Logiweb aspects of lemma pair2formula in pyk

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The predefined "pyk" aspect

define pyk of lemma pair2formula 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 p unicode small a unicode small i unicode small r unicode two unicode small f unicode small o unicode small r unicode small m unicode small u unicode small l unicode small a unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma pair2formula as text unicode start of text unicode capital p unicode small a unicode small i unicode small r unicode two unicode capital f unicode small o unicode small r unicode small m unicode small u unicode small l unicode small a unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma pair2formula 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 metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair infer 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 end define

The user defined "the proof aspect" aspect

define proof of lemma pair2formula 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 metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair 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 second 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 metavar var s end metavar zermelo in zermelo pair metavar var x end metavar comma metavar var y end metavar end pair conclude 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 end quote state proof state cache var c end expand end define