Logiweb aspects of lemma nonreciprocalToRight(Eq)(1 term) in pyk

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The predefined "pyk" aspect

define pyk of lemma nonreciprocalToRight(Eq)(1 term) 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 o unicode small n unicode small r unicode small e unicode small c unicode small i unicode small p unicode small r unicode small o unicode small c unicode small a unicode small l unicode capital t unicode small o unicode capital r unicode small i unicode small g unicode small h unicode small t unicode left parenthesis unicode capital e unicode small q unicode right parenthesis unicode left parenthesis unicode one unicode space unicode small t unicode small e unicode small r unicode small m unicode right parenthesis unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of lemma nonreciprocalToRight(Eq)(1 term) as text unicode start of text unicode capital n unicode small o unicode small n unicode small r unicode small e unicode small c unicode small i unicode small p unicode small r unicode small o unicode small c unicode small a unicode small l unicode capital t unicode small o unicode capital r unicode small i unicode small g unicode small h unicode small t unicode left parenthesis unicode capital e unicode small q unicode right parenthesis unicode left parenthesis unicode one unicode space unicode small t unicode small e unicode small r unicode small m unicode right parenthesis unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of lemma nonreciprocalToRight(Eq)(1 term) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar * metavar var y end metavar = 1 infer metavar var x end metavar = 1/ metavar var y end metavar end define

The user defined "the proof aspect" aspect

define proof of lemma nonreciprocalToRight(Eq)(1 term) 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 metavar var x end metavar * metavar var y end metavar = 1 infer lemma eqMultiplication modus ponens metavar var x end metavar * metavar var y end metavar = 1 conclude metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar = 1 * 1/ metavar var y end metavar cut lemma 0<1 conclude not0 0 <= 1 imply not0 not0 0 = 1 cut lemma positiveNonzero modus ponens not0 0 <= 1 imply not0 not0 0 = 1 conclude not0 1 = 0 cut lemma eqSymmetry modus ponens metavar var x end metavar * metavar var y end metavar = 1 conclude 1 = metavar var x end metavar * metavar var y end metavar cut lemma subNeqLeft modus ponens 1 = metavar var x end metavar * metavar var y end metavar modus ponens not0 1 = 0 conclude not0 metavar var x end metavar * metavar var y end metavar = 0 cut lemma nonzeroProduct(2) modus ponens not0 metavar var x end metavar * metavar var y end metavar = 0 conclude not0 metavar var y end metavar = 0 cut lemma x=x*y*(1/y) modus ponens not0 metavar var y end metavar = 0 conclude metavar var x end metavar = metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar cut lemma times1Left conclude 1 * 1/ metavar var y end metavar = 1/ metavar var y end metavar cut lemma eqTransitivity4 modus ponens metavar var x end metavar = metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar modus ponens metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar = 1 * 1/ metavar var y end metavar modus ponens 1 * 1/ metavar var y end metavar = 1/ metavar var y end metavar conclude metavar var x end metavar = 1/ metavar var y end metavar end quote state proof state cache var c end expand end define