define pyk of pred lemma allNegated(Imply) 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 l unicode small l unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode left parenthesis unicode capital i unicode small m unicode small p unicode small l unicode small y unicode right parenthesis unicode end of text end unicode text end text end define
define tex of pred lemma allNegated(Imply) as text unicode start of text unicode capital a unicode small l unicode small l unicode capital n unicode small e unicode small g unicode small a unicode small t unicode small e unicode small d unicode left parenthesis unicode capital i unicode small m unicode small p unicode small l unicode small y unicode right parenthesis unicode end of text end unicode text end text end define
define statement of pred lemma allNegated(Imply) as system Q infer all metavar var v1 end metavar indeed all metavar var a end metavar indeed not0 for all objects metavar var v1 end metavar indeed metavar var a end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar end define
define proof of pred lemma allNegated(Imply) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var v1 end metavar indeed all metavar var a end metavar indeed for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar infer lemma a4 at metavar var x end metavar modus ponens for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar conclude not0 not0 metavar var a end metavar cut prop lemma remove double neg modus ponens not0 not0 metavar var a end metavar conclude metavar var a end metavar cut 1rule gen modus ponens metavar var a end metavar conclude for all objects metavar var v1 end metavar indeed metavar var a end metavar cut all metavar var v1 end metavar indeed all metavar var a end metavar indeed 1rule deduction modus ponens all metavar var v1 end metavar indeed all metavar var a end metavar indeed for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar infer for all objects metavar var v1 end metavar indeed metavar var a end metavar conclude for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar imply for all objects metavar var v1 end metavar indeed metavar var a end metavar cut prop lemma contrapositive modus ponens for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar imply for all objects metavar var v1 end metavar indeed metavar var a end metavar conclude not0 for all objects metavar var v1 end metavar indeed metavar var a end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar cut 1rule repetition modus ponens not0 for all objects metavar var v1 end metavar indeed metavar var a end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar conclude not0 for all objects metavar var v1 end metavar indeed metavar var a end metavar imply not0 for all objects metavar var v1 end metavar indeed not0 not0 metavar var a end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,