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import NNG.MyNat.Multiplication
namespace MyNat
def le (a b : ℕ) := ∃ (c : ℕ), b = a + c
-- Another choice is to define it recursively:
-- | le 0 _
-- | le (succ a) (succ b) = le ab
-- notation
instance : LE MyNat := ⟨MyNat.le⟩
--@[leakage] theorem le_def' : MyNat.le = (≤) := rfl
theorem le_iff_exists_add (a b : ℕ) : a ≤ b ↔ ∃ (c : ℕ), b = a + c := Iff.rfl
end MyNat