Logiweb aspects of hypothetical inference axiom prime s two in pyk

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The predefined "pyk" aspect

define pyk of hypothetical inference axiom prime s two as text unicode start of text unicode small h unicode small y unicode small p unicode small o unicode small t unicode small h unicode small e unicode small t unicode small i unicode small c unicode small a unicode small l 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 t unicode small w unicode small o unicode end of text end unicode text end text end define

The predefined "tex" aspect

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

The user defined "the statement aspect" aspect

define statement of hypothetical inference axiom prime s two as system prime s infer all metavar var h end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed ( ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var b end metavar ) ) infer ( metavar var h end metavar peano imply ( metavar var a end metavar peano succ peano is ( metavar var b end metavar peano succ ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of hypothetical inference axiom prime s two as lambda var c dot lambda var x dot proof expand quote system prime s infer all metavar var h end metavar indeed all metavar var a end metavar indeed all metavar var b end metavar indeed ( ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var b end metavar ) ) infer ( ( mendelson lemma one eight conclude ( metavar var h end metavar peano imply metavar var h end metavar ) ) cut ( ( axiom prime s two conclude ( ( metavar var a end metavar peano is metavar var b end metavar ) peano imply ( metavar var a end metavar peano succ peano is ( metavar var b end metavar peano succ ) ) ) ) cut ( ( ( inference axiom prime a one modus ponens ( ( metavar var a end metavar peano is metavar var b end metavar ) peano imply ( metavar var a end metavar peano succ peano is ( metavar var b end metavar peano succ ) ) ) ) conclude ( metavar var h end metavar peano imply ( ( metavar var a end metavar peano is metavar var b end metavar ) peano imply ( metavar var a end metavar peano succ peano is ( metavar var b end metavar peano succ ) ) ) ) ) cut ( ( ( ( inference inference axiom prime a two modus ponens ( metavar var h end metavar peano imply ( ( metavar var a end metavar peano is metavar var b end metavar ) peano imply ( metavar var a end metavar peano succ peano is ( metavar var b end metavar peano succ ) ) ) ) ) modus ponens ( metavar var h end metavar peano imply ( metavar var a end metavar peano is metavar var b end metavar ) ) ) conclude ( metavar var h end metavar peano imply ( metavar var a end metavar peano succ peano is ( metavar var b end metavar peano succ ) ) ) ) cut ( ( inference mendelson lemma one eight modus ponens ( metavar var h end metavar peano imply ( metavar var a end metavar peano succ peano is ( metavar var b end metavar peano succ ) ) ) ) conclude ( metavar var h end metavar peano imply ( metavar var a end metavar peano succ peano is ( metavar var b end metavar peano succ ) ) ) ) ) ) ) ) ) end quote state proof state cache var c end expand end define