define pyk of lemma nonreciprocalToLeft(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 l unicode small e unicode small f 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 nonreciprocalToLeft(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 l unicode small e unicode small f 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 nonreciprocalToLeft(Eq)(1 term) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed 1 = metavar var x end metavar * metavar var y end metavar infer 1/ metavar var y end metavar = metavar var x end metavar end define
define proof of lemma nonreciprocalToLeft(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 1 = metavar var x end metavar * metavar var y end metavar infer lemma eqSymmetry modus ponens 1 = metavar var x end metavar * metavar var y end metavar conclude metavar var x end metavar * metavar var y end metavar = 1 cut lemma nonreciprocalToRight(Eq)(1 term) modus ponens metavar var x end metavar * metavar var y end metavar = 1 conclude metavar var x end metavar = 1/ metavar var y end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar = 1/ metavar var y end metavar conclude 1/ metavar var y end metavar = metavar var x end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,