Logiweb aspects of pred lemma exist mp in pyk

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The predefined "pyk" aspect

define pyk of pred lemma exist mp as text unicode start of text unicode small p unicode small r unicode small e unicode small d unicode space unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small e unicode small x unicode small i unicode small s unicode small t unicode space unicode small m unicode small p unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of pred lemma exist mp as text unicode start of text unicode capital e unicode small x unicode small i unicode small s unicode small t unicode capital m unicode capital p unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of pred lemma exist mp as system Q infer all metavar var v1 end metavar indeed 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 infer not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar infer metavar var b end metavar end define

The user defined "the proof aspect" aspect

define proof of pred lemma exist mp 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 a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar imply metavar var b end metavar infer not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar infer not0 metavar var b end metavar infer prop lemma mt modus ponens metavar var a end metavar imply metavar var b end metavar modus ponens not0 metavar var b end metavar conclude not0 metavar var a end metavar cut 1rule gen modus ponens not0 metavar var a end metavar conclude for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar cut 1rule repetition modus ponens not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar conclude not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar cut prop lemma from contradiction modus ponens for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar modus ponens not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar conclude not0 not0 metavar var b end metavar cut all metavar var v1 end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed 1rule deduction modus ponens all metavar var v1 end metavar indeed 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 infer not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar infer not0 metavar var b end metavar infer not0 not0 metavar var b end metavar conclude metavar var a end metavar imply metavar var b end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar imply not0 metavar var b end metavar imply not0 not0 metavar var b end metavar cut metavar var a end metavar imply metavar var b end metavar infer not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar infer prop lemma mp2 modus ponens metavar var a end metavar imply metavar var b end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar imply not0 metavar var b end metavar imply not0 not0 metavar var b end metavar modus ponens metavar var a end metavar imply metavar var b end metavar modus ponens not0 for all objects metavar var v1 end metavar indeed not0 metavar var a end metavar conclude not0 metavar var b end metavar imply not0 not0 metavar var b end metavar cut prop lemma imply negation modus ponens not0 metavar var b end metavar imply not0 not0 metavar var b end metavar conclude not0 not0 metavar var b end metavar cut prop lemma remove double neg modus ponens not0 not0 metavar var b end metavar conclude metavar var b end metavar end quote state proof state cache var c end expand end define