Logiweb aspects of lemma neqMultiplication in pyk

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The predefined "pyk" aspect

define pyk of lemma neqMultiplication 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 n unicode small e unicode small q unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small i unicode small c unicode small a unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma neqMultiplication as text unicode start of text unicode capital n unicode small e unicode small q unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small i unicode small c unicode small a unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma neqMultiplication as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed not0 metavar var z end metavar = 0 infer not0 metavar var x end metavar = metavar var y end metavar infer not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma neqMultiplication as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed not0 metavar var z end metavar = 0 infer not0 metavar var x end metavar = metavar var y end metavar infer metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar infer lemma x=x*y*(1/y) modus ponens not0 metavar var z end metavar = 0 conclude metavar var x end metavar = metavar var x end metavar * metavar var z end metavar * 1/ metavar var z end metavar cut lemma eqMultiplication modus ponens metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar conclude metavar var x end metavar * metavar var z end metavar * 1/ metavar var z end metavar = metavar var y end metavar * metavar var z end metavar * 1/ metavar var z end metavar cut lemma x=x*y*(1/y) modus ponens not0 metavar var z end metavar = 0 conclude metavar var y end metavar = metavar var y end metavar * metavar var z end metavar * 1/ metavar var z end metavar cut lemma eqSymmetry modus ponens metavar var y end metavar = metavar var y end metavar * metavar var z end metavar * 1/ metavar var z end metavar conclude metavar var y end metavar * metavar var z end metavar * 1/ metavar var z end metavar = metavar var y end metavar cut lemma eqTransitivity4 modus ponens metavar var x end metavar = metavar var x end metavar * metavar var z end metavar * 1/ metavar var z end metavar modus ponens metavar var x end metavar * metavar var z end metavar * 1/ metavar var z end metavar = metavar var y end metavar * metavar var z end metavar * 1/ metavar var z end metavar modus ponens metavar var y end metavar * metavar var z end metavar * 1/ metavar var z end metavar = metavar var y end metavar conclude metavar var x end metavar = metavar var y end metavar cut prop lemma from contradiction modus ponens metavar var x end metavar = metavar var y end metavar modus ponens not0 metavar var x end metavar = metavar var y end metavar conclude not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar cut all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed 1rule deduction modus ponens all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed not0 metavar var z end metavar = 0 infer not0 metavar var x end metavar = metavar var y end metavar infer metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar infer not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar conclude not0 metavar var z end metavar = 0 imply not0 metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar imply not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar cut not0 metavar var z end metavar = 0 infer not0 metavar var x end metavar = metavar var y end metavar infer prop lemma mp2 modus ponens not0 metavar var z end metavar = 0 imply not0 metavar var x end metavar = metavar var y end metavar imply metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar imply not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar modus ponens not0 metavar var z end metavar = 0 modus ponens not0 metavar var x end metavar = metavar var y end metavar conclude metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar imply not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar cut prop lemma imply negation modus ponens metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar imply not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar conclude not0 metavar var x end metavar * metavar var z end metavar = metavar var y end metavar * metavar var z end metavar end quote state proof state cache var c end expand end define