define pyk of pred lemma addExist helper1 as text unicode start of text unicode small p unicode small r unicode small e unicode small d unicode space unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small a unicode small d unicode small d unicode capital e unicode small x unicode small i unicode small s unicode small t unicode space unicode small h unicode small e unicode small l unicode small p unicode small e unicode small r unicode one unicode end of text end unicode text end text end define
define tex of pred lemma addExist helper1 as text unicode start of text unicode capital a unicode small d unicode small d unicode capital e unicode small x unicode small i unicode small s unicode small t unicode left parenthesis unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r unicode one unicode right parenthesis unicode end of text end unicode text end text end define
define statement of pred lemma addExist helper1 as system Q infer all metavar var y end metavar indeed all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed 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 meta-sub not0 metavar var b end metavar is not0 metavar var d end metavar where metavar var v2 end metavar is metavar var y end metavar end sub endorse metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar imply for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar imply not0 for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar end define
define proof of pred lemma addExist helper1 as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var y end metavar indeed all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed 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 meta-sub not0 metavar var b end metavar is not0 metavar var d end metavar where metavar var v2 end metavar is metavar var y end metavar end sub endorse metavar var a end metavar imply metavar var b end metavar infer metavar var c end metavar imply metavar var a end metavar infer not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar infer for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar infer lemma a4 at metavar var y end metavar modus ponens for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar conclude not0 metavar var b end metavar cut prop lemma mt modus ponens metavar var a end metavar imply metavar var b end metavar modus ponens not0 metavar var b end metavar conclude not0 metavar var a end metavar cut prop lemma mt modus ponens metavar var c end metavar imply metavar var a end metavar modus ponens not0 metavar var a end metavar conclude not0 metavar var c end metavar cut 1rule gen modus ponens not0 metavar var c end metavar conclude for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar cut 1rule repetition modus ponens not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar conclude not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar cut prop lemma from contradiction modus ponens for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar modus ponens not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar conclude not0 for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar cut all metavar var y end metavar indeed all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed 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 y end metavar indeed all metavar var v1 end metavar indeed all metavar var v2 end metavar indeed 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 meta-sub not0 metavar var b end metavar is not0 metavar var d end metavar where metavar var v2 end metavar is metavar var y end metavar end sub endorse metavar var a end metavar imply metavar var b end metavar infer metavar var c end metavar imply metavar var a end metavar infer not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar infer for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar infer not0 for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar conclude meta-sub not0 metavar var b end metavar is not0 metavar var d end metavar where metavar var v2 end metavar is metavar var y end metavar end sub endorse metavar var a end metavar imply metavar var b end metavar imply metavar var c end metavar imply metavar var a end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 metavar var c end metavar imply for all objects metavar var v2 end metavar indeed not0 metavar var d end metavar imply not0 for all objects metavar var v2 end metavar indeed 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,