Logiweb aspects of imply transitivity in pyk

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The predefined "pyk" aspect

define pyk of imply transitivity as text unicode start of text unicode small i unicode small m unicode small p unicode small l unicode small y unicode space unicode small t unicode small r unicode small a unicode small n unicode small s unicode small i 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 imply transitivity as text unicode start of text unicode capital i unicode small m unicode small p unicode small l unicode small y unicode capital t unicode small r unicode small a unicode small n unicode small s unicode small i 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 imply transitivity as system prime s infer all metavar var d end metavar indeed all metavar var e end metavar indeed all metavar var f end metavar indeed ( ( metavar var d end metavar peano imply metavar var e end metavar ) infer ( ( metavar var e end metavar peano imply metavar var f end metavar ) infer ( metavar var d end metavar peano imply metavar var f end metavar ) ) ) end define

The user defined "the proof aspect" aspect

define proof of imply transitivity as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var d end metavar indeed all metavar var e end metavar indeed all metavar var f end metavar indeed ( ( metavar var d end metavar peano imply metavar var e end metavar ) infer ( ( metavar var e end metavar peano imply metavar var f end metavar ) infer ( ( ( weakening modus ponens ( metavar var e end metavar peano imply metavar var f end metavar ) ) conclude ( metavar var d end metavar peano imply ( metavar var e end metavar peano imply metavar var f end metavar ) ) ) cut ( ( ( conditioned mp prime modus ponens ( metavar var d end metavar peano imply ( metavar var e end metavar peano imply metavar var f end metavar ) ) ) modus ponens ( metavar var d end metavar peano imply metavar var e end metavar ) ) conclude ( metavar var d end metavar peano imply metavar var f end metavar ) ) ) ) ) end quote state proof state cache var c end expand end define