define pyk of lemma multiplyEquations(Leq) 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 m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small y unicode capital e unicode small q unicode small u unicode small a unicode small t unicode small i unicode small o unicode small n unicode small s unicode left parenthesis unicode capital l unicode small e unicode small q unicode right parenthesis unicode end of text end unicode text end text end define
define tex of lemma multiplyEquations(Leq) as text unicode start of text unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small y unicode capital e unicode small q unicode small u unicode small a unicode small t unicode small i unicode small o unicode small n unicode small s unicode left parenthesis unicode capital l unicode small e unicode small q unicode right parenthesis unicode end of text end unicode text end text end define
define statement of lemma multiplyEquations(Leq) 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 all metavar var u end metavar indeed 0 <= metavar var x end metavar infer 0 <= metavar var z end metavar infer metavar var x end metavar <= metavar var y end metavar infer metavar var z end metavar <= metavar var u end metavar infer metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var u end metavar end define
define proof of lemma multiplyEquations(Leq) 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 all metavar var u end metavar indeed 0 <= metavar var x end metavar infer 0 <= metavar var z end metavar infer metavar var x end metavar <= metavar var y end metavar infer metavar var z end metavar <= metavar var u end metavar infer lemma leqMultiplication modus ponens 0 <= metavar var z end metavar modus ponens metavar var x 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 z end metavar cut lemma leqTransitivity modus ponens 0 <= metavar var x end metavar modus ponens metavar var x end metavar <= metavar var y end metavar conclude 0 <= metavar var y end metavar cut lemma leqMultiplicationLeft modus ponens 0 <= metavar var y end metavar modus ponens metavar var z end metavar <= metavar var u end metavar conclude metavar var y end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var u end metavar cut lemma leqTransitivity modus ponens metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar modus ponens metavar var y end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var u end metavar conclude metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var u end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,