Theorem errorBoundedPlus : forall p q pq : float, (Fbounded b p) -> (Fbounded b q) -> (Closest b radix (p + q) pq) -> exists error : float, error = (p + q - pq)%R :>R /\ (Fbounded b error) /\ (Fexp error) = (Zmin (Fexp p) (Fexp q)).