Canonical tag_eqType := Eval hnf in EqType {i : I & T_ i} tag_eqMixin.

(* Specifications: *)
Lemma tag_eqE : tag_eq = eq_op. Proof. by []. Qed.
Lemma eq_tag u v : u == v -> tag u = tag v.
Lemma inj_homo_in : {in D & D', injective f} ->
{in D & D', {homo f : x y / aR x y >-> rR x y}} ->
{in D & D', {homo f : x y / aR' x y >-> rR' x y}}.