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axiom MyNat : Type
--notation "ℕ" => MyNat
--axiom zero : ℕ
axiom succ : ℕ → ℕ
@[instance] axiom MyOfNat (n : Nat) : OfNat ℕ n
@[instance] axiom myAddition : HAdd ℕℕℕ
@[instance] axiom myMultiplication : HMul ℕℕℕ
axiom add_zero : ∀ a : ℕ, a + 0 = a
axiom add_succ : ∀ a b : ℕ, a + succ b = succ (a + b)
@[elab_as_elim] axiom myInduction {P : ℕ → Prop} (n : ℕ) (h₀ : P 0) (h : ∀ n, P n → P (succ n)) : P n