Theorem plusExpBound : forall P, RoundedModeP b radix P -> forall p q pq : float, P (p + q)%R pq -> Fbounded b p -> Fbounded b q -> exists r : float, Fbounded b r /\ r = pq :>R /\ (Zmin (Fexp p) (Fexp q) <= Fexp r)%Z /\ (Fexp r <= Zsucc (Zmax (Fexp p) (Fexp q)))%Z.