intros p q r H' H'0 H'1 H'2.
case (Rle_or_lt 0 p); intros Rl1.
apply plusExact2Aux; auto.
replace (p + q)%R with (- (Fopp p + Fopp q))%R.
rewrite <- (plusExact2Aux (Fopp p) (Fopp q) (Fopp r)); auto.
unfold FtoRradix in |- *; rewrite Fopp_correct; ring.
unfold FtoRradix in |- *; rewrite Fopp_correct.
apply Rlt_le; replace 0%R with (-0)%R; auto with real.
apply FcanonicFopp; auto with arith.
apply oppBounded; auto.
replace (Fopp p + Fopp q)%R with (- (p + q))%R.
apply ClosestOpp; auto.
unfold FtoRradix in |- *; repeat rewrite Fopp_correct; ring.
unfold FtoRradix in |- *; repeat rewrite Fopp_correct; ring.
Qed.

Theorem plusExactR0 :
forall p q r : float,
Fbounded b p ->
Fbounded b q ->
Closest b radix (p + q) r -> r = 0%R :>R -> r = (p + q)%R :>R.