Logiweb aspects of lemma pair subset in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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