define pyk of lemma leqMultiplication 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 l unicode small e unicode small q unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small i unicode small c unicode small a unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define
define tex of lemma leqMultiplication as text unicode start of text unicode small l unicode small e unicode small q unicode capital m unicode small u unicode small l unicode small t unicode small i unicode small p unicode small l unicode small i unicode small c unicode small a unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define
define statement of lemma leqMultiplication 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 0 <= metavar var z end metavar infer metavar var x end metavar <= metavar var y end metavar infer metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar end define
define proof of lemma leqMultiplication 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 0 <= metavar var z end metavar infer metavar var x end metavar <= metavar var y end metavar infer axiom leqMultiplication conclude 0 <= metavar var z end metavar imply metavar var x end metavar <= metavar var y end metavar imply metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar cut prop lemma mp2 modus ponens 0 <= metavar var z end metavar imply metavar var x end metavar <= metavar var y end metavar imply metavar var x end metavar * metavar var z end metavar <= metavar var y end metavar * metavar var z end metavar 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 end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,