define pyk of lemma x+y=zBackwards 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 x unicode plus sign unicode small y unicode equal sign unicode small z unicode capital b unicode small a unicode small c unicode small k unicode small w unicode small a unicode small r unicode small d unicode small s unicode end of text end unicode text end text end define
define tex of lemma x+y=zBackwards as text unicode start of text unicode small x unicode plus sign unicode small y unicode equal sign unicode small z unicode capital b unicode small a unicode small c unicode small k unicode small w unicode small a unicode small r unicode small d unicode small s unicode end of text end unicode text end text end define
define statement of lemma x+y=zBackwards 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 infer metavar var z end metavar = metavar var y end metavar + metavar var x end metavar end define
define proof of lemma x+y=zBackwards 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 metavar var x end metavar + metavar var y end metavar = metavar var z end metavar infer axiom plusCommutativity conclude metavar var x end metavar + metavar var y end metavar = metavar var y end metavar + metavar var x end metavar cut lemma equality modus ponens metavar var x end metavar + metavar var y end metavar = metavar var z end metavar conclude metavar var z end metavar = metavar var y 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,