(* A function that returns a bounded greater than a given r *)
 
Definition boundR (r : R) := boundNat (Zabs_nat (up (Rabs r))).

(* Specifications: *)
Theorem boundRCorrect1 : forall r : R, (r < boundR r)%R.
Theorem boundRrOpp : forall r : R, boundR r = boundR (- r).
Theorem boundRCorrect2 : forall r : R, (Fopp (boundR r) < r)%R.