#[export] Instance Rle_Antisymmetric : Antisymmetric R eq Rle | 10 := Rle_antisym.

(* Specifications: *)
Lemma Rge_antisym : forall r1 r2, r1 >= r2 -> r2 >= r1 -> r1 = r2.
Lemma Rge_ge_eq : forall r1 r2, r1 >= r2 /\ r2 >= r1 <-> r1 = r2.
(** *** Compatibility with equality *)
Lemma Rlt_eq_compat :
forall r1 r2 r3 r4, r1 = r2 -> r2 < r4 -> r4 = r3 -> r1 < r3.