proposition: Lemma anti_mono_in : {in D &, {mono f : x y / aR x y >-> rR x y}} -> {in D &, {mono f : x y / aR' x y >-> rR' x y}}.
proof: Proof. move=> mf x y ??; rewrite rR'E aR'E mf// (@inj_in_eq _ _ D)//. exact: mono_inj_in. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool)