Logiweb aspects of lemma inPair(2) in pyk

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The predefined "pyk" aspect

define pyk of lemma inPair(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 i unicode small n 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 inPair(2) as text unicode start of text unicode capital i unicode small n 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 inPair(2) as system Q infer all metavar var sx end metavar indeed all metavar var sy end metavar indeed metavar var sy end metavar in0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair end define

The user defined "the proof aspect" aspect

define proof of lemma inPair(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 sy end metavar indeed lemma eqReflexivity conclude metavar var sy end metavar = metavar var sy end metavar cut prop lemma weaken or first modus ponens metavar var sy end metavar = metavar var sy end metavar conclude not0 metavar var sy end metavar = metavar var sx end metavar imply metavar var sy end metavar = metavar var sy end metavar cut lemma formula2pair modus ponens not0 metavar var sy end metavar = metavar var sx end metavar imply metavar var sy end metavar = metavar var sy end metavar conclude metavar var sy end metavar in0 zermelo pair metavar var sx end metavar comma metavar var sy end metavar end pair end quote state proof state cache var c end expand end define