define pyk of prop lemma to negated or 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 t unicode small o 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 o unicode small r unicode end of text end unicode text end text end define
define tex of prop lemma to negated or as text unicode start of text unicode capital t unicode small o unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode capital o unicode small r unicode end of text end unicode text end text end define
define statement of prop lemma to negated or as system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed not0 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar infer not0 not0 metavar var a end metavar imply metavar var b end metavar end define
define proof of prop lemma to negated or 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 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar infer not0 metavar var a end metavar imply metavar var b end metavar infer prop lemma first conjunct modus ponens not0 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar conclude not0 metavar var a end metavar cut prop lemma second conjunct modus ponens not0 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar conclude not0 metavar var b end metavar cut prop lemma negate first disjunct modus ponens not0 metavar var a end metavar imply metavar var b end metavar modus ponens not0 metavar var a end metavar conclude metavar var b end metavar cut prop lemma from contradiction modus ponens metavar var b end metavar modus ponens not0 metavar var b end metavar conclude not0 not0 metavar var a end metavar imply 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 not0 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar infer not0 metavar var a end metavar imply metavar var b end metavar infer not0 not0 metavar var a end metavar imply metavar var b end metavar conclude not0 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar imply not0 metavar var a end metavar imply metavar var b end metavar imply not0 not0 metavar var a end metavar imply metavar var b end metavar cut not0 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar infer 1rule mp modus ponens not0 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar imply not0 metavar var a end metavar imply metavar var b end metavar imply not0 not0 metavar var a end metavar imply metavar var b end metavar modus ponens not0 not0 metavar var a end metavar imply not0 not0 metavar var b end metavar conclude not0 metavar var a end metavar imply metavar var b end metavar imply not0 not0 metavar var a end metavar imply metavar var b end metavar cut prop lemma imply negation modus ponens not0 metavar var a end metavar imply metavar var b end metavar imply not0 not0 metavar var a end metavar imply metavar var b end metavar conclude not0 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,