## Logiweb aspects of 3.2g in pyk

### The "pyk" aspect

Define pyk of 3.2g as "3.2g" end define

### The "proof/kg" aspect

define proof of 3.2g as \ p . \ c . taceval1 ( quote PA end quote , quote Line L01 : S5 >> { x suc + 0 } = { x suc } ; Line L02 : S5 >> { x + 0 } = x ; Line L03 : S2 mp L02 >> { x + 0 } suc = { x suc } ; Line L04 : { 3.2d mp L01 } mp L03 >> { x suc + 0 } = { { x + 0 } suc } ; Line L05 : Block >> Begin ; Line L06 : Hypothesis >> { x suc + y } = { { x + y } suc } ; Line L07 : S2 mp L06 >> { x suc + y } suc = { { x + y } suc suc } ; Line L08 : S6 >> { x suc + { y suc } } = { { x suc + y } suc } ; Line L09 : { 3.2c mp L08 } mp L07 >> { x suc + { y suc } } = { { x + y } suc suc } ; Line L10 : S6 >> { x + { y suc } } = { { x + y } suc } ; Line L11 : S2 mp L10 >> { x + { y suc } } suc = { { x + y } suc suc } ; { { { 3.2d mp L09 } mp L11 } conclude { { x suc + { y suc } } = { { x + { y suc } } suc } } } line L13 : Block >> End ; Line L14 : { { Induction at y } ponens L04 } ponens L13 >> { x suc + y } = { { x + y } suc } ; { { Gen2 ponens L14 } conclude f.allfunc \ x . f.allfunc \ y . { { x suc + y } = { { x + y } suc } } } end quote , c ) end define

### The "unitac/kg" aspect

define unitac of 3.2g as \ u . unitac-lemma ( u ) end define

### The "statement/kg" aspect

define statement of 3.2g as PA infer f.allfunc \ x . f.allfunc \ y . { { x suc + y } = { { x + y } suc } } 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