define pyk of lemma plusTimesMinus 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 p unicode small l unicode small u unicode small s unicode capital t unicode small i unicode small m unicode small e unicode small s unicode capital m unicode small i unicode small n unicode small u unicode small s unicode end of text end unicode text end text end define
define tex of lemma plusTimesMinus as text unicode start of text unicode capital p unicode small l unicode small u unicode small s unicode capital t unicode small i unicode small m unicode small e unicode small s unicode capital m unicode small i unicode small n unicode small u unicode small s unicode end of text end unicode text end text end define
define statement of lemma plusTimesMinus as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed metavar var x end metavar * - metavar var y end metavar = - metavar var x end metavar * metavar var y end metavar end define
define proof of lemma plusTimesMinus 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 lemma times(-1)Left conclude - 1 * metavar var y end metavar = - metavar var y end metavar cut lemma eqMultiplicationLeft modus ponens - 1 * metavar var y end metavar = - metavar var y end metavar conclude metavar var x end metavar * - 1 * metavar var y end metavar = metavar var x end metavar * - metavar var y end metavar cut axiom timesAssociativity conclude metavar var x end metavar * - 1 * metavar var y end metavar = metavar var x end metavar * - 1 * metavar var y end metavar cut axiom timesCommutativity conclude metavar var x end metavar * - 1 = - 1 * metavar var x end metavar cut lemma eqMultiplication modus ponens metavar var x end metavar * - 1 = - 1 * metavar var x end metavar conclude metavar var x end metavar * - 1 * metavar var y end metavar = - 1 * metavar var x end metavar * metavar var y end metavar cut axiom timesAssociativity conclude - 1 * metavar var x end metavar * metavar var y end metavar = - 1 * metavar var x end metavar * metavar var y end metavar cut lemma times(-1)Left conclude - 1 * metavar var x end metavar * metavar var y end metavar = - metavar var x end metavar * metavar var y end metavar cut lemma eqTransitivity4 modus ponens metavar var x end metavar * - 1 * metavar var y end metavar = - 1 * metavar var x end metavar * metavar var y end metavar modus ponens - 1 * metavar var x end metavar * metavar var y end metavar = - 1 * metavar var x end metavar * metavar var y end metavar modus ponens - 1 * metavar var x end metavar * metavar var y end metavar = - metavar var x end metavar * metavar var y end metavar conclude metavar var x end metavar * - 1 * metavar var y end metavar = - metavar var x end metavar * metavar var y end metavar cut lemma equality modus ponens metavar var x end metavar * - 1 * metavar var y end metavar = - metavar var x end metavar * metavar var y end metavar modus ponens metavar var x end metavar * - 1 * metavar var y end metavar = metavar var x end metavar * - 1 * metavar var y end metavar conclude - metavar var x end metavar * metavar var y end metavar = metavar var x end metavar * - 1 * metavar var y end metavar cut lemma eqTransitivity modus ponens - metavar var x end metavar * metavar var y end metavar = metavar var x end metavar * - 1 * metavar var y end metavar modus ponens metavar var x end metavar * - 1 * metavar var y end metavar = metavar var x end metavar * - metavar var y end metavar conclude - metavar var x end metavar * metavar var y end metavar = metavar var x end metavar * - metavar var y end metavar cut lemma eqSymmetry modus ponens - metavar var x end metavar * metavar var y end metavar = metavar var x end metavar * - metavar var y end metavar conclude metavar var x end metavar * - metavar var y end metavar = - metavar var x end metavar * 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,