Logiweb aspects of equal transitivity conditioned rule in pyk

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The predefined "pyk" aspect

define pyk of equal transitivity conditioned rule as text unicode start of text unicode small e unicode small q unicode small u unicode small a unicode small l 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 space unicode small c unicode small o unicode small n unicode small d unicode small i unicode small t unicode small i unicode small o unicode small n unicode small e unicode small d unicode space unicode small r unicode small u unicode small l unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of equal transitivity conditioned rule as text unicode start of text unicode capital e unicode small q unicode small u unicode small a unicode small l 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 capital c unicode small o unicode small n unicode small d unicode capital r unicode small u unicode small l unicode small e unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of equal transitivity conditioned rule as system prime s infer all metavar var a end metavar indeed all metavar var t end metavar indeed all metavar var r end metavar indeed all metavar var s end metavar indeed ( ( metavar var a end metavar peano imply ( metavar var t end metavar peano is metavar var r end metavar ) ) infer ( ( metavar var a end metavar peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) infer ( metavar var a end metavar peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of equal transitivity conditioned rule 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 t end metavar indeed all metavar var r end metavar indeed all metavar var s end metavar indeed ( ( metavar var a end metavar peano imply ( metavar var t end metavar peano is metavar var r end metavar ) ) infer ( ( metavar var a end metavar peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) infer ( ( equal transitivity conclude ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( ( metavar var r end metavar peano is metavar var s end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) cut ( ( ( weakening modus ponens ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( ( metavar var r end metavar peano is metavar var s end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) conclude ( metavar var a end metavar peano imply ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( ( metavar var r end metavar peano is metavar var s end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) ) cut ( ( ( ( double conditioned mp prime modus ponens ( metavar var a end metavar peano imply ( ( metavar var t end metavar peano is metavar var r end metavar ) peano imply ( ( metavar var r end metavar peano is metavar var s end metavar ) peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) ) modus ponens ( metavar var a end metavar peano imply ( metavar var t end metavar peano is metavar var r end metavar ) ) ) modus ponens ( metavar var a end metavar peano imply ( metavar var r end metavar peano is metavar var s end metavar ) ) ) conclude ( metavar var a end metavar peano imply ( metavar var t end metavar peano is metavar var s end metavar ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define