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

Lemma Rinv_pos : forall r : R, (sum (r < IQR 0) (IQR 0 < r)) -> IQR 0 < r -> IQR 0 < / r.