Logiweb aspects of lemma separation subset in pyk

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The predefined "pyk" aspect

define pyk of lemma separation 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 s unicode small e unicode small p unicode small a unicode small r unicode small a unicode small t unicode small i unicode small o unicode small n 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 separation subset as text unicode start of text unicode capital s unicode small e unicode small p unicode small a unicode small r unicode small a unicode small t unicode small i unicode small o unicode small n 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 separation subset as system zf infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y 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 metavar var x end metavar zermelo is metavar var y end metavar imply not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar imply metavar var s end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply metavar var s end metavar zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set end define

The user defined "the proof aspect" aspect

define proof of lemma separation subset as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y 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 metavar var x end metavar zermelo is metavar var y end metavar infer not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar infer metavar var s end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set infer lemma separation2formula modus ponens metavar var s end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set conclude not0 metavar var s end metavar zermelo in metavar var x end metavar imply not0 metavar var a end metavar cut prop lemma first conjunct modus ponens not0 metavar var s end metavar zermelo in metavar var x end metavar imply not0 metavar var a end metavar conclude metavar var s end metavar zermelo in metavar var x end metavar cut lemma set equality nec condition 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 modus ponens metavar var s end metavar zermelo in metavar var x end metavar conclude metavar var s end metavar zermelo in metavar var y end metavar cut prop lemma second conjunct modus ponens not0 metavar var s end metavar zermelo in metavar var x end metavar imply not0 metavar var a end metavar conclude metavar var a end metavar cut prop lemma iff second modus ponens not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar modus ponens metavar var a end metavar conclude metavar var b end metavar cut lemma formula2separation modus ponens metavar var s end metavar zermelo in metavar var y end metavar modus ponens metavar var b end metavar conclude metavar var s end metavar zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set cut all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed 1rule deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y 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 metavar var x end metavar zermelo is metavar var y end metavar infer not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar infer metavar var s end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set infer metavar var s end metavar zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set 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 metavar var x end metavar zermelo is metavar var y end metavar imply not0 metavar var a end metavar imply metavar var b end metavar imply not0 metavar var b end metavar imply metavar var a end metavar imply metavar var s end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply metavar var s end metavar zermelo in the set of ph in metavar var y end metavar such that metavar var b end metavar end set end quote state proof state cache var c end expand end define