## Logiweb aspects of 3.2h in pyk

### The "pyk" aspect

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

### The "proof/kg" aspect

define proof of 3.2h as \ p . \ c . taceval1 ( quote PA end quote , quote Line L01 : S5 >> { x + 0 } = x ; Line L02 : 3.2f >> x = { 0 + x } ; Line L03 : { 3.2c mp L01 } mp L02 >> { x + 0 } = { 0 + x } ; Line L04 : Block >> Begin ; Line L05 : Hypothesis >> { x + y } = { y + x } ; Line L06 : S2 mp L05 >> { x + y } suc = { { y + x } suc } ; Line L07 : S6 >> { x + { y suc } } = { { x + y } suc } ; Line L08 : { 3.2c mp L07 } mp L06 >> { x + { y suc } } = { { y + x } suc } ; Line L09 : 3.2g >> { y suc + x } = { { y + x } suc } ; { { { 3.2d mp L08 } mp L09 } conclude { { x + { y suc } } = { y suc + x } } } line L11 : Block >> End ; Line L12 : { { Induction at y } ponens L03 } ponens L11 >> { x + y } = { y + x } ; { { Gen2 ponens L12 } conclude f.allfunc \ x . f.allfunc \ y . { { x + y } = { y + x } } } end quote , c ) end define

### The "unitac/kg" aspect

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

### The "statement/kg" aspect

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