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import NNG.MyNat.Theorems.Addition
namespace MyNat
open MyNat
axiom succ_inj {a b : ℕ} : succ a = succ b → a = b
axiom zero_ne_succ (a : ℕ) : zero ≠ succ a
axiom add_right_cancel (a t b : ℕ) : a + t = b + t → a = b
axiom add_left_cancel (a b c : ℕ) : a + b = a + c → b = c