## Logiweb aspects of 3.2e in pyk

### The "pyk" aspect

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

### The "proof/kg" aspect

define proof of 3.2e as \ p . \ c . taceval1 ( quote PA end quote , quote Line L01 : Block >> Begin ; Line L02 : Hypothesis >> x = y ; Line L03 : S5 >> { x + 0 } = x ; Line L04 : { 3.2c mp L03 } mp L02 >> { x + 0 } = y ; Line L05 : S5 >> { y + 0 } = y ; { { { 3.2d mp L04 } mp L05 } conclude { { x + 0 } = { y + 0 } } } line L07 : Block >> End ; Line L08 : Block >> Begin ; Line L09 : Hypothesis >> { x = y } imply { { x + z } = { y + z } } ; Line L10 : Hypothesis >> x = y ; Line L11 : { MP' ponens L09 } ponens L10 >> { x + z } = { y + z } ; Line L12 : S2 mp L11 >> { x + z } suc = { { y + z } suc } ; Line L13 : S6 >> { x + { z suc } } = { { x + z } suc } ; Line L14 : { 3.2c mp L13 } mp L12 >> { x + { z suc } } = { { y + z } suc } ; Line L15 : S6 >> { y + { z suc } } = { { y + z } suc } ; { { { 3.2d mp L14 } mp L15 } conclude { { x + { z suc } } = { y + { z suc } } } } line L17 : Block >> End ; Line L18 : { { Induction at z } ponens L07 } ponens L17 >> { x = y } imply { { x + z } = { y + z } } ; { { Gen3 ponens L18 } conclude f.allfunc \ x . f.allfunc \ y . f.allfunc \ z . { { x = y } imply { { x + z } = { y + z } } } } end quote , c ) end define

### The "unitac/kg" aspect

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

### The "statement/kg" aspect

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