define pyk of lemma distributionOutLeft 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 capital l unicode small e unicode small f unicode small t unicode end of text end unicode text end text end define
define tex of lemma distributionOutLeft 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 capital l unicode small e unicode small f unicode small t unicode end of text end unicode text end text end define
define statement of lemma distributionOutLeft 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 y end metavar * metavar var x end metavar + metavar var z end metavar * metavar var x end metavar = metavar var x end metavar * metavar var y end metavar + metavar var z end metavar end define
define proof of lemma distributionOutLeft 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 axiom timesCommutativity conclude metavar var y end metavar * metavar var x end metavar = metavar var x end metavar * metavar var y end metavar cut axiom timesCommutativity conclude metavar var z end metavar * metavar var x end metavar = metavar var x end metavar * metavar var z end metavar cut lemma addEquations modus ponens metavar var y end metavar * metavar var x end metavar = metavar var x end metavar * metavar var y end metavar modus ponens metavar var z end metavar * metavar var x end metavar = metavar var x end metavar * metavar var z end metavar conclude metavar var y end metavar * metavar var x end metavar + metavar var z end metavar * metavar var x 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 y end metavar * metavar var x end metavar + metavar var z end metavar * metavar var x 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 y end metavar * metavar var x end metavar + metavar var z end metavar * metavar var x 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,