Logiweb aspects of lemma singletonmembersEqual in pyk

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The predefined "pyk" aspect

define pyk of lemma singletonmembersEqual 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 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 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 singletonmembersEqual as text unicode start of text unicode capital 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 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 singletonmembersEqual 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 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair infer metavar var sx end metavar = metavar var sy end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma singletonmembersEqual 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 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair infer lemma inPair(1) conclude metavar var sx end metavar in0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair cut lemma set equality nec condition(1) modus ponens zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair modus ponens metavar var sx end metavar in0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair conclude metavar var sx end metavar in0 zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair cut lemma fromSingleton modus ponens metavar var sx end metavar in0 zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair conclude metavar var sx end metavar = metavar var sz end metavar cut lemma inPair(2) conclude metavar var sy end metavar in0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair cut lemma set equality nec condition(1) modus ponens zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair modus ponens metavar var sy end metavar in0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair conclude metavar var sy end metavar in0 zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair cut lemma fromSingleton modus ponens metavar var sy end metavar in0 zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair conclude metavar var sy end metavar = metavar var sz end metavar cut lemma eqSymmetry modus ponens metavar var sy end metavar = metavar var sz end metavar conclude metavar var sz end metavar = metavar var sy end metavar cut lemma eqTransitivity modus ponens metavar var sx end metavar = metavar var sz end metavar modus ponens metavar var sz end metavar = metavar var sy end metavar conclude metavar var sx end metavar = metavar var sy end metavar end quote state proof state cache var c end expand end define