Canonical amulr_linear := Eval hnf in AddLinear amulr_is_lrmorphism.
Canonical amulr_rmorphism := Eval hnf in AddRMorphism amulr_is_lrmorphism.
Canonical amulr_lrmorphism := Eval hnf in LRMorphism amulr_is_lrmorphism.

Lemma prodvDr : right_distributive prodv addv.
Canonical addv_addoid := Monoid.AddLaw prodvDl prodvDr.