#[global]
Instance CR_of_Q_morph_T
: forall {R : ConstructiveReals}, CMorphisms.Proper
(CMorphisms.respectful Qeq (CReq R)) (CR_of_Q R).

(* In particular x * y == 1 implies that 0 # x, 0 # y and that x and y are inverses of each other. *)
Lemma CRmult_pos_appart_zero
: forall {R : ConstructiveReals} (x y : CRcarrier R),
0 < x * y -> 0 ≶ x.