Logiweb aspects of lemma fromSameSingleton in pyk

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The predefined "pyk" aspect

define pyk of lemma fromSameSingleton 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 f unicode small r unicode small o unicode small m unicode capital s unicode small a unicode small m unicode small e 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromSameSingleton as text unicode start of text unicode capital f unicode small r unicode small o unicode small m unicode capital s unicode small a unicode small m unicode small e 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 end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma fromSameSingleton as system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sy end metavar comma metavar var sy 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 fromSameSingleton 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 zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair infer lemma eqReflexivity conclude metavar var sx end metavar = metavar var sx end metavar cut lemma toSingleton modus ponens metavar var sx end metavar = metavar var sx end metavar conclude metavar var sx end metavar in0 zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair cut lemma set equality nec condition(1) modus ponens zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair modus ponens metavar var sx end metavar in0 zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair conclude metavar var sx end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair cut lemma fromSingleton modus ponens metavar var sx end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair conclude metavar var sx end metavar = metavar var sy end metavar end quote state proof state cache var c end expand end define