proposition: Lemma mantissa_UP_small_pos : forall x ex, (bpow (ex - 1) <= x < bpow ex)%R -> (ex <= fexp ex)%Z -> Zceil (x * bpow (- fexp ex)) = 1%Z.
proof: Proof. intros x ex Hx He. apply Zceil_imp. simpl. assert (H := mantissa_small_pos x ex Hx He). split ; try apply Rlt_le ; apply H. Qed.
imports: Coq(ZArith Reals Lia) Zaux Raux Defs Round_pred Float_prop