intros p q r H' H'0 H'1 H'2.
cut (r = FtoRradix (Fzero (- dExp b)) :>R);
[ intros Eq1; rewrite Eq1
| rewrite H'2; apply sym_eq; unfold FtoRradix in |- *; apply FzeroisZero ].
apply plusExact1; auto.
apply (ClosestCompatible b radix (p + q)%R (p + q)%R r); auto.
apply FboundedFzero; auto.
simpl in |- *; auto.
unfold Zmin in |- *; case (Fexp p ?= Fexp q)%Z; auto with float.
Qed.

Theorem plusErrorBound1 :
forall p q r : float,
Fbounded b p ->
Fbounded b q ->
Closest b radix (p + q) r ->
~ is_Fzero r ->
(Rabs (r - (p + q)) < Rabs r * / 2%nat * (radix * / pPred (vNum b)))%R.