define pyk of prop lemma expand 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 e unicode small x unicode small p unicode small a unicode small n unicode small d 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 expand disjuncts as text unicode start of text unicode capital e unicode small x unicode small p unicode small a unicode small n unicode small d 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 expand 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 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 not0 metavar var b end metavar imply not0 metavar var d end metavar imply not0 metavar var a end metavar imply not0 metavar var c end metavar end define
define proof of prop lemma expand 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 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 not0 metavar var b end metavar infer not0 metavar var d end metavar infer prop lemma negate second disjunct modus ponens not0 metavar var a end metavar imply metavar var b end metavar modus ponens not0 metavar var b end metavar conclude metavar var a end metavar cut prop lemma negate second disjunct modus ponens not0 metavar var c end metavar imply metavar var d end metavar modus ponens not0 metavar var d end metavar conclude metavar var c end metavar cut prop lemma join conjuncts modus ponens metavar var a end metavar modus ponens metavar var c end metavar conclude not0 metavar var a end metavar imply not0 metavar var c 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 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 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 not0 metavar var b end metavar infer not0 metavar var d end metavar infer not0 metavar var a end metavar imply not0 metavar var c 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 not0 metavar var b end metavar imply not0 metavar var d end metavar imply not0 metavar var a end metavar imply not0 metavar var c 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 prop lemma mp2 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 not0 metavar var b end metavar imply not0 metavar var d end metavar imply not0 metavar var a end metavar imply not0 metavar var c 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 conclude not0 metavar var b end metavar imply not0 metavar var d end metavar imply not0 metavar var a end metavar imply not0 metavar var c end metavar cut 1rule repetition modus ponens not0 metavar var b end metavar imply not0 metavar var d end metavar imply not0 metavar var a end metavar imply not0 metavar var c end metavar conclude not0 metavar var b end metavar imply not0 metavar var d end metavar imply not0 metavar var a end metavar imply 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,