Module K0 := knot_full_variant.Knot_MixVariantHeredTOthRel(Input).
Module KL0 := knot_full_variant.KnotLemmas_MixVariantHeredTOthRel(K0).
Existing Instance K0.ageable_knot.
Definition ag_knot_other := ag_prod K0.knot KI.other K0.ageable_knot.
Existing Instance ag_knot_other.
Definition expandR : relation (K0.knot * KI.other) :=
fun x y => K0.knot_rel (fst x) (fst y) /\ KI.ORel (snd x) (snd y).

Lemma expandM_trans : transitive _ expandM.
Hint Resolve expandM_refl expandM_trans.