(* The constructive equality on R. *)
Definition Req_constr (x y : R) : Prop
:= (x < y -> False) /\ (y < x -> False).

Lemma RabsLUB : forall x y : R, (y < x -> False) /\ (y < - x -> False) <-> (y < Rabst (CReal_abs (Rrepr x)) -> False).