define pyk of lemma times(-1) 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 t unicode small i unicode small m unicode small e unicode small s unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma times(-1) as text unicode start of text unicode capital t unicode small i unicode small m unicode small e unicode small s unicode left parenthesis unicode hyphen unicode one unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma times(-1) as system Q infer all metavar var x end metavar indeed metavar var x end metavar * - 1 = - metavar var x end metavar end define
define proof of lemma times(-1) as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed axiom negative conclude 1 + - 1 = 0 cut axiom plusCommutativity conclude - 1 + 1 = 1 + - 1 cut lemma eqTransitivity modus ponens - 1 + 1 = 1 + - 1 modus ponens 1 + - 1 = 0 conclude - 1 + 1 = 0 cut lemma eqMultiplicationLeft modus ponens - 1 + 1 = 0 conclude metavar var x end metavar * - 1 + 1 = metavar var x end metavar * 0 cut lemma x*0=0 conclude metavar var x end metavar * 0 = 0 cut lemma eqTransitivity modus ponens metavar var x end metavar * - 1 + 1 = metavar var x end metavar * 0 modus ponens metavar var x end metavar * 0 = 0 conclude metavar var x end metavar * - 1 + 1 = 0 cut axiom distribution conclude metavar var x end metavar * - 1 + 1 = metavar var x end metavar * - 1 + metavar var x end metavar * 1 cut lemma eqSymmetry modus ponens metavar var x end metavar * - 1 + 1 = metavar var x end metavar * - 1 + metavar var x end metavar * 1 conclude metavar var x end metavar * - 1 + metavar var x end metavar * 1 = metavar var x end metavar * - 1 + 1 cut lemma eqTransitivity modus ponens metavar var x end metavar * - 1 + metavar var x end metavar * 1 = metavar var x end metavar * - 1 + 1 modus ponens metavar var x end metavar * - 1 + 1 = 0 conclude metavar var x end metavar * - 1 + metavar var x end metavar * 1 = 0 cut lemma positiveToRight(Eq) modus ponens metavar var x end metavar * - 1 + metavar var x end metavar * 1 = 0 conclude metavar var x end metavar * - 1 = 0 + - metavar var x end metavar * 1 cut lemma plus0Left conclude 0 + - metavar var x end metavar * 1 = - metavar var x end metavar * 1 cut lemma eqTransitivity modus ponens metavar var x end metavar * - 1 = 0 + - metavar var x end metavar * 1 modus ponens 0 + - metavar var x end metavar * 1 = - metavar var x end metavar * 1 conclude metavar var x end metavar * - 1 = - metavar var x end metavar * 1 cut axiom times1 conclude metavar var x end metavar * 1 = metavar var x end metavar cut lemma eqNegated modus ponens metavar var x end metavar * 1 = metavar var x end metavar conclude - metavar var x end metavar * 1 = - metavar var x end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar * - 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 * - 1 = - 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,