Logiweb aspects of lemma orderedPairEquality in pyk

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The predefined "pyk" aspect

define pyk of lemma orderedPairEquality 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 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 capital e unicode small q unicode small u unicode small a unicode small l unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma orderedPairEquality as text unicode start of text 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 capital e unicode small q unicode small u unicode small a unicode small l unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma orderedPairEquality 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 all metavar var sz end metavar indeed all metavar var sz1 end metavar indeed all metavar var su end metavar indeed all metavar var su1 end metavar indeed 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 sx1 end metavar end pair end pair = zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma metavar var sy1 end metavar end pair end pair infer zermelo pair zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair comma zermelo pair metavar var sz end metavar comma metavar var sz1 end metavar end pair end pair = zermelo pair zermelo pair metavar var su end metavar comma metavar var su end metavar end pair comma zermelo pair metavar var su end metavar comma metavar var su1 end metavar end pair end pair infer metavar var sx end metavar = metavar var sz end metavar infer metavar var sy end metavar = metavar var su end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma orderedPairEquality 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 all metavar var sz end metavar indeed all metavar var sz1 end metavar indeed all metavar var su end metavar indeed all metavar var su1 end metavar indeed 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 sx1 end metavar end pair end pair = zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma metavar var sy1 end metavar end pair end pair infer zermelo pair zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair comma zermelo pair metavar var sz end metavar comma metavar var sz1 end metavar end pair end pair = zermelo pair zermelo pair metavar var su end metavar comma metavar var su end metavar end pair comma zermelo pair metavar var su end metavar comma metavar var su1 end metavar end pair end pair infer metavar var sx end metavar = metavar var sz end metavar infer lemma fromOrderedPair(1) 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 sx1 end metavar end pair end pair = zermelo pair zermelo pair metavar var sy end metavar comma metavar var sy end metavar end pair comma zermelo pair metavar var sy end metavar comma metavar var sy1 end metavar end pair end pair conclude metavar var sx end metavar = metavar var sy end metavar cut lemma eqSymmetry modus ponens metavar var sx end metavar = metavar var sy end metavar conclude metavar var sy end metavar = metavar var sx end metavar cut lemma fromOrderedPair(1) modus ponens zermelo pair zermelo pair metavar var sz end metavar comma metavar var sz end metavar end pair comma zermelo pair metavar var sz end metavar comma metavar var sz1 end metavar end pair end pair = zermelo pair zermelo pair metavar var su end metavar comma metavar var su end metavar end pair comma zermelo pair metavar var su end metavar comma metavar var su1 end metavar end pair end pair conclude metavar var sz end metavar = metavar var su end metavar cut lemma eqTransitivity4 modus ponens metavar var sy end metavar = metavar var sx end metavar modus ponens metavar var sx end metavar = metavar var sz end metavar modus ponens metavar var sz end metavar = metavar var su end metavar conclude metavar var sy end metavar = metavar var su end metavar end quote state proof state cache var c end expand end define