define pyk of plus commutativity base 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 b unicode small a unicode small s unicode small e unicode end of text end unicode text end text end define
define tex of plus commutativity base 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 b unicode small a unicode small s unicode small e unicode end of text end unicode text end text end define
define statement of plus commutativity base as system prime s infer ( ( var t peano var peano plus peano zero ) peano is ( peano zero peano plus ( var t peano var ) ) ) end define
define proof of plus commutativity base as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( axiom prime s five conclude ( ( var t peano var peano plus peano zero ) peano is ( var t peano var ) ) ) cut ( ( mendelson three two f conclude ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) ) cut ( ( ( equal transitivity rule modus ponens ( ( var t peano var peano plus peano zero ) peano is ( var t peano var ) ) ) modus ponens ( var t peano var peano is ( peano zero peano plus ( var t peano var ) ) ) ) conclude ( ( var t peano var peano plus peano zero ) peano is ( peano zero 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,