![case: ifP]=> Cy Cx // eqxy; first exact: act_inj eqxy.
  by rewrite -eqxy acts_dom ?Cx in Cy.
by rewrite eqxy acts_dom ?Cy in Cx.Lemma actpermM : {in D &, {morph actperm : a b /

(* Specifications: *)
Lemma actpermE a x : actperm a x = to x a.