define pyk of lemma x=x*y*(1/y) 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 x unicode equal sign unicode small x unicode asterisk unicode small y unicode asterisk unicode left parenthesis unicode one unicode slash unicode small y unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma x=x*y*(1/y) as text unicode start of text unicode small x unicode equal sign unicode small x unicode asterisk unicode small y unicode asterisk unicode left parenthesis unicode one unicode slash unicode small y unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma x=x*y*(1/y) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var y end metavar = 0 infer metavar var x end metavar = metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar end define
define proof of lemma x=x*y*(1/y) 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 not0 metavar var y end metavar = 0 infer axiom times1 conclude metavar var x end metavar * 1 = metavar var x end metavar cut lemma reciprocal modus ponens not0 metavar var y end metavar = 0 conclude metavar var y end metavar * 1/ metavar var y end metavar = 1 cut lemma three2twoFactors modus ponens metavar var y end metavar * 1/ metavar var y end metavar = 1 conclude metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar = metavar var x end metavar * 1 cut lemma eqTransitivity modus ponens metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar = metavar var x end metavar * 1 modus ponens metavar var x end metavar * 1 = metavar var x end metavar conclude metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar = metavar var x end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar * metavar var y end metavar * 1/ metavar var y end metavar = metavar var x end metavar conclude metavar var x end metavar = metavar var x end metavar * metavar var y 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,