define pyk of prop lemma first conjunct as text unicode start of text unicode small p unicode small r unicode small o unicode small p unicode space unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small f unicode small i unicode small r unicode small s unicode small t unicode space unicode small c unicode small o unicode small n unicode small j unicode small u unicode small n unicode small c unicode small t unicode end of text end unicode text end text end define
define tex of prop lemma first conjunct as text unicode start of text unicode capital f unicode small i unicode small r unicode small s unicode small t unicode capital c unicode small o unicode small n unicode small j unicode small u unicode small n unicode small c unicode small t unicode end of text end unicode text end text end define
define statement of prop lemma first conjunct as system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed not0 metavar var a end metavar imply not0 metavar var b end metavar infer metavar var a end metavar end define
define proof of prop lemma first conjunct as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed not0 metavar var a end metavar imply not0 metavar var b end metavar infer prop lemma and commutativity modus ponens not0 metavar var a end metavar imply not0 metavar var b end metavar conclude not0 metavar var b end metavar imply not0 metavar var a end metavar cut prop lemma second conjunct modus ponens not0 metavar var b end metavar imply not0 metavar var a end metavar conclude metavar var a end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,