define pyk of lemma x*0+x=x 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 asterisk unicode zero unicode plus sign unicode small x unicode equal sign unicode small x unicode end of text end unicode text end text end define
define tex of lemma x*0+x=x as text unicode start of text unicode small x unicode asterisk unicode zero unicode plus sign unicode small x unicode equal sign unicode small x unicode end of text end unicode text end text end define
define statement of lemma x*0+x=x as system Q infer all metavar var x end metavar indeed metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar end define
define proof of lemma x*0+x=x as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed axiom times1 conclude metavar var x end metavar * 1 = metavar var x end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar * 1 = metavar var x end metavar conclude metavar var x end metavar = metavar var x end metavar * 1 cut lemma eqAdditionLeft modus ponens metavar var x end metavar = metavar var x end metavar * 1 conclude metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar * 0 + metavar var x end metavar * 1 cut axiom distribution conclude metavar var x end metavar * 0 + 1 = metavar var x end metavar * 0 + metavar var x end metavar * 1 cut lemma eqSymmetry modus ponens metavar var x end metavar * 0 + 1 = metavar var x end metavar * 0 + metavar var x end metavar * 1 conclude metavar var x end metavar * 0 + metavar var x end metavar * 1 = metavar var x end metavar * 0 + 1 cut lemma plus0Left conclude 0 + 1 = 1 cut lemma eqMultiplicationLeft modus ponens 0 + 1 = 1 conclude metavar var x end metavar * 0 + 1 = metavar var x end metavar * 1 cut lemma eqTransitivity5 modus ponens metavar var x end metavar * 0 + metavar var x end metavar = metavar var x end metavar * 0 + metavar var x end metavar * 1 modus ponens metavar var x end metavar * 0 + metavar var x end metavar * 1 = metavar var x end metavar * 0 + 1 modus ponens metavar var x end metavar * 0 + 1 = 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 * 0 + metavar var x 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,