Logiweb aspects of plus commutativity in pyk

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The predefined "pyk" aspect

define pyk of plus commutativity 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 end of text end unicode text end text end define

The predefined "tex" aspect

define tex of plus commutativity 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 end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of plus commutativity 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 ) ) ) end define

The user defined "the proof aspect" aspect

define proof of plus commutativity as lambda var c dot lambda var x dot proof expand quote system prime s infer ( ( plus commutativity base conclude ( ( var t peano var peano plus peano zero ) peano is ( peano zero peano plus ( var t peano var ) ) ) ) cut ( ( plus commutativity induction 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 ) ) ) ) ) cut ( ( ( induction macro modus ponens ( ( var t peano var peano plus peano zero ) peano is ( peano zero peano plus ( var t peano var ) ) ) ) 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 succ peano plus ( var t peano var ) ) ) ) ) conclude ( ( var t peano var peano plus ( var r peano var ) ) peano is ( var r peano var peano plus ( var t peano var ) ) ) ) ) ) end quote state proof state cache var c end expand end define