Description: Peano postulate: 0s is a non-negative surreal integer. (Contributed by Scott Fenton, 17-Mar-2025)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 0n0s | |- 0s e. NN0_s | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | df-n0s | |- NN0_s = ( rec ( ( x e. _V |-> ( x +s 1s ) ) , 0s ) " _om ) | |
| 2 | 1 | a1i | |- ( T. -> NN0_s = ( rec ( ( x e. _V |-> ( x +s 1s ) ) , 0s ) " _om ) ) | 
| 3 | 0sno | |- 0s e. No | |
| 4 | 3 | a1i | |- ( T. -> 0s e. No ) | 
| 5 | 2 4 | noseq0 | |- ( T. -> 0s e. NN0_s ) | 
| 6 | 5 | mptru | |- 0s e. NN0_s |