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

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The predefined "pyk" aspect

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

The predefined "tex" aspect

define tex of lemma set equality suff condition(t) 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 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) 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 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 y end metavar imply object var var t 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(t) 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 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 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 y end metavar imply object var var t end var zermelo in metavar var x end metavar infer 1rule gen 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 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 cut lemma set equality suff condition(t)0 modus probans quote object var var t end var end quote avoid zero quote metavar var x end metavar end quote modus probans quote object var var t end var end quote avoid zero quote metavar var y end metavar end quote conclude 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 cut 1rule mp modus ponens 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 modus ponens 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 conclude 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 cut 1rule gen modus ponens object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar conclude for all objects object var var t end var indeed object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar cut lemma set equality suff condition(t)0 modus probans quote object var var t end var end quote avoid zero quote metavar var y end metavar end quote modus probans quote object var var t end var end quote avoid zero quote metavar var x end metavar end quote conclude for all objects object var var t end var indeed object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar imply 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 mp modus ponens for all objects object var var t end var indeed object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar imply 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 modus ponens for all objects object var var t end var indeed object var var t end var zermelo in metavar var y end metavar imply object var var t end var zermelo in metavar var x end metavar conclude 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 lemma set equality suff condition 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 metavar var x end metavar zermelo is metavar var y end metavar end quote state proof state cache var c end expand end define