define pyk of prop lemma imply transitivity 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 i unicode small m unicode small p unicode small l unicode small y unicode space unicode small t unicode small r unicode small a unicode small n unicode small s unicode small i unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define
define tex of prop lemma imply transitivity as text unicode start of text unicode capital i unicode small m unicode small p unicode small l unicode small y unicode capital t unicode small r unicode small a unicode small n unicode small s unicode small i unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define
define statement of prop lemma imply transitivity 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 metavar var a end metavar imply metavar var b end metavar infer metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar imply metavar var c end metavar end define
define proof of prop lemma imply transitivity 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 metavar var a end metavar imply metavar var b end metavar infer metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar infer 1rule mp modus ponens metavar var a end metavar imply metavar var b end metavar modus ponens 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 modus ponens metavar var b end metavar conclude 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 metavar var a end metavar imply metavar var b end metavar infer metavar var b end metavar imply metavar var c end metavar infer 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 metavar var a end metavar imply metavar var b end metavar infer metavar var b end metavar imply metavar var c end metavar infer metavar var a end metavar infer metavar var c end metavar conclude metavar var a end metavar imply metavar var b end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply 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 b end metavar imply metavar var c end metavar imply metavar var a end metavar imply metavar var c end metavar modus ponens metavar var a end metavar imply metavar var b end metavar modus ponens metavar var b end metavar imply metavar var c end metavar conclude metavar var a end metavar imply 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,