Section F2.
Variable b : Fbound.
Variable precision : nat.
Let radix := 2%Z.
Let FtoRradix := FtoR radix.
Local Coercion FtoRradix : float >-> R.
red in |- *; simpl in |- *; auto.
Qed.
Hint Resolve TwoMoreThanOne.
Hypothesis precisionNotZero : 1 < precision.
Hypothesis pGivesBound : Zpos (vNum b) = Zpower_nat radix precision.

Theorem plusUpperBound :
forall P,
RoundedModeP b 2%nat P ->
forall p q pq : float,
P (p + q)%R pq ->
Fbounded b p ->
Fbounded b q -> (Rabs pq <= radix * Rmax (Rabs p) (Rabs q))%R.