Logiweb aspects of lemma separation2formula in pyk

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The predefined "pyk" aspect

define pyk of lemma separation2formula 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 s unicode small e unicode small p unicode small a unicode small r unicode small a unicode small t unicode small i unicode small o unicode small n 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 separation2formula as text unicode start of text unicode capital s unicode small e unicode small p 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 separation2formula as system zf infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var p end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var p end metavar is placeholder-var and ph-sub0 quote metavar var b end metavar end quote is quote metavar var a end metavar end quote where quote metavar var p end metavar end quote is quote metavar var y end metavar end quote end sub endorse metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set infer not0 metavar var y end metavar zermelo in metavar var x end metavar imply not0 metavar var b end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma separation2formula as lambda var c dot lambda var x dot proof expand quote system zf infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var p end metavar indeed all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var p end metavar is placeholder-var and ph-sub0 quote metavar var b end metavar end quote is quote metavar var a end metavar end quote where quote metavar var p end metavar end quote is quote metavar var y end metavar end quote end sub endorse metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set infer axiom separation definition modus probans metavar var p end metavar is placeholder-var and ph-sub0 quote metavar var b end metavar end quote is quote metavar var a end metavar end quote where quote metavar var p end metavar end quote is quote metavar var y end metavar end quote end sub conclude not0 metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply not0 metavar var y end metavar zermelo in metavar var x end metavar imply not0 metavar var b end metavar imply not0 not0 metavar var y end metavar zermelo in metavar var x end metavar imply not0 metavar var b end metavar imply metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set cut prop lemma first conjunct modus ponens not0 metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply not0 metavar var y end metavar zermelo in metavar var x end metavar imply not0 metavar var b end metavar imply not0 not0 metavar var y end metavar zermelo in metavar var x end metavar imply not0 metavar var b end metavar imply metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set conclude metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply not0 metavar var y end metavar zermelo in metavar var x end metavar imply not0 metavar var b end metavar cut 1rule mp modus ponens metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set imply not0 metavar var y end metavar zermelo in metavar var x end metavar imply not0 metavar var b end metavar modus ponens metavar var y end metavar zermelo in the set of ph in metavar var x end metavar such that metavar var a end metavar end set conclude not0 metavar var y end metavar zermelo in metavar var x end metavar imply not0 metavar var b end metavar end quote state proof state cache var c end expand end define