define pyk of lemma same binary union 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 b unicode small i unicode small n unicode small a unicode small r unicode small y unicode space unicode small u unicode small n unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define
define tex of lemma same binary union as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital b unicode small i unicode small n unicode small a unicode small r unicode small y unicode capital u unicode small n unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define
define statement of lemma same binary union 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 t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x 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 y end metavar end pair 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 v 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 w end metavar comma metavar var w end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair end quote endorse quote object var var t end var end quote avoid zero quote zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end quote endorse quote object var var t end var end quote avoid zero quote zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair 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 union zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end union zermelo is union zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair end union end define
define proof of lemma same binary union 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 t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x 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 y end metavar end pair 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 v 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 w end metavar comma metavar var w end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end quote endorse quote object var var s end var end quote avoid zero quote zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair end quote endorse quote object var var t end var end quote avoid zero quote zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end quote endorse quote object var var t end var end quote avoid zero quote zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair 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 same singleton 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 t end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x 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 y end metavar end pair end quote modus ponens metavar var x end metavar zermelo is metavar var y end metavar conclude zermelo pair metavar var x end metavar comma metavar var x end metavar end pair zermelo is zermelo pair metavar var y end metavar comma metavar var y end metavar end pair cut lemma same singleton 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 probans quote object var var t end var end quote avoid zero quote zermelo pair metavar var v 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 w end metavar comma metavar var w end metavar end pair end quote modus ponens metavar var v end metavar zermelo is metavar var w end metavar conclude zermelo pair metavar var v end metavar comma metavar var v end metavar end pair zermelo is zermelo pair metavar var w end metavar comma metavar var w end metavar end pair cut lemma same pair modus probans quote object var var s end var end quote avoid zero quote zermelo pair metavar var x end metavar comma metavar var x end metavar end pair end quote modus probans quote object var var s end var end quote avoid zero quote zermelo pair metavar var y end metavar comma metavar var y end metavar end pair end quote modus probans quote object var var s end var end quote avoid zero quote zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end quote modus probans quote object var var s end var end quote avoid zero quote zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end quote modus probans quote object var var t end var end quote avoid zero quote zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end quote modus probans quote object var var t end var end quote avoid zero quote zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair end quote modus ponens zermelo pair metavar var x end metavar comma metavar var x end metavar end pair zermelo is zermelo pair metavar var y end metavar comma metavar var y end metavar end pair modus ponens zermelo pair metavar var v end metavar comma metavar var v end metavar end pair zermelo is zermelo pair metavar var w end metavar comma metavar var w end metavar end pair conclude zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair zermelo is zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair cut lemma same union modus probans quote object var var s end var end quote avoid zero quote zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end quote modus probans quote object var var s end var end quote avoid zero quote zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair end quote modus ponens zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair zermelo is zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair conclude union zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end union zermelo is union zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair end union cut 1rule repetition modus ponens union zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end union zermelo is union zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair end union conclude union zermelo pair zermelo pair metavar var x end metavar comma metavar var x end metavar end pair comma zermelo pair metavar var v end metavar comma metavar var v end metavar end pair end pair end union zermelo is union zermelo pair zermelo pair metavar var y end metavar comma metavar var y end metavar end pair comma zermelo pair metavar var w end metavar comma metavar var w end metavar end pair end pair end union end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,