intros p q pq H' H'0 H'1.
case (errorBoundedPlusAbs p q pq); auto.
intros x H'2; elim H'2; intros H'3 H'4; elim H'4; intros H'5 H'6;
clear H'4 H'2.
generalize H'3; clear H'3.
unfold Rabs in |- *; case (Rcase_abs (p + q - pq)).
intros H'2 H'3; exists (Fopp x); split; auto.
unfold FtoRradix in |- *; rewrite Fopp_correct; auto.
unfold FtoRradix in H'3; rewrite H'3; ring.
split.
apply oppBounded; auto.
rewrite <- H'6; auto.
intros H'2 H'3; exists x; split; auto.
Qed.

Theorem plusExact1 :
forall p q r : float,
Fbounded b p ->
Fbounded b q ->
Closest b radix (p + q) r ->
(Fexp r <= Zmin (Fexp p) (Fexp q))%Z -> r = (p + q)%R :>R.