define pyk of lemma nonreciprocalToRight(Eq) 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 end of text end unicode text end text end define
define tex of lemma nonreciprocalToRight(Eq) 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 end of text end unicode text end text end define
define statement of lemma nonreciprocalToRight(Eq) 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 y end metavar = 0 infer metavar var x end metavar * metavar var y end metavar = metavar var z end metavar infer metavar var x end metavar = metavar var z end metavar * 1/ metavar var y end metavar end define
define proof of lemma nonreciprocalToRight(Eq) 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 y end metavar = 0 infer metavar var x end metavar * metavar var y end metavar = metavar var z end metavar infer lemma eqMultiplication modus ponens metavar var x end metavar * metavar var y end metavar = metavar var z end metavar conclude metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar = metavar var z end metavar * 1/ metavar var y end metavar 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 eqTransitivity 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 = metavar var z end metavar * 1/ metavar var y end metavar conclude metavar var x end metavar = metavar var z 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,