Metamath Proof Explorer


Definition df-zs

Description: Define the surreal integers. Compare dfz2 . (Contributed by Scott Fenton, 17-May-2025)

Ref Expression
Assertion df-zs ℤs = ( -s “ ( ℕs × ℕs ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 czs ⊢ ℤs
1 csubs ⊢ -s
2 cnns ⊢ ℕs
3 2 2 cxp ⊢ ( ℕs × ℕs )
4 1 3 cima ⊢ ( -s “ ( ℕs × ℕs ) )
5 0 4 wceq ⊢ ℤs = ( -s “ ( ℕs × ℕs ) )