define pyk of lemma same pair 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 s unicode small a unicode small m unicode small e unicode space unicode small p unicode small a unicode small i unicode small r unicode end of text end unicode text end text end define
define tex of lemma same pair as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital p unicode small a unicode small i unicode small r unicode end of text end unicode text end text end define
define statement of lemma same pair as system zf infer 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 t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var v end metavar end pair end quote endorse quote object var var t end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var w end metavar end pair 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 zermelo pair metavar var x end metavar comma metavar var v end metavar end pair zermelo is zermelo pair metavar var y end metavar comma metavar var w end metavar end pair end define
define proof of lemma same pair as lambda var c dot lambda var x dot proof expand quote system zf infer 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 t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var v end metavar end pair end quote endorse quote object var var t end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var w end metavar end pair 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 lemma pair subset 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 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 x end metavar zermelo is metavar var y end metavar imply metavar var v end metavar zermelo is metavar var w end metavar imply object var var t end var zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair imply object var var t end var zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair cut prop lemma mp2 modus ponens 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 object var var t end var zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair imply object var var t end var zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair modus ponens metavar var x end metavar zermelo is metavar var y end metavar modus ponens metavar var v end metavar zermelo is metavar var w end metavar conclude object var var t end var zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair imply object var var t end var zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair cut lemma =symmetry 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 ponens metavar var x end metavar zermelo is metavar var y end metavar conclude metavar var y end metavar zermelo is metavar var x end metavar cut lemma =symmetry 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 modus ponens metavar var v end metavar zermelo is metavar var w end metavar conclude metavar var w end metavar zermelo is metavar var v end metavar cut lemma pair subset 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 x 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 modus probans quote object var var s end var end quote avoid zero quote metavar var v end metavar end quote conclude metavar var y end metavar zermelo is metavar var x end metavar imply metavar var w end metavar zermelo is metavar var v end metavar imply object var var t end var zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair imply object var var t end var zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair cut prop lemma mp2 modus ponens metavar var y end metavar zermelo is metavar var x end metavar imply metavar var w end metavar zermelo is metavar var v end metavar imply object var var t end var zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair imply object var var t end var zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair modus ponens metavar var y end metavar zermelo is metavar var x end metavar modus ponens metavar var w end metavar zermelo is metavar var v end metavar conclude object var var t end var zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair imply object var var t end var zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair cut lemma set equality suff condition(t) modus probans quote object var var t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var v end metavar end pair end quote modus probans quote object var var t end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var w end metavar end pair end quote modus ponens object var var t end var zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair imply object var var t end var zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair modus ponens object var var t end var zermelo in zermelo pair metavar var y end metavar comma metavar var w end metavar end pair imply object var var t end var zermelo in zermelo pair metavar var x end metavar comma metavar var v end metavar end pair conclude zermelo pair metavar var x end metavar comma metavar var v end metavar end pair zermelo is 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,