Logiweb aspects of lemma toSingleton in pyk

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The predefined "pyk" aspect

define pyk of lemma toSingleton 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 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 toSingleton as text unicode start of text unicode capital t unicode small o 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 toSingleton as 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 metavar var sx end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair end define

The user defined "the proof aspect" aspect

define proof of lemma toSingleton 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 prop lemma weaken or first modus ponens metavar var sx end metavar = metavar var sy end metavar conclude not0 metavar var sx end metavar = metavar var sy end metavar imply metavar var sx end metavar = metavar var sy end metavar cut lemma formula2pair modus ponens not0 metavar var sx end metavar = metavar var sy end metavar imply metavar var sx end metavar = metavar var sy end metavar conclude metavar var sx end metavar in0 zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair cut 1rule repetition 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 in0 zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair end quote state proof state cache var c end expand end define