define pyk of lemma plus00 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 zero unicode end of text end unicode text end text end define
define tex of lemma plus00 as text unicode start of text unicode capital p unicode small l unicode small u unicode small s unicode zero unicode zero unicode end of text end unicode text end text end define
define statement of lemma plus00 as system Q infer all metavar var fx end metavar indeed R( var fx +f var fy ) == R( metavar var fx end metavar ) end define
define proof of lemma plus00 as lambda var c dot lambda var x dot proof expand quote system Q infer all metavar var fx end metavar indeed lemma plus0f conclude metavar var fx end metavar +f 0f =f metavar var fx end metavar cut lemma =f to sameF modus ponens metavar var fx end metavar +f 0f =f metavar var fx end metavar conclude metavar var fx end metavar +f 0f sameF metavar var fx end metavar cut lemma f2R(Plus) modus ponens metavar var fx end metavar +f 0f sameF metavar var fx end metavar conclude R( var fx +f var fy ) == R( metavar var fx end metavar ) cut 1rule repetition modus ponens R( var fx +f var fy ) == R( metavar var fx end metavar ) conclude R( var fx +f var fy ) == R( metavar var fx end metavar ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20060417+ by Klaus Grue,