Logiweb aspects of lemma set equality suff condition(t)0 in pyk

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The predefined "pyk" aspect

define pyk of lemma set equality suff condition(t)0 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 zero unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma set equality suff condition(t)0 as text unicode start of text unicode capital h unicode small e unicode small l unicode small p unicode small e unicode small r 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

The user defined "the statement aspect" aspect

define statement of lemma set equality suff condition(t)0 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 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 end define

The user defined "the proof aspect" aspect

define proof of lemma set equality suff condition(t)0 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 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 1rule repetition 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 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 all metavar var x end metavar indeed all metavar var y end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar 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 infer 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 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 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 end quote state proof state cache var c end expand end define