Logiweb aspects of lemma unequalsNotInSingleton in pyk

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The predefined "pyk" aspect

define pyk of lemma unequalsNotInSingleton 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 u unicode small n unicode small e unicode small q unicode small u unicode small a unicode small l unicode small s unicode capital n unicode small o unicode small t unicode capital i unicode small n 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 unequalsNotInSingleton as text unicode start of text unicode capital u unicode small n unicode small e unicode small q unicode small u unicode small a unicode small l unicode small s unicode capital n unicode small o unicode small t unicode capital i unicode small n 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 unequalsNotInSingleton 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 not0 metavar var sx end metavar = metavar var sy end metavar infer not0 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 end define

The user defined "the proof aspect" aspect

define proof of lemma unequalsNotInSingleton 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 singletonmembersEqual 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 conclude metavar var sx end metavar = metavar var sy end metavar cut all metavar var sx end metavar indeed all metavar var sy end metavar indeed all metavar var sz end metavar indeed 1rule deduction modus ponens 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 conclude 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 imply metavar var sx end metavar = metavar var sy end metavar cut not0 metavar var sx end metavar = metavar var sy end metavar infer prop lemma mt 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 imply metavar var sx end metavar = metavar var sy end metavar modus ponens not0 metavar var sx end metavar = metavar var sy end metavar conclude not0 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 end quote state proof state cache var c end expand end define