define pyk of prop lemma weaken or second 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 w unicode small e unicode small a unicode small k unicode small e unicode small n unicode space unicode small o unicode small r unicode space unicode small s unicode small e unicode small c unicode small o unicode small n unicode small d unicode end of text end unicode text end text end define
define tex of prop lemma weaken or second as text unicode start of text unicode capital w unicode small e unicode small a unicode small k unicode small e unicode small n unicode capital o unicode small r unicode two unicode end of text end unicode text end text end define
define statement of prop lemma weaken or second as system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar infer not0 metavar var a end metavar imply metavar var b end metavar end define
define proof of prop lemma weaken or second 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 metavar var a end metavar infer not0 metavar var a end metavar infer prop lemma from contradiction modus ponens metavar var a end metavar modus ponens not0 metavar var a end metavar conclude metavar var b end metavar cut all metavar var a end metavar indeed all metavar var b end metavar indeed 1rule deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var a end metavar infer not0 metavar var a end metavar infer metavar var b end metavar conclude metavar var a end metavar imply not0 metavar var a end metavar imply metavar var b end metavar cut metavar var a end metavar infer 1rule mp modus ponens metavar var a end metavar imply not0 metavar var a end metavar imply metavar var b end metavar modus ponens metavar var a end metavar conclude not0 metavar var a end metavar imply metavar var b end metavar cut 1rule repetition modus ponens not0 metavar var a end metavar imply metavar var b end metavar conclude not0 metavar var a end metavar imply metavar var b end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,