Logiweb aspects of lemma same pair in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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