Logiweb aspects of commutative imply in pyk

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The predefined "pyk" aspect

define pyk of commutative imply as text unicode start of text 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 e unicode space unicode small i unicode small m unicode small p unicode small l unicode small y unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of commutative imply as text unicode start of text unicode capital c unicode capital i unicode small m unicode small p unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of commutative imply as system prime s infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed ( ( metavar var a end metavar peano imply ( metavar var c end metavar peano imply metavar var b end metavar ) ) infer ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) end define

The user defined "the proof aspect" aspect

define proof of commutative imply as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var a end metavar indeed all metavar var b end metavar indeed all metavar var c end metavar indeed ( ( metavar var a end metavar peano imply ( metavar var c end metavar peano imply metavar var b end metavar ) ) infer ( ( axiom prime a two conclude ( ( metavar var a end metavar peano imply ( metavar var c end metavar peano imply metavar var b end metavar ) ) peano imply ( ( metavar var a end metavar peano imply metavar var c end metavar ) peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( metavar var a end metavar peano imply ( metavar var c end metavar peano imply metavar var b end metavar ) ) peano imply ( ( metavar var a end metavar peano imply metavar var c end metavar ) peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) modus ponens ( metavar var a end metavar peano imply ( metavar var c end metavar peano imply metavar var b end metavar ) ) ) conclude ( ( metavar var a end metavar peano imply metavar var c end metavar ) peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) cut ( ( ( int mvar modus ponens ( ( metavar var a end metavar peano imply metavar var c end metavar ) peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) conclude ( metavar var c end metavar peano imply ( ( metavar var a end metavar peano imply metavar var c end metavar ) peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) cut ( ( axiom prime a two conclude ( ( metavar var c end metavar peano imply ( ( metavar var a end metavar peano imply metavar var c end metavar ) peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) peano imply ( ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) ) cut ( ( ( ( rule prime mp modus ponens ( ( metavar var c end metavar peano imply ( ( metavar var a end metavar peano imply metavar var c end metavar ) peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) peano imply ( ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) ) modus ponens ( metavar var c end metavar peano imply ( ( metavar var a end metavar peano imply metavar var c end metavar ) peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) conclude ( ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) cut ( ( axiom prime a one conclude ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) cut ( ( ( rule prime mp modus ponens ( ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) modus ponens ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var c end metavar ) ) ) conclude ( metavar var c end metavar peano imply ( metavar var a end metavar peano imply metavar var b end metavar ) ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define