define pyk of lemma intersection 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 i unicode small n unicode small t unicode small e unicode small r unicode small s unicode small e unicode small c 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 intersection subset as text unicode start of text unicode capital i unicode small n unicode small t unicode small e unicode small r unicode small s unicode small e unicode small c 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 intersection 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 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 not0 metavar var s end metavar zermelo in metavar var x end metavar imply not0 metavar var s end metavar zermelo in metavar var v end metavar imply not0 metavar var s end metavar zermelo in metavar var y end metavar imply not0 metavar var s end metavar zermelo in metavar var w end metavar end define
define proof of lemma intersection 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 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 not0 metavar var s end metavar zermelo in metavar var x end metavar imply not0 metavar var s end metavar zermelo in metavar var v end metavar infer prop lemma first conjunct modus ponens not0 metavar var s end metavar zermelo in metavar var x end metavar imply not0 metavar var s end metavar zermelo in metavar var v 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 s end metavar zermelo in metavar var v end metavar conclude metavar var s end metavar zermelo in metavar var v end metavar cut lemma set equality nec condition 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 modus ponens metavar var s end metavar zermelo in metavar var v end metavar conclude metavar var s end metavar zermelo in metavar var w end metavar cut prop lemma join conjuncts modus ponens metavar var s end metavar zermelo in metavar var y end metavar modus ponens metavar var s end metavar zermelo in metavar var w end metavar conclude not0 metavar var s end metavar zermelo in metavar var y end metavar imply not0 metavar var s end metavar zermelo in metavar var w end metavar 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 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 not0 metavar var s end metavar zermelo in metavar var x end metavar imply not0 metavar var s end metavar zermelo in metavar var v end metavar infer not0 metavar var s end metavar zermelo in metavar var y end metavar imply not0 metavar var s end metavar zermelo in metavar var w end metavar 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 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 not0 metavar var s end metavar zermelo in metavar var x end metavar imply not0 metavar var s end metavar zermelo in metavar var v end metavar imply not0 metavar var s end metavar zermelo in metavar var y end metavar imply not0 metavar var s end metavar zermelo in metavar var w end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,