Logiweb aspects of lemma fpart-Bounded base in pyk

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The predefined "pyk" aspect

define pyk of lemma fpart-Bounded base as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small f unicode small p unicode small a unicode small r unicode small t unicode hyphen unicode capital b unicode small o unicode small u unicode small n unicode small d unicode small e unicode small d unicode space unicode small b unicode small a unicode small s unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fpart-Bounded base as text unicode start of text unicode capital f unicode small p unicode small a unicode small r unicode small t unicode hyphen unicode capital b unicode small o unicode small u unicode small n unicode small d unicode small e unicode small d unicode left parenthesis unicode capital b unicode small a unicode small s unicode small e unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma fpart-Bounded base as system Q infer all metavar var v1 end metavar indeed all metavar var v2n end metavar indeed all metavar var fx end metavar indeed not0 for all objects metavar var v1 end metavar indeed not0 for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= 0 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma fpart-Bounded base as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var v1 end metavar indeed all metavar var v2n end metavar indeed all metavar var fx end metavar indeed metavar var v2n end metavar <= 0 infer lemma leqLessEq modus ponens metavar var v2n end metavar <= 0 conclude not0 not0 metavar var v2n end metavar <= 0 imply not0 not0 metavar var v2n end metavar = 0 imply metavar var v2n end metavar = 0 cut axiom nonnegative(N) conclude 0 <= metavar var v2n end metavar cut lemma toNotLess modus ponens 0 <= metavar var v2n end metavar conclude not0 not0 metavar var v2n end metavar <= 0 imply not0 not0 metavar var v2n end metavar = 0 cut prop lemma negate first disjunct modus ponens not0 not0 metavar var v2n end metavar <= 0 imply not0 not0 metavar var v2n end metavar = 0 imply metavar var v2n end metavar = 0 modus ponens not0 not0 metavar var v2n end metavar <= 0 imply not0 not0 metavar var v2n end metavar = 0 conclude metavar var v2n end metavar = 0 cut lemma sameSeries modus ponens metavar var v2n end metavar = 0 conclude [ metavar var fx end metavar ; metavar var v2n end metavar ] = [ metavar var fx end metavar ; 0 ] cut lemma sameNumerical modus ponens [ metavar var fx end metavar ; metavar var v2n end metavar ] = [ metavar var fx end metavar ; 0 ] conclude | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; 0 ] | cut lemma eqAddition modus ponens | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; 0 ] | conclude | [ metavar var fx end metavar ; metavar var v2n end metavar ] | + 1 = | [ metavar var fx end metavar ; 0 ] | + 1 cut axiom leqReflexivity conclude | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; metavar var v2n end metavar ] | cut lemma leqPlus1 modus ponens | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; metavar var v2n end metavar ] | conclude not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; metavar var v2n end metavar ] | + 1 imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; metavar var v2n end metavar ] | + 1 cut lemma subLessRight modus ponens | [ metavar var fx end metavar ; metavar var v2n end metavar ] | + 1 = | [ metavar var fx end metavar ; 0 ] | + 1 modus ponens not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; metavar var v2n end metavar ] | + 1 imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; metavar var v2n end metavar ] | + 1 conclude not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; 0 ] | + 1 imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; 0 ] | + 1 cut all metavar var v1 end metavar indeed all metavar var v2n end metavar indeed all metavar var fx end metavar indeed 1rule deduction modus ponens all metavar var v1 end metavar indeed all metavar var v2n end metavar indeed all metavar var fx end metavar indeed metavar var v2n end metavar <= 0 infer not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; 0 ] | + 1 imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; 0 ] | + 1 conclude metavar var v2n end metavar <= 0 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; 0 ] | + 1 imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; 0 ] | + 1 cut 1rule gen modus ponens metavar var v2n end metavar <= 0 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; 0 ] | + 1 imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; 0 ] | + 1 conclude for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= 0 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; 0 ] | + 1 imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; 0 ] | + 1 cut pred lemma intro exist at | [ metavar var fx end metavar ; 0 ] | + 1 modus ponens for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= 0 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= | [ metavar var fx end metavar ; 0 ] | + 1 imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = | [ metavar var fx end metavar ; 0 ] | + 1 conclude not0 for all objects metavar var v1 end metavar indeed not0 for all objects metavar var v2n end metavar indeed metavar var v2n end metavar <= 0 imply not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | <= metavar var v1 end metavar imply not0 not0 | [ metavar var fx end metavar ; metavar var v2n end metavar ] | = metavar var v1 end metavar end quote state proof state cache var c end expand end define