define pyk of prop lemma doubly conditioned join conjuncts 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 d unicode small o unicode small u unicode small b unicode small l unicode small y unicode space unicode small c unicode small o unicode small n unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode small e unicode small d unicode space unicode small j unicode small o unicode small i unicode small n unicode space unicode small c unicode small o unicode small n 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 doubly conditioned join conjuncts as text unicode start of text unicode capital j unicode small o unicode small i unicode small n unicode capital c unicode small o unicode small n unicode small j unicode small u unicode small n unicode small c unicode small t unicode small s unicode left parenthesis unicode two unicode small c unicode small o unicode small n unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode small s unicode right parenthesis unicode end of text end unicode text end text end define
define statement of prop lemma doubly conditioned join conjuncts 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 metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar infer metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply not0 metavar var d end metavar end define
define proof of prop lemma doubly conditioned join conjuncts 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 metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar infer metavar var a end metavar infer metavar var b end metavar infer prop lemma mp2 modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar modus ponens metavar var a end metavar modus ponens metavar var b end metavar conclude metavar var c end metavar cut prop lemma mp2 modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar modus ponens metavar var a end metavar modus ponens metavar var b end metavar conclude metavar var d end metavar cut prop lemma join conjuncts modus ponens metavar var c end metavar modus ponens metavar var d end metavar conclude not0 metavar var c end metavar imply not0 metavar var d 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 metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar infer metavar var a end metavar infer metavar var b end metavar infer not0 metavar var c end metavar imply not0 metavar var d end metavar conclude metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar imply metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply not0 metavar var d end metavar cut metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar infer prop lemma mp2 modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar imply metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply not0 metavar var d end metavar modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar modus ponens metavar var a end metavar imply metavar var b end metavar imply metavar var d end metavar conclude metavar var a end metavar imply metavar var b end metavar imply not0 metavar var c end metavar imply not0 metavar var d end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,