proposition: Theorem scaled_mantissa_mult_bpow : forall x, (scaled_mantissa x * bpow (cexp x))%R = x.
proof: Proof. intros x. unfold scaled_mantissa. rewrite Rmult_assoc, <- bpow_plus, Zplus_opp_l. apply Rmult_1_r. Qed.
imports: Coq(ZArith Reals Lia) Zaux Raux Defs Round_pred Float_prop