## Logiweb aspects of Induction in pyk

### The "pyk" aspect

Define pyk of Induction as "Induction" end define

### The "proof/kg" aspect

define proof of Induction as \ p . \ c . taceval ( quote Line L01 : Premise >> PA ; All #x : All #h : All #a : All #z : All #i : Line L03 : Condition >> \ c . sub0 ( quote #z end quote , quote #a end quote , quote #x end quote , quote 0 end quote , c ) ; Line L04 : Condition >> \ c . sub0 ( quote #i end quote , quote #a end quote , quote #x end quote , quote #x suc end quote , c ) ; Line L05 : Condition >> \ c . { quote #x end quote objectavoid ( c ) quote #h end quote } ; Line L06 : Premise >> #h imply #z ; Line L07 : Premise >> #h imply { #a imply #i } ; Line L08 : { Gen1 probans L05 } ponens L07 >> #h imply f.allfunc \ #x . { #a imply #i } ; Line L09 : { S9 probans L03 } probans L04 >> #z imply { { f.allfunc \ #x . { #a imply #i } } imply #a } ; Line L10 : A1' ponens L09 >> #h imply { #z imply { { f.allfunc \ #x . { #a imply #i } } imply #a } } ; Line L11 : { A2' ponens L10 } ponens L06 >> #h imply { { f.allfunc \ #x . { #a imply #i } } imply #a } ; { { { A2' ponens L11 } ponens L08 } conclude { #h imply #a } } end quote , tacstate0 , c ) end define

### The "unitac/kg" aspect

define unitac of Induction as \ u . unitac-lemma ( u ) end define

### The "statement/kg" aspect

define statement of Induction as PA infer All #x : All #h : All #a : All #z : All #i : { { \ c . sub0 ( quote #z end quote , quote #a end quote , quote #x end quote , quote 0 end quote , c ) } endorse { { \ c . sub0 ( quote #i end quote , quote #a end quote , quote #x end quote , quote #x suc end quote , c ) } endorse { { \ c . { quote #x end quote objectavoid ( c ) quote #h end quote } } endorse { { #h imply #z } infer { { #h imply { #a imply #i } } infer { #h imply #a } } } } } } end define

The pyk compiler, version 0.1.9 by Klaus Grue,
GRD-2007-07-12.UTC:20:13:13.678589 = MJD-54293.TAI:20:13:46.678589 = LGT-4690988026678589e-6