Logiweb aspects of lemma toBinaryUnion(1) in pyk

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The predefined "pyk" aspect

define pyk of lemma toBinaryUnion(1) 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 t unicode small o unicode capital b unicode small i unicode small n unicode small a unicode small r unicode small y unicode capital u unicode small n unicode small i unicode small o unicode small n unicode left parenthesis unicode one unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma toBinaryUnion(1) as text unicode start of text unicode capital t unicode small o unicode capital b unicode small i unicode small n unicode small a unicode small r unicode small y unicode capital u unicode small n unicode small i unicode small o unicode small n unicode left parenthesis unicode one 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 toBinaryUnion(1) as system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed metavar var sx end metavar in0 metavar var sy end metavar infer metavar var sx end metavar in0 U( zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair ) end define

The user defined "the proof aspect" aspect

define proof of lemma toBinaryUnion(1) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed all metavar var su end metavar indeed metavar var sx end metavar in0 metavar var sy end metavar infer lemma inPair(1) conclude metavar var sy end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair cut prop lemma join conjuncts modus ponens metavar var sx end metavar in0 metavar var sy end metavar modus ponens metavar var sy end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair conclude not0 metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sy end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair cut pred lemma intro exist at metavar var sy end metavar modus ponens not0 metavar var sx end metavar in0 metavar var sy end metavar imply not0 metavar var sy end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair conclude not0 for all objects metavar var su end metavar indeed not0 not0 metavar var sx end metavar in0 metavar var su end metavar imply not0 metavar var su end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair cut lemma formula2union modus ponens not0 for all objects metavar var su end metavar indeed not0 not0 metavar var sx end metavar in0 metavar var su end metavar imply not0 metavar var su end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair conclude metavar var sx end metavar in0 U( zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair ) cut 1rule repetition modus ponens metavar var sx end metavar in0 U( zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair ) conclude metavar var sx end metavar in0 U( zermelo pair metavar var sy end metavar comma metavar var sz end metavar end pair ) end quote state proof state cache var c end expand end define