define pyk of lemma distributionOut(Minus) 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 d unicode small i unicode small s unicode small t unicode small r unicode small i unicode small b unicode small u unicode small t unicode small i unicode small o unicode small n unicode capital o unicode small u unicode small t unicode left parenthesis unicode capital m unicode small i unicode small n unicode small u unicode small s unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma distributionOut(Minus) as text unicode start of text unicode capital d unicode small i unicode small s unicode small t unicode small r unicode small i unicode small b unicode small u unicode small t unicode small i unicode small o unicode small n unicode capital o unicode small u unicode small t unicode left parenthesis unicode capital m unicode small i unicode small n unicode small u unicode small s unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma distributionOut(Minus) as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed all metavar var z end metavar indeed metavar var x end metavar * metavar var y end metavar + - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + - metavar var z end metavar end define
define proof of lemma distributionOut(Minus) 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 all metavar var z end metavar indeed lemma times(-1)Left conclude - 1 * metavar var x end metavar * metavar var z end metavar = - metavar var x end metavar * metavar var z end metavar cut lemma eqSymmetry modus ponens - 1 * metavar var x end metavar * metavar var z end metavar = - metavar var x end metavar * metavar var z end metavar conclude - metavar var x end metavar * metavar var z end metavar = - 1 * metavar var x end metavar * metavar var z end metavar cut axiom timesCommutativity conclude - 1 * metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var z end metavar * - 1 cut axiom timesAssociativity conclude metavar var x end metavar * metavar var z end metavar * - 1 = metavar var x end metavar * metavar var z end metavar * - 1 cut lemma times(-1) conclude metavar var z end metavar * - 1 = - metavar var z end metavar cut lemma eqMultiplicationLeft modus ponens metavar var z end metavar * - 1 = - metavar var z end metavar conclude metavar var x end metavar * metavar var z end metavar * - 1 = metavar var x end metavar * - metavar var z end metavar cut lemma eqTransitivity5 modus ponens - metavar var x end metavar * metavar var z end metavar = - 1 * metavar var x end metavar * metavar var z end metavar modus ponens - 1 * metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var z end metavar * - 1 modus ponens metavar var x end metavar * metavar var z end metavar * - 1 = metavar var x end metavar * metavar var z end metavar * - 1 modus ponens metavar var x end metavar * metavar var z end metavar * - 1 = metavar var x end metavar * - metavar var z end metavar conclude - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * - metavar var z end metavar cut lemma eqAdditionLeft modus ponens - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * - metavar var z end metavar conclude metavar var x end metavar * metavar var y end metavar + - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * - metavar var z end metavar cut lemma distributionOut conclude metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * - metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + - metavar var z end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar * metavar var y end metavar + - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * - metavar var z end metavar modus ponens metavar var x end metavar * metavar var y end metavar + metavar var x end metavar * - metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + - metavar var z end metavar conclude metavar var x end metavar * metavar var y end metavar + - metavar var x end metavar * metavar var z end metavar = metavar var x end metavar * metavar var y end metavar + - metavar var z end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,