define pyk of lemma three2threeFactors 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 h unicode small r unicode small e unicode small e unicode two unicode small t unicode small h unicode small r unicode small e unicode small e unicode capital f unicode small a unicode small c unicode small t unicode small o unicode small r unicode small s unicode end of text end unicode text end text end define
define tex of lemma three2threeFactors as text unicode start of text unicode capital t unicode small h unicode small r unicode small e unicode small e unicode two unicode small t unicode small h unicode small r unicode small e unicode small e unicode capital f unicode small a unicode small c unicode small t unicode small o unicode small r unicode small s unicode end of text end unicode text end text end define
define statement of lemma three2threeFactors 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 z end metavar = metavar var x end metavar * metavar var z end metavar * metavar var y end metavar end define
define proof of lemma three2threeFactors 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 z end metavar = metavar var z end metavar * metavar var y end metavar cut lemma three2twoFactors modus ponens metavar var y end metavar * metavar var z end metavar = metavar var z end metavar * metavar var y end metavar conclude metavar var x end metavar * metavar var y end metavar * metavar var z end metavar = metavar var x end metavar * metavar var z end metavar * metavar var y end metavar cut axiom timesAssociativity conclude metavar var x end metavar * metavar var z end metavar * metavar var y end metavar = metavar var x end metavar * metavar var z end metavar * metavar var y end metavar cut lemma eqSymmetry modus ponens metavar var x end metavar * metavar var z end metavar * metavar var y end metavar = metavar var x end metavar * metavar var z end metavar * metavar var y end metavar conclude metavar var x end metavar * metavar var z end metavar * metavar var y end metavar = metavar var x end metavar * metavar var z end metavar * metavar var y end metavar cut lemma eqTransitivity modus ponens metavar var x end metavar * metavar var y end metavar * metavar var z end metavar = metavar var x end metavar * metavar var z end metavar * metavar var y end metavar modus ponens metavar var x end metavar * metavar var z end metavar * metavar var y end metavar = metavar var x end metavar * metavar var z end metavar * metavar var y end metavar conclude metavar var x end metavar * metavar var y end metavar * metavar var z end metavar = metavar var x end metavar * metavar var z 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,