define pyk of prop lemma from negated double imply 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 r unicode small o unicode small m unicode space unicode small n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode space unicode small d unicode small o unicode small u unicode small b unicode small l unicode small e unicode space unicode small i unicode small m unicode small p unicode small l unicode small y unicode end of text end unicode text end text end define
define tex of prop lemma from negated double imply as text unicode start of text unicode capital f unicode small r unicode small o unicode small m unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode left parenthesis unicode two unicode asterisk unicode capital i unicode small m unicode small p unicode small l unicode small y unicode right parenthesis unicode end of text end unicode text end text end define
define statement of prop lemma from negated double imply as system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed not0 metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer not0 not0 metavar var a end metavar imply not0 metavar var b end metavar imply not0 not0 metavar var c end metavar end define
define proof of prop lemma from negated double imply 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 all metavar var c end metavar indeed not0 metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer prop lemma from negated imply modus ponens not0 metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar conclude not0 metavar var a end metavar imply not0 not0 metavar var b end metavar imply metavar var c end metavar cut prop lemma first conjunct modus ponens not0 metavar var a end metavar imply not0 not0 metavar var b end metavar imply metavar var c end metavar conclude metavar var a end metavar cut prop lemma second conjunct modus ponens not0 metavar var a end metavar imply not0 not0 metavar var b end metavar imply metavar var c end metavar conclude not0 metavar var b end metavar imply metavar var c end metavar cut prop lemma from negated imply modus ponens not0 metavar var b end metavar imply metavar var c end metavar conclude not0 metavar var b end metavar imply not0 not0 metavar var c end metavar cut prop lemma first conjunct modus ponens not0 metavar var b end metavar imply not0 not0 metavar var c end metavar conclude metavar var b end metavar cut prop lemma second conjunct modus ponens not0 metavar var b end metavar imply not0 not0 metavar var c end metavar conclude not0 metavar var c end metavar cut prop lemma join conjuncts modus ponens metavar var a end metavar modus ponens metavar var b end metavar conclude not0 metavar var a end metavar imply not0 metavar var b end metavar cut prop lemma join conjuncts modus ponens not0 metavar var a end metavar imply not0 metavar var b end metavar modus ponens not0 metavar var c end metavar conclude not0 not0 metavar var a end metavar imply not0 metavar var b end metavar imply not0 not0 metavar var c end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,