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
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
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
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
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,