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
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
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
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
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,