Section TagEqType.
Variables (I : eqType) (T_ : I -> eqType).
Implicit Types u v : {i : I & T_ i}.
Definition tag_eq u v := (tag u == tag v) && (tagged u == tagged_as u v).
Canonical tag_eqMixin := EqMixin tag_eqP.
Canonical tag_eqType := Eval hnf in EqType {i : I & T_ i} tag_eqMixin.
End DifferentDom.
Hypothesis aR_anti : antisymmetric aR.
Hypothesis rR_anti : antisymmetric rR.

Lemma total_homo_mono_in : total aR ->
{in D &, {homo f : x y / aR' x y >-> rR' x y}} ->
{in D &, {mono f : x y / aR x y >-> rR x y}}.