define pyk of lemma set equality nec condition 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 t unicode space unicode small e unicode small q unicode small u unicode small a unicode small l unicode small i unicode small t unicode small y unicode space unicode small n unicode small e unicode small c unicode space unicode small c unicode small o unicode small n unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define
define tex of lemma set equality nec condition as text unicode start of text unicode capital f unicode small r unicode small o unicode small m unicode capital s unicode small e unicode small t unicode capital e unicode small q unicode small u unicode small a unicode small l unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define
define statement of lemma set equality nec condition 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 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 metavar var s end metavar zermelo in metavar var x end metavar infer metavar var s end metavar zermelo in metavar var y end metavar end define
define proof of lemma set equality nec condition 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 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 metavar var s end metavar zermelo in metavar var x end metavar infer axiom extensionality conclude not0 metavar var x end metavar zermelo is metavar var y end metavar imply for all objects object var var s end var indeed not0 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply not0 object var var s end var zermelo in metavar var y end metavar imply object var var s end var zermelo in metavar var x end metavar imply not0 for all objects object var var s end var indeed not0 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply not0 object var var s end var zermelo in metavar var y end metavar imply object var var s end var zermelo in metavar var x end metavar imply metavar var x end metavar zermelo is metavar var y end metavar cut prop lemma iff second modus ponens not0 metavar var x end metavar zermelo is metavar var y end metavar imply for all objects object var var s end var indeed not0 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply not0 object var var s end var zermelo in metavar var y end metavar imply object var var s end var zermelo in metavar var x end metavar imply not0 for all objects object var var s end var indeed not0 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply not0 object var var s end var zermelo in metavar var y end metavar imply object var var s end var zermelo in metavar var x end metavar imply metavar var x end metavar zermelo is metavar var y end metavar modus ponens metavar var x end metavar zermelo is metavar var y end metavar conclude for all objects object var var s end var indeed not0 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply not0 object var var s end var zermelo in metavar var y end metavar imply object var var s end var zermelo in metavar var x end metavar cut lemma set equality skip quantifier 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 conclude for all objects object var var s end var indeed not0 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply not0 object var var s end var zermelo in metavar var y end metavar imply object var var s end var zermelo in metavar var x end metavar imply not0 metavar var s end metavar zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in metavar var y end metavar imply not0 metavar var s end metavar zermelo in metavar var y end metavar imply metavar var s end metavar zermelo in metavar var x end metavar cut 1rule mp modus ponens for all objects object var var s end var indeed not0 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply not0 object var var s end var zermelo in metavar var y end metavar imply object var var s end var zermelo in metavar var x end metavar imply not0 metavar var s end metavar zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in metavar var y end metavar imply not0 metavar var s end metavar zermelo in metavar var y end metavar imply metavar var s end metavar zermelo in metavar var x end metavar modus ponens for all objects object var var s end var indeed not0 object var var s end var zermelo in metavar var x end metavar imply object var var s end var zermelo in metavar var y end metavar imply not0 object var var s end var zermelo in metavar var y end metavar imply object var var s end var zermelo in metavar var x end metavar conclude not0 metavar var s end metavar zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in metavar var y end metavar imply not0 metavar var s end metavar zermelo in metavar var y end metavar imply metavar var s end metavar zermelo in metavar var x end metavar cut prop lemma iff second modus ponens not0 metavar var s end metavar zermelo in metavar var x end metavar imply metavar var s end metavar zermelo in metavar var y end metavar imply not0 metavar var s end metavar zermelo in metavar var y end metavar imply metavar var s end metavar zermelo in metavar var x 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 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,