equal priority unicode small o x equal priority unicode small p x equal priority unicode small q x equal priority unicode small r x equal priority unicode small s x equal priority unicode small t x equal priority unicode small u x equal priority unicode small v x equal priority unicode small w x equal priority unicode small x x equal priority unicode small y x equal priority unicode small z x equal priority unicode left brace x equal priority unicode vertical line x equal priority unicode right brace x equal priority unicode tilde x equal priority preassociative x greater than x equal priority postassociative x greater than x equal priority priority x equal x equal priority priority x end priority equal priority newline x equal priority macro newline x end priority greater than preassociative priority x bit nil equal priority x bit one equal priority binary equal priority x color x end color equal priority x color star x end color end priority greater than preassociative priority x apply x equal priority x tagged apply x end priority greater than preassociative priority x raw head equal priority x raw tail equal priority x cardinal untag equal priority x head equal priority x tail equal priority x is singular equal priority x is cardinal equal priority x is data equal priority x is atomic equal priority x cardinal retract equal priority x tagged retract equal priority x boolean retract equal priority x ref equal priority x id equal priority x debug equal priority x root equal priority x zeroth equal priority x first equal priority x second equal priority x third equal priority x fourth equal priority x fifth equal priority x sixth equal priority x seventh equal priority x eighth equal priority x ninth equal priority x is error equal priority x is metavar equal priority x is metaclosed equal priority x is metaclosed star end priority greater than preassociative priority x times x equal priority x times zero x end priority greater than preassociative priority x plus x equal priority x plus zero x equal priority x plus one x equal priority x minus x equal priority x minus zero x equal priority x minus one x end priority greater than preassociative priority x term plus x end plus equal priority x term union x equal priority x term minus x end minus end priority greater than postassociative priority x raw pair x equal priority x eager pair x equal priority x tagged pair x equal priority x untagged double x equal priority x pair x equal priority x double x end priority greater than postassociative priority x comma x end priority greater than preassociative priority x boolean equal x equal priority x data equal x equal priority x cardinal equal x equal priority x peano equal x equal priority x tagged equal x equal priority x math equal x equal priority x reduce to x equal priority x term equal x equal priority x term list equal x equal priority x term root equal x equal priority x term in x equal priority x term subset x equal priority x term set equal x equal priority x sequent equal x equal priority x free in x equal priority x free in star x equal priority x free for x in x equal priority x free for star x in x equal priority x claim in x equal priority x less x equal priority x less zero x equal priority x less one x end priority greater than preassociative priority not x end priority greater than preassociative priority x and x equal priority x macro and x equal priority x simple and x equal priority x claim and x end priority greater than preassociative priority x or x equal priority x parallel x equal priority x macro or x end priority greater than postassociative priority x macro imply x end priority greater than postassociative priority x guard x equal priority x tagged guard x end priority greater than postassociative priority x imply x end priority greater than preassociative priority x select x else x end select end priority greater than preassociative priority lambda x dot x equal priority tagging x equal priority open if x then x else x equal priority let x be x in x equal priority let x abbreviate x in x end priority greater than preassociative priority x init equal priority x modus equal priority x verify equal priority x curry plus equal priority x curry minus equal priority x dereference end priority greater than preassociative priority x at x equal priority x modus ponens x equal priority x modus probans x equal priority x conclude x end priority greater than postassociative priority x infer x equal priority x endorse x equal priority x id est x end priority greater than preassociative priority all x indeed x end priority greater than postassociative priority x rule plus x end priority greater than postassociative priority x cut x end priority greater than preassociative priority x proves x end priority greater than preassociative priority x proof of x reads x equal priority line x because x indeed x cut x equal priority because x indeed x qed equal priority line x premise x cut x equal priority line x side condition x cut x equal priority arbitrary x cut x equal priority locally define x as x cut x end priority greater than postassociative priority x
then x equal priority x
begin x
end x end priority greater than preassociative priority x tab x end priority greater than preassociative priority x row
x end priority greater than unicode end of text end define end math end left
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The pyk compiler, version 0.grue.20050502+ by Klaus Grue,