Logiweb aspects of lemma leqLessTransitivity in pyk

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The predefined "pyk" aspect

define pyk of lemma leqLessTransitivity 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 l unicode small e unicode small q unicode capital l unicode small e unicode small s unicode small s unicode capital t unicode small r unicode small a unicode small n unicode small s unicode small i unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma leqLessTransitivity as text unicode start of text unicode small l unicode small e unicode small q unicode capital l unicode small e unicode small s unicode small s unicode capital t unicode small r unicode small a unicode small n unicode small s unicode small i unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma leqLessTransitivity as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y end metavar infer not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar infer not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma leqLessTransitivity as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y end metavar infer not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar infer metavar var x end metavar = metavar var z end metavar infer prop lemma first conjunct modus ponens not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar conclude metavar var y end metavar <= metavar var z end metavar cut prop lemma second conjunct modus ponens not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar conclude not0 metavar var y end metavar = metavar var z end metavar cut lemma subLeqLeft modus ponens metavar var x end metavar = metavar var z end metavar modus ponens metavar var x end metavar <= metavar var y end metavar conclude metavar var z end metavar <= metavar var y end metavar cut lemma leqAntisymmetry modus ponens metavar var y end metavar <= metavar var z end metavar modus ponens metavar var z end metavar <= metavar var y end metavar conclude metavar var y end metavar = metavar var z end metavar cut prop lemma from contradiction modus ponens metavar var y end metavar = metavar var z end metavar modus ponens not0 metavar var y end metavar = metavar var z end metavar conclude not0 metavar var x end metavar = metavar var z end metavar cut all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar <= metavar var y end metavar infer not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar infer metavar var x end metavar = metavar var z end metavar infer not0 metavar var x end metavar = metavar var z end metavar conclude metavar var x end metavar <= metavar var y end metavar imply not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar imply metavar var x end metavar = metavar var z end metavar imply not0 metavar var x end metavar = metavar var z end metavar cut metavar var x end metavar <= metavar var y end metavar infer not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar infer prop lemma mp2 modus ponens metavar var x end metavar <= metavar var y end metavar imply not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar imply metavar var x end metavar = metavar var z end metavar imply not0 metavar var x end metavar = metavar var z end metavar modus ponens metavar var x end metavar <= metavar var y end metavar modus ponens not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar conclude metavar var x end metavar = metavar var z end metavar imply not0 metavar var x end metavar = metavar var z end metavar cut prop lemma imply negation modus ponens metavar var x end metavar = metavar var z end metavar imply not0 metavar var x end metavar = metavar var z end metavar conclude not0 metavar var x end metavar = metavar var z end metavar cut prop lemma first conjunct modus ponens not0 metavar var y end metavar <= metavar var z end metavar imply not0 not0 metavar var y end metavar = metavar var z end metavar conclude metavar var y end metavar <= metavar var z end metavar cut lemma leqTransitivity modus ponens metavar var x end metavar <= metavar var y end metavar modus ponens metavar var y end metavar <= metavar var z end metavar conclude metavar var x end metavar <= metavar var z end metavar cut prop lemma join conjuncts modus ponens metavar var x end metavar <= metavar var z end metavar modus ponens not0 metavar var x end metavar = metavar var z end metavar conclude not0 metavar var x end metavar <= metavar var z end metavar imply not0 not0 metavar var x end metavar = metavar var z end metavar end quote state proof state cache var c end expand end define