proposition: Lemma sum_mul_carry : forall xh xl yh yl wc cc, [|wc|]*wB^2 + [[cc]] = [|xh|] * [|yl|] + [|xl|] * [|yh|] -> 0 <= [|wc|] <= 1.
proof: Proof. intros. apply (sum_mul_carry [|xh|] [|xl|] [|yh|] [|yl|] [|wc|][[cc]] wB);zarith. apply wB_pos. Qed.
imports: ZArith Lia BigNumPrelude DoubleType DoubleBase