Logiweb aspects of lemma sameOrderedPair in pyk

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The predefined "pyk" aspect

define pyk of lemma sameOrderedPair 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 a unicode small m unicode small e unicode capital o unicode small r unicode small d unicode small e unicode small r unicode small e unicode small d unicode capital p unicode small a unicode small i unicode small r unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma sameOrderedPair as text unicode start of text unicode small s unicode small a unicode small m unicode small e unicode capital o unicode small r unicode small d unicode small e unicode small r unicode small e unicode small d unicode capital p unicode small a unicode small i unicode small r unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma sameOrderedPair as system Q infer all metavar var sx end metavar indeed all metavar var sx1 end metavar indeed all metavar var sy end metavar indeed all metavar var sy1 end metavar indeed metavar var sx end metavar = metavar var sx1 end metavar infer metavar var sy end metavar = metavar var sy1 end metavar infer zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair end pair = zermelo pair zermelo pair metavar var sx1 end metavar comma metavar var sx1 end metavar end pair comma zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair end pair end define

The user defined "the proof aspect" aspect

define proof of lemma sameOrderedPair 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 sx1 end metavar indeed all metavar var sy end metavar indeed all metavar var sy1 end metavar indeed metavar var sx end metavar = metavar var sx1 end metavar infer metavar var sy end metavar = metavar var sy1 end metavar infer lemma same singleton modus ponens metavar var sx end metavar = metavar var sx1 end metavar conclude zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sx1 end metavar comma metavar var sx1 end metavar end pair cut lemma same pair modus ponens metavar var sx end metavar = metavar var sx1 end metavar modus ponens metavar var sy end metavar = metavar var sy1 end metavar conclude zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair cut lemma same pair modus ponens zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair = zermelo pair metavar var sx1 end metavar comma metavar var sx1 end metavar end pair modus ponens zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair = zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair conclude zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair end pair = zermelo pair zermelo pair metavar var sx1 end metavar comma metavar var sx1 end metavar end pair comma zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair end pair cut 1rule repetition modus ponens zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair end pair = zermelo pair zermelo pair metavar var sx1 end metavar comma metavar var sx1 end metavar end pair comma zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair end pair conclude zermelo pair zermelo pair metavar var sx end metavar comma metavar var sx end metavar end pair comma zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair end pair = zermelo pair zermelo pair metavar var sx1 end metavar comma metavar var sx1 end metavar end pair comma zermelo pair metavar var sx1 end metavar comma metavar var sy1 end metavar end pair end pair end quote state proof state cache var c end expand end define