define pyk of lemma set equality skip quantifier 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 s unicode small k unicode small i unicode small p unicode space unicode small q unicode small u unicode small a unicode small n unicode small t unicode small i unicode small f unicode small i unicode small e unicode small r unicode end of text end unicode text end text end define
define tex of lemma set equality skip quantifier as text unicode start of text unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r 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 skip quantifier 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 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 end define
define proof of lemma set equality skip quantifier 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 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 infer 1rule repetition modus ponens 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 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 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 x end metavar indeed all metavar var y end metavar 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 infer 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 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 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 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,