case: (a \in _); first move/act_inj.
have Da := astabs_dom Na; have Db := astabs_dom Nb.
by rewrite !val_subact Na Nb groupM ?actMin.Canonical qact_dom_group := [group ofEnd Quotient.

(* Specifications: *)
a \in D -> a \in 'N(H) -> x \in range -> modact