Logiweb aspects of inference inference axiom prime s one in pyk

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The predefined "pyk" aspect

define pyk of inference inference axiom prime s one as text unicode start of text unicode small i unicode small n unicode small f unicode small e unicode small r unicode small e unicode small n unicode small c unicode small e unicode space unicode small i unicode small n unicode small f unicode small e unicode small r unicode small e unicode small n unicode small c unicode small e unicode space unicode small a unicode small x unicode small i unicode small o unicode small m unicode space unicode small p unicode small r unicode small i unicode small m unicode small e unicode space unicode small s unicode space unicode small o unicode small n unicode small e unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of inference inference axiom prime s one as text unicode start of text unicode capital s unicode one unicode apostrophe unicode underscore unicode left brace unicode small i unicode small i unicode right brace unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of inference inference axiom prime s one 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 is metavar var b end metavar ) infer ( ( metavar var a end metavar peano is metavar var c end metavar ) infer ( metavar var b end metavar peano is metavar var c end metavar ) ) ) end define

The user defined "the proof aspect" aspect

define proof of inference inference axiom prime s one 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 is metavar var b end metavar ) infer ( ( metavar var a end metavar peano is metavar var c end metavar ) infer ( ( ( inference axiom prime s one modus ponens ( metavar var a end metavar peano is metavar var b end metavar ) ) conclude ( ( metavar var a end metavar peano is metavar var c end metavar ) peano imply ( metavar var b end metavar peano is metavar var c end metavar ) ) ) cut ( ( ( rule prime mp modus ponens ( ( metavar var a end metavar peano is metavar var c end metavar ) peano imply ( metavar var b end metavar peano is metavar var c end metavar ) ) ) modus ponens ( metavar var a end metavar peano is metavar var c end metavar ) ) conclude ( metavar var b end metavar peano is metavar var c end metavar ) ) ) ) ) end quote state proof state cache var c end expand end define