Logiweb aspects of lemma same binary union in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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