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 |