Theorem plusExactExp : forall p q pq : float, Fbounded b p -> Fbounded b q -> Closest b radix (p + q) pq -> ex (fun r : float => ex (fun s : float => Fbounded b r /\ Fbounded b s /\ s = pq :>R /\ r = (p + q - s)%R :>R /\ Fexp r = Zmin (Fexp p) (Fexp q) :>Z /\ (Fexp r <= Fexp s)%Z /\ (Fexp s <= Zsucc (Zmax (Fexp p) (Fexp q)))%Z)).