define pyk of lemma plus0Left 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 p unicode small l unicode small u unicode small s unicode zero 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 plus0Left as text unicode start of text unicode small p unicode small l unicode small u unicode small s unicode zero 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 plus0Left as system Q infer all metavar var x end metavar indeed 0 + metavar var x end metavar = metavar var x end metavar end define
define proof of lemma plus0Left as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var x end metavar indeed axiom plus0 conclude metavar var x end metavar + 0 = metavar var x end metavar cut axiom plusCommutativity conclude 0 + metavar var x end metavar = metavar var x end metavar + 0 cut lemma eqTransitivity modus ponens 0 + metavar var x end metavar = metavar var x end metavar + 0 modus ponens metavar var x end metavar + 0 = metavar var x end metavar conclude 0 + metavar var x end metavar = metavar var x end metavar end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,