Logiweb aspects of lemma nonsingletonmembersUnequal in pyk

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The predefined "pyk" aspect

define pyk of lemma nonsingletonmembersUnequal 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 n unicode small o unicode small n unicode small s unicode small i unicode small n unicode small g unicode small l unicode small e unicode small t unicode small o unicode small n unicode small m unicode small e unicode small m unicode small b unicode small e unicode small r unicode small s unicode capital u unicode small n unicode small e unicode small q unicode small u unicode small a unicode small l unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma nonsingletonmembersUnequal as text unicode start of text unicode capital n unicode small o unicode small n unicode small s unicode small i unicode small n unicode small g unicode small l unicode small e unicode small t unicode small o unicode small n unicode small m unicode small e unicode small m unicode small b unicode small e unicode small r unicode small s unicode capital u unicode small n unicode small e unicode small q unicode small u unicode small a unicode small l unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma nonsingletonmembersUnequal as system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed not0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair infer not0 metavar var sx end metavar = metavar var sy end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma nonsingletonmembersUnequal 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 metavar var sx end metavar = metavar var sy end metavar infer lemma eqReflexivity conclude metavar var sx end metavar = metavar var sx end metavar cut lemma same pair modus ponens metavar var sx end metavar = metavar var sx end metavar modus ponens metavar var sx end metavar = metavar var sy end metavar conclude zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair cut 1rule repetition modus ponens zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair conclude zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair cut lemma eqSymmetry modus ponens zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair conclude zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair cut all metavar var sx end metavar indeed all metavar var sy end metavar indeed 1rule deduction modus ponens all metavar var sx end metavar indeed all metavar var sy end metavar indeed metavar var sx end metavar = metavar var sy end metavar infer zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair conclude metavar var sx end metavar = metavar var sy end metavar imply zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair cut not0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair infer prop lemma mt modus ponens metavar var sx end metavar = metavar var sy end metavar imply zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair modus ponens not0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair conclude not0 metavar var sx end metavar = metavar var sy end metavar end quote state proof state cache var c end expand end define