Logiweb aspects of lemma fromOrderedPair(2) in pyk

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The predefined "pyk" aspect

define pyk of lemma fromOrderedPair(2) 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 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 left parenthesis unicode two unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma fromOrderedPair(2) as text unicode start of text unicode capital f unicode small r unicode small o unicode small m 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 left parenthesis unicode two unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma fromOrderedPair(2) 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 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 infer metavar var sy end metavar = metavar var sy1 end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma fromOrderedPair(2) 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 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 infer lemma fromOrderedPair 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 not0 metavar var sx end metavar = metavar var sx1 end metavar imply not0 metavar var sy end metavar = metavar var sy1 end metavar cut prop lemma second conjunct modus ponens not0 metavar var sx end metavar = metavar var sx1 end metavar imply not0 metavar var sy end metavar = metavar var sy1 end metavar conclude metavar var sy end metavar = metavar var sy1 end metavar end quote state proof state cache var c end expand end define