Theorem ExactMinusIntervalAux : forall P, RoundedModeP b radix P -> forall p q : float, (0 < p)%R -> (2%nat * p < q)%R -> Fcanonic radix b p -> Fcanonic radix b q -> (exists r : float, Fbounded b r /\ r = (q - p)%R :>R) -> forall r : float, Fcanonic radix b r -> (2%nat * p < r)%R -> (r <= q)%R -> exists r' : float, Fbounded b r' /\ r' = (r - p)%R :>R.