Logiweb aspects of lemma union subset in pyk

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The predefined "pyk" aspect

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

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

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

The user defined "the proof aspect" aspect

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