proposition: Theorem mBFadic_correct4 : forall r : R, In (Float 0 (- dExp b)) (mBFloat r).
proof: Proof. intros p; unfold mBFloat in |- *. replace (Float 0 (- dExp b)) with ((fun p : Z * Z => Float (fst p) (snd p)) (Fnum (Float 0 (- dExp b)), Fexp (Float 0 (- dExp b)))). apply in_map with (f := fun p : Z * Z => Float (fst p) (snd p)); auto. apply mProd_correct; auto. apply mZlist_correct; auto. simpl in |- *; auto with zarith. replace 0%Z with (- (0))%Z; [ idtac | simpl in |- *; auto ]. apply Zle_Zopp; unfold pPred in |- *; apply Zle_Zpred. red in |- *; simpl in |- *; auto with zarith. simpl in |- *; auto with zarith. unfold pPred in |- *; apply Zle_Zpred. red in |- *; simpl in |- *; auto with zarith. apply mZlist_correct; auto. simpl in |- *; auto with zarith. unfold boundR, boundNat in |- *; simpl in |- *; lia. case (dExp b); auto with zarith. Qed.
imports: Reals ZArith List PeanoNat Psatz