Definition nat_norm := (Nat.add_0_r, Nat.add_succ_r, Nat.sub_0_r, Nat.mul_1_r, Nat.div_1_r).

Lemma divides_frac_diff {m n} : m mod (n + 1) = 0 -> (m * (n + 2) / (n + 1) - m) * (1 + n) = m.