define pyk of lemma union 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 u unicode small n 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 union subset as text unicode start of text unicode capital u unicode small n 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 union 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 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 metavar var s end metavar zermelo in union metavar var x end metavar end union imply metavar var s end metavar zermelo in union metavar var y end metavar end union end define
define proof of lemma union 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 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 union metavar var x end metavar end union infer lemma union2formula modus ponens metavar var s end metavar zermelo in union metavar var x end metavar end union conclude not0 metavar var s end metavar zermelo in existential var var j end var imply not0 existential var var j end var zermelo in metavar var x end metavar cut prop lemma first conjunct modus ponens not0 metavar var s end metavar zermelo in existential var var j end var imply not0 existential var var j end var zermelo in metavar var x end metavar conclude metavar var s end metavar zermelo in existential var var j end var cut prop lemma second conjunct modus ponens not0 metavar var s end metavar zermelo in existential var var j end var imply not0 existential var var j end var zermelo in metavar var x end metavar conclude existential var var j end var 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 existential var var j end var zermelo in metavar var x end metavar conclude existential var var j end var zermelo in metavar var y end metavar cut lemma formula2union modus ponens metavar var s end metavar zermelo in existential var var j end var modus ponens existential var var j end var zermelo in metavar var y end metavar conclude metavar var s end metavar zermelo in union metavar var y end metavar end union 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 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 union metavar var x end metavar end union infer metavar var s end metavar zermelo in union metavar var y end metavar end union 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 metavar var s end metavar zermelo in union metavar var x end metavar end union imply metavar var s end metavar zermelo in union metavar var y end metavar end union end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,