define pyk of lemma pair subset as text unicode start of text unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small p unicode small a unicode small i unicode small r unicode space unicode small s unicode small u unicode small b unicode small s unicode small e unicode small t unicode end of text end unicode text end text end define
define tex of lemma pair subset as text unicode start of text unicode capital p unicode small a unicode small i unicode small r unicode capital s unicode small u unicode small b unicode small s unicode small e unicode small t unicode end of text end unicode text end text end define
define statement of lemma pair subset as system zf infer all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var v end metavar indeed all metavar var w end metavar indeed quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var v end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar imply metavar var v end metavar zermelo is metavar var w end metavar imply metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair imply metavar var s end metavar zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair end define
define proof of lemma pair subset as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var v end metavar indeed all metavar var w end metavar indeed quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var v end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar infer metavar var v end metavar zermelo is metavar var w end metavar infer metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair infer lemma pair2formula modus ponens metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair conclude not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var v end metavar cut lemma pair subset0 modus probans quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote conclude metavar var x end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var x end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar cut 1rule mp modus ponens metavar var x end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var x end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar modus ponens metavar var x end metavar zermelo is metavar var y end metavar conclude metavar var s end metavar zermelo is metavar var x end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar cut lemma pair subset1 modus probans quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var v end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote conclude metavar var v end metavar zermelo is metavar var w end metavar imply metavar var s end metavar zermelo is metavar var v end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar cut 1rule mp modus ponens metavar var v end metavar zermelo is metavar var w end metavar imply metavar var s end metavar zermelo is metavar var v end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar modus ponens metavar var v end metavar zermelo is metavar var w end metavar conclude metavar var s end metavar zermelo is metavar var v end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar cut prop lemma from disjuncts modus ponens not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var v end metavar modus ponens metavar var s end metavar zermelo is metavar var x end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar modus ponens metavar var s end metavar zermelo is metavar var v end metavar imply not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar conclude not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar cut lemma formula2pair modus ponens not0 metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo is metavar var w end metavar conclude metavar var s end metavar zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair cut all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var v end metavar indeed all metavar var w end metavar indeed 1rule deduction modus ponens all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var v end metavar indeed all metavar var w end metavar indeed quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var v end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar infer metavar var v end metavar zermelo is metavar var w end metavar infer metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair infer metavar var s end metavar zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair conclude quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var v end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var w end metavar end quote endorse quote object var var s end var end quote avoid zero quote metavar var s end metavar end quote endorse metavar var x end metavar zermelo is metavar var y end metavar imply metavar var v end metavar zermelo is metavar var w end metavar imply metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair imply metavar var s end metavar zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,