Logiweb aspects of rule induction in pyk

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The predefined "pyk" aspect

define pyk of rule induction as text unicode start of text unicode small r unicode small u unicode small l unicode small e unicode space unicode small i unicode small n unicode small d unicode small u unicode small c unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The predefined "tex" aspect

define tex of rule induction as text unicode start of text unicode capital i unicode small n unicode small d unicode small u unicode small c unicode small t unicode small i unicode small o unicode small n unicode end of text end unicode text end text end define

The user defined "the statement aspect" aspect

define statement of rule induction 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 ( peano sub quote metavar var a end metavar end quote is quote metavar var a end metavar end quote where quote metavar var y end metavar end quote is quote metavar var y end metavar end quote end sub endorse ( metavar var b end metavar infer ( ( metavar var a end metavar peano imply metavar var c end metavar ) infer metavar var a end metavar ) ) ) ) ) end define

The user defined "the proof aspect" aspect

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