Logiweb aspects of inference inference axiom prime s nine in pyk

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The predefined "pyk" aspect

define pyk of inference inference axiom prime s nine 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 n unicode small i 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 nine as text unicode start of text unicode capital s unicode nine 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 nine 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 all metavar var y end metavar indeed ( peano sub metavar var b end metavar is metavar var a end metavar where metavar var y end metavar is peano zero end sub endorse ( peano sub metavar var c end metavar is metavar var a end metavar where metavar var y end metavar is metavar var y end metavar peano succ end sub endorse ( metavar var b end metavar infer ( ( peano all metavar var y end metavar indeed ( metavar var a end metavar peano imply metavar var c end metavar ) ) infer peano all metavar var y end metavar indeed metavar var a end metavar ) ) ) ) end define

The user defined "the proof aspect" aspect

define proof of inference inference axiom prime s nine 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 all metavar var y end metavar indeed ( peano sub metavar var b end metavar is metavar var a end metavar where metavar var y end metavar is peano zero end sub endorse ( peano sub metavar var c end metavar is metavar var a end metavar where metavar var y end metavar is metavar var y end metavar peano succ end sub endorse ( metavar var b end metavar infer ( ( peano all metavar var y end metavar indeed ( metavar var a end metavar peano imply metavar var c end metavar ) ) infer ( ( ( ( axiom prime s nine modus probans peano sub metavar var b end metavar is metavar var a end metavar where metavar var y end metavar is peano zero end sub ) modus probans peano sub metavar var c end metavar is metavar var a end metavar where metavar var y end metavar is metavar var y end metavar peano succ end sub ) conclude ( metavar var b end metavar peano imply ( ( peano all metavar var y end metavar indeed ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply peano all metavar var y end metavar indeed metavar var a end metavar ) ) ) cut ( ( ( ( double rule prime mp modus ponens ( metavar var b end metavar peano imply ( ( peano all metavar var y end metavar indeed ( metavar var a end metavar peano imply metavar var c end metavar ) ) peano imply peano all metavar var y end metavar indeed metavar var a end metavar ) ) ) modus ponens metavar var b end metavar ) modus ponens peano all metavar var y end metavar indeed ( metavar var a end metavar peano imply metavar var c end metavar ) ) conclude peano all metavar var y end metavar indeed metavar var a end metavar ) ) ) ) ) ) end quote state proof state cache var c end expand end define