Logiweb aspects of lemma set equality suff condition in pyk

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The predefined "pyk" aspect

define pyk of lemma set equality suff condition 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma set equality suff condition 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 end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma set equality suff condition as system zf infer all metavar var x end metavar indeed all metavar var y end metavar indeed 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 infer 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 metavar var x end metavar zermelo is metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma set equality suff condition 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 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 infer 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 prop lemma join conjuncts 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 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 1rule gen 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 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 cut axiom extensionality conclude not0 metavar var x end metavar zermelo is metavar var y end metavar imply 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 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 metavar var x end metavar zermelo is metavar var y end metavar cut prop lemma second conjunct modus ponens not0 metavar var x end metavar zermelo is metavar var y end metavar imply 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 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 metavar var x end metavar zermelo is metavar var y end metavar conclude 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 metavar var x end metavar zermelo is metavar var y end metavar cut 1rule mp modus ponens 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 metavar var x end metavar zermelo is metavar var y end metavar modus ponens 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 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