Logiweb aspects of lemma same union in pyk

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The predefined "pyk" aspect

define pyk of lemma same union 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 a unicode small m unicode small e unicode space unicode small u unicode small n unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma same union as text unicode start of text unicode capital s unicode small a unicode small m unicode small e unicode capital u unicode small n unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma same union as system zf infer 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 union metavar var x end metavar end union zermelo is union metavar var y end metavar end union end define

The user defined "the proof aspect" aspect

define proof of lemma same union 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 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 lemma union subset 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 metavar var x end metavar zermelo is metavar var y end metavar imply object var var s end var zermelo in union metavar var x end metavar end union imply object var var s end var zermelo in union metavar var y end metavar end union cut 1rule mp modus ponens metavar var x end metavar zermelo is metavar var y end metavar imply object var var s end var zermelo in union metavar var x end metavar end union imply object var var s end var zermelo in union metavar var y end metavar end union modus ponens metavar var x end metavar zermelo is metavar var y end metavar conclude object var var s end var zermelo in union metavar var x end metavar end union imply object var var s end var zermelo in union metavar var y end metavar end union cut lemma =symmetry 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 conclude metavar var y end metavar zermelo is metavar var x end metavar cut lemma union subset modus probans quote object var var s end var end quote avoid zero quote metavar var y end metavar end quote modus probans quote object var var s end var end quote avoid zero quote metavar var x end metavar end quote conclude metavar var y end metavar zermelo is metavar var x end metavar imply object var var s end var zermelo in union metavar var y end metavar end union imply object var var s end var zermelo in union metavar var x end metavar end union cut 1rule mp modus ponens metavar var y end metavar zermelo is metavar var x end metavar imply object var var s end var zermelo in union metavar var y end metavar end union imply object var var s end var zermelo in union metavar var x end metavar end union modus ponens metavar var y end metavar zermelo is metavar var x end metavar conclude object var var s end var zermelo in union metavar var y end metavar end union imply object var var s end var zermelo in union metavar var x end metavar end union cut lemma set equality suff condition modus ponens object var var s end var zermelo in union metavar var x end metavar end union imply object var var s end var zermelo in union metavar var y end metavar end union modus ponens object var var s end var zermelo in union metavar var y end metavar end union imply object var var s end var zermelo in union metavar var x end metavar end union conclude union metavar var x end metavar end union zermelo is union metavar var y end metavar end union end quote state proof state cache var c end expand end define