Logiweb aspects of lemma thirdGeq in pyk

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The predefined "pyk" aspect

define pyk of lemma thirdGeq 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 t unicode small h unicode small i unicode small r unicode small d unicode capital g unicode small e unicode small q unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma thirdGeq as text unicode start of text unicode small t unicode small h unicode small i unicode small r unicode small d unicode capital g unicode small e unicode small q unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma thirdGeq as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var end define

The user defined "the proof aspect" aspect

define proof of lemma thirdGeq 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 metavar var x end metavar <= metavar var y end metavar infer axiom leqReflexivity conclude metavar var y end metavar <= metavar var y end metavar cut prop lemma join conjuncts modus ponens metavar var x end metavar <= metavar var y end metavar modus ponens metavar var y end metavar <= metavar var y end metavar conclude not0 metavar var x end metavar <= metavar var y end metavar imply not0 metavar var y end metavar <= metavar var y end metavar cut 1rule exist intro at existential var var c end var at metavar var y end metavar modus ponens not0 metavar var x end metavar <= metavar var y end metavar imply not0 metavar var y end metavar <= metavar var y end metavar conclude not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var cut all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var y end metavar <= metavar var x end metavar infer axiom leqReflexivity conclude metavar var x end metavar <= metavar var x end metavar cut prop lemma join conjuncts modus ponens metavar var x end metavar <= metavar var x end metavar modus ponens metavar var y end metavar <= metavar var x end metavar conclude not0 metavar var x end metavar <= metavar var x end metavar imply not0 metavar var y end metavar <= metavar var x end metavar cut 1rule exist intro at existential var var c end var at metavar var x end metavar modus ponens not0 metavar var x end metavar <= metavar var x end metavar imply not0 metavar var y end metavar <= metavar var x end metavar conclude not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var cut all metavar var x end metavar indeed all metavar var y end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar <= metavar var y end metavar infer not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var conclude metavar var x end metavar <= metavar var y end metavar imply not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var cut 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var y end metavar <= metavar var x end metavar infer not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var conclude metavar var y end metavar <= metavar var x end metavar imply not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var cut axiom leqTotality conclude not0 metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var x end metavar cut prop lemma from disjuncts modus ponens not0 metavar var x end metavar <= metavar var y end metavar imply metavar var y end metavar <= metavar var x end metavar modus ponens metavar var x end metavar <= metavar var y end metavar imply not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var modus ponens metavar var y end metavar <= metavar var x end metavar imply not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var conclude not0 metavar var x end metavar <= existential var var c end var imply not0 metavar var y end metavar <= existential var var c end var end quote state proof state cache var c end expand end define