Logiweb aspects of prop lemma and commutativity in pyk

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The predefined "pyk" aspect

define pyk of prop lemma and commutativity as text unicode start of text unicode small p unicode small r unicode small o unicode small p unicode space unicode small l unicode small e unicode small m unicode small m unicode small a unicode space unicode small a unicode small n unicode small d unicode space unicode small c unicode small o unicode small m unicode small m unicode small u unicode small t unicode small a unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of prop lemma and commutativity as text unicode start of text unicode capital a unicode small n unicode small d unicode capital c unicode small o unicode small m unicode small m unicode small u unicode small t unicode small a unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of prop lemma and commutativity as system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed not0 metavar var a end metavar imply not0 metavar var b end metavar infer not0 metavar var b end metavar imply not0 metavar var a end metavar end define

The user defined "the proof aspect" aspect

define proof of prop lemma and commutativity as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var b end metavar imply not0 metavar var a end metavar infer metavar var a end metavar infer prop lemma add double neg modus ponens metavar var a end metavar conclude not0 not0 metavar var a end metavar cut prop lemma mt modus ponens metavar var b end metavar imply not0 metavar var a end metavar modus ponens not0 not0 metavar var a end metavar conclude not0 metavar var b end metavar cut all metavar var a end metavar indeed all metavar var b end metavar indeed 1rule deduction modus ponens all metavar var a end metavar indeed all metavar var b end metavar indeed metavar var b end metavar imply not0 metavar var a end metavar infer metavar var a end metavar infer not0 metavar var b end metavar conclude metavar var b end metavar imply not0 metavar var a end metavar imply metavar var a end metavar imply not0 metavar var b end metavar cut not0 metavar var a end metavar imply not0 metavar var b end metavar infer 1rule repetition conclude not0 metavar var a end metavar imply not0 metavar var b end metavar cut prop lemma mt modus ponens metavar var b end metavar imply not0 metavar var a end metavar imply metavar var a end metavar imply not0 metavar var b end metavar modus ponens not0 metavar var a end metavar imply not0 metavar var b end metavar conclude not0 metavar var b end metavar imply not0 metavar var a end metavar cut 1rule repetition modus ponens not0 metavar var b end metavar imply not0 metavar var a end metavar conclude not0 metavar var b end metavar imply not0 metavar var a end metavar end quote state proof state cache var c end expand end define