Logiweb aspects of lemma formula2pair in pyk

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The predefined "pyk" aspect

define pyk of lemma formula2pair 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 o unicode small r unicode small m unicode small u unicode small l unicode small a unicode two unicode small 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 formula2pair as text unicode start of text unicode capital f unicode small o unicode small r unicode small m unicode small u unicode small l unicode small a unicode two 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 formula2pair as system zf infer all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar infer metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair end define

The user defined "the proof aspect" aspect

define proof of lemma formula2pair as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var s end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar infer axiom pair definition conclude not0 metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair imply not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar imply not0 not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair cut prop lemma iff first modus ponens not0 metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair imply not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar imply not0 not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar imply metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair modus ponens not0 metavar var s end metavar zermelo is metavar var x end metavar imply metavar var s end metavar zermelo is metavar var y end metavar conclude metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair end quote state proof state cache var c end expand end define