define pyk of lemma set equality suff condition(t) 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 u unicode small f unicode small f 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 left parenthesis unicode small t unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma set equality suff condition(t) as text unicode start of text unicode capital t unicode small o 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 left parenthesis unicode small t unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma set equality suff condition(t) as system zf infer all metavar var x end metavar indeed all metavar var y end metavar indeed quote object var var t end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var y end metavar end quote endorse object var var t end var zermelo in metavar var x end metavar imply object var var t end var zermelo in metavar var y end metavar infer object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar infer metavar var x end metavar zermelo is metavar var y end metavar end define
define proof of lemma set equality suff condition(t) 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 quote object var var t end var end quote avoid zero quote metavar var x end metavar end quote endorse quote object var var t end var end quote avoid zero quote metavar var y end metavar end quote endorse object var var t end var zermelo in metavar var x end metavar imply object var var t end var zermelo in metavar var y end metavar infer object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar infer 1rule gen modus ponens object var var t end var zermelo in metavar var x end metavar imply object var var t end var zermelo in metavar var y end metavar conclude for all objects object var var t end var indeed object var var t end var zermelo in metavar var x end metavar imply object var var t end var zermelo in metavar var y end metavar cut lemma set equality suff condition(t)0 modus probans quote object var var t end var end quote avoid zero quote metavar var x end metavar end quote modus probans quote object var var t end var end quote avoid zero quote metavar var y end metavar end quote conclude for all objects object var var t end var indeed object var var t end var zermelo in metavar var x end metavar imply object var var t end var zermelo in metavar var y end metavar imply 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 cut 1rule mp modus ponens for all objects object var var t end var indeed object var var t end var zermelo in metavar var x end metavar imply object var var t end var zermelo in metavar var y end metavar imply 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 modus ponens for all objects object var var t end var indeed object var var t end var zermelo in metavar var x end metavar imply object var var t end var zermelo in metavar var y end metavar conclude 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 cut 1rule gen modus ponens object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar conclude for all objects object var var t end var indeed object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar cut lemma set equality suff condition(t)0 modus probans quote object var var t end var end quote avoid zero quote metavar var y end metavar end quote modus probans quote object var var t end var end quote avoid zero quote metavar var x end metavar end quote conclude for all objects object var var t end var indeed object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar imply 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 1rule mp modus ponens for all objects object var var t end var indeed object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar imply 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 modus ponens for all objects object var var t end var indeed object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar conclude 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 suff condition modus ponens 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 modus ponens 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 metavar var x end metavar zermelo is 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,