define pyk of plus commutativity induction as text unicode start of text unicode small p unicode small l unicode small u unicode small s unicode space unicode small c unicode small o unicode small m unicode small m unicode small u unicode small t unicode small a unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode space unicode small i unicode small n unicode small d unicode small u unicode small c 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 plus commutativity induction as text unicode start of text unicode capital p unicode small l unicode small u unicode small s unicode capital c unicode small o unicode small m unicode small m unicode small u unicode small t unicode small a unicode small t unicode small i unicode small v unicode small i unicode small t unicode small y unicode capital i unicode small n unicode small d unicode small u unicode end of text end unicode text end text end define
define statement of plus commutativity induction as system prime s infer ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( var r peano var peano succ peano plus ( var t peano var ) ) ) ) end define
define proof of plus commutativity induction as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( axiom prime s two conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( axiom prime s six conclude ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) cut ( ( ( weakening modus ponens ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) ) cut ( ( ( ( equal transitivity conditioned rule modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var t peano var peano plus ( var r peano var ) ) peano succ ) ) ) ) modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var ) ) peano succ peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( mendelson three two g rt switch conclude ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) cut ( ( ( weakening modus ponens ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) cut ( ( ( mendelson three two d conditioned rule modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) modus ponens ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var r peano var peano succ peano plus ( var t peano var ) ) peano is ( ( var r peano var peano plus ( var t peano var ) ) peano succ ) ) ) ) conclude ( ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) peano imply ( ( var t peano var peano plus ( var r peano var peano succ ) ) peano is ( var r peano var peano succ peano plus ( var t peano var ) ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define
The pyk compiler, version 0.grue.20050603 by Klaus Grue,