define pyk of lemma nonzeroFactors 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 n unicode small o unicode small n unicode small z unicode small e unicode small r unicode small o 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 nonzeroFactors as text unicode start of text unicode capital n unicode small o unicode small n unicode small z unicode small e unicode small r unicode small o 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 nonzeroFactors as system Q infer all metavar var x end metavar indeed all metavar var y end metavar indeed not0 metavar var x end metavar = 0 infer not0 metavar var y end metavar = 0 infer not0 metavar var x end metavar * metavar var y end metavar = 0 end define
define proof of lemma nonzeroFactors 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 not0 metavar var x end metavar = 0 infer not0 metavar var y end metavar = 0 infer lemma neqMultiplication modus ponens not0 metavar var y end metavar = 0 modus ponens not0 metavar var x end metavar = 0 conclude not0 metavar var x end metavar * metavar var y end metavar = 0 * metavar var y end metavar cut axiom timesCommutativity conclude 0 * metavar var y end metavar = metavar var y end metavar * 0 cut lemma x*0=0 conclude metavar var y end metavar * 0 = 0 cut lemma eqTransitivity modus ponens 0 * metavar var y end metavar = metavar var y end metavar * 0 modus ponens metavar var y end metavar * 0 = 0 conclude 0 * metavar var y end metavar = 0 cut lemma subNeqRight modus ponens 0 * metavar var y end metavar = 0 modus ponens not0 metavar var x end metavar * metavar var y end metavar = 0 * metavar var y end metavar conclude not0 metavar var x end metavar * metavar var y end metavar = 0 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,