define pyk of prop lemma from two times two disjuncts 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 t unicode small w unicode small o unicode space unicode small t unicode small i unicode small m unicode small e unicode small s unicode space unicode small t unicode small w unicode small o unicode space unicode small d unicode small i unicode small s unicode small j unicode small u unicode small n unicode small c unicode small t unicode small s unicode end of text end unicode text end text end define
define tex of prop lemma from two times two disjuncts as text unicode start of text unicode capital f unicode small r unicode small o unicode small m unicode two unicode asterisk unicode two unicode capital d unicode small i unicode small s unicode small j unicode small u unicode small n unicode small c unicode small t unicode small s unicode end of text end unicode text end text end define
define statement of prop lemma from two times two disjuncts 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 all metavar var d end metavar indeed all metavar var e end metavar indeed not0 metavar var a end metavar imply metavar var b end metavar infer not0 metavar var c end metavar imply metavar var d end metavar infer metavar var a end metavar imply metavar var c end metavar imply metavar var e end metavar infer metavar var a end metavar imply metavar var d end metavar imply metavar var e end metavar infer metavar var b end metavar imply metavar var c end metavar imply metavar var e end metavar infer metavar var b end metavar imply metavar var d end metavar imply metavar var e end metavar infer metavar var e end metavar end define
define proof of prop lemma from two times two disjuncts 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 all metavar var d end metavar indeed all metavar var e end metavar indeed not0 metavar var c end metavar imply metavar var d end metavar infer metavar var a end metavar imply metavar var c end metavar imply metavar var e end metavar infer metavar var a end metavar imply metavar var d end metavar imply metavar var e end metavar infer metavar var a end metavar infer 1rule mp modus ponens metavar var a end metavar imply metavar var c end metavar imply metavar var e end metavar modus ponens metavar var a end metavar conclude metavar var c end metavar imply metavar var e end metavar cut 1rule mp modus ponens metavar var a end metavar imply metavar var d end metavar imply metavar var e end metavar modus ponens metavar var a end metavar conclude metavar var d end metavar imply metavar var e end metavar cut prop lemma from disjuncts modus ponens not0 metavar var c end metavar imply metavar var d end metavar modus ponens metavar var c end metavar imply metavar var e end metavar modus ponens metavar var d end metavar imply metavar var e end metavar conclude metavar var e end metavar cut all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed all metavar var e end metavar indeed not0 metavar var a end metavar imply metavar var b end metavar infer not0 metavar var c end metavar imply metavar var d end metavar infer metavar var b end metavar imply metavar var c end metavar imply metavar var e end metavar infer metavar var b end metavar imply metavar var d end metavar imply metavar var e end metavar infer not0 metavar var a end metavar infer 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 1rule mp modus ponens metavar var b end metavar imply metavar var c end metavar imply metavar var e end metavar modus ponens metavar var b end metavar conclude metavar var c end metavar imply metavar var e end metavar cut 1rule mp modus ponens metavar var b end metavar imply metavar var d end metavar imply metavar var e end metavar modus ponens metavar var b end metavar conclude metavar var d end metavar imply metavar var e end metavar cut prop lemma from disjuncts modus ponens not0 metavar var c end metavar imply metavar var d end metavar modus ponens metavar var c end metavar imply metavar var e end metavar modus ponens metavar var d end metavar imply metavar var e end metavar conclude metavar var e end metavar cut all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed all metavar var e end metavar indeed 1rule deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed all metavar var e end metavar indeed not0 metavar var c end metavar imply metavar var d end metavar infer metavar var a end metavar imply metavar var c end metavar imply metavar var e end metavar infer metavar var a end metavar imply metavar var d end metavar imply metavar var e end metavar infer metavar var a end metavar infer metavar var e end metavar conclude not0 metavar var c end metavar imply metavar var d end metavar imply metavar var a end metavar imply metavar var c end metavar imply metavar var e end metavar imply metavar var a end metavar imply metavar var d end metavar imply metavar var e end metavar imply metavar var a end metavar imply metavar var e end metavar cut 1rule deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed all metavar var d end metavar indeed all metavar var e end metavar indeed not0 metavar var a end metavar imply metavar var b end metavar infer not0 metavar var c end metavar imply metavar var d end metavar infer metavar var b end metavar imply metavar var c end metavar imply metavar var e end metavar infer metavar var b end metavar imply metavar var d end metavar imply metavar var e end metavar infer not0 metavar var a end metavar infer metavar var e end metavar conclude not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply metavar var d end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var e end metavar imply metavar var b end metavar imply metavar var d end metavar imply metavar var e end metavar imply not0 metavar var a end metavar imply metavar var e end metavar cut not0 metavar var a end metavar imply metavar var b end metavar infer not0 metavar var c end metavar imply metavar var d end metavar infer metavar var a end metavar imply metavar var c end metavar imply metavar var e end metavar infer metavar var a end metavar imply metavar var d end metavar imply metavar var e end metavar infer metavar var b end metavar imply metavar var c end metavar imply metavar var e end metavar infer metavar var b end metavar imply metavar var d end metavar imply metavar var e end metavar infer prop lemma mp3 modus ponens not0 metavar var c end metavar imply metavar var d end metavar imply metavar var a end metavar imply metavar var c end metavar imply metavar var e end metavar imply metavar var a end metavar imply metavar var d end metavar imply metavar var e end metavar imply metavar var a end metavar imply metavar var e end metavar modus ponens not0 metavar var c end metavar imply metavar var d end metavar modus ponens metavar var a end metavar imply metavar var c end metavar imply metavar var e end metavar modus ponens metavar var a end metavar imply metavar var d end metavar imply metavar var e end metavar conclude metavar var a end metavar imply metavar var e end metavar cut prop lemma mp4 modus ponens not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply metavar var d end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var e end metavar imply metavar var b end metavar imply metavar var d end metavar imply metavar var e end metavar imply not0 metavar var a end metavar imply metavar var e end metavar modus ponens not0 metavar var a end metavar imply metavar var b end metavar modus ponens not0 metavar var c end metavar imply metavar var d end metavar modus ponens metavar var b end metavar imply metavar var c end metavar imply metavar var e end metavar modus ponens metavar var b end metavar imply metavar var d end metavar imply metavar var e end metavar conclude not0 metavar var a end metavar imply metavar var e end metavar cut prop lemma from negations modus ponens metavar var a end metavar imply metavar var e end metavar modus ponens not0 metavar var a end metavar imply metavar var e end metavar conclude metavar var e end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,