Canonical quotm_morphism := [morphism G / H of quotm].

(* Specifications: *)
Lemma quotmE x : x \in G -> quotm (coset H x) = coset (f @* H) (f x).
Lemma ker_quotm : 'ker quotm = 'ker f / H.
Lemma val_qisom Gx : val (qisom Gx) = val Gx.
Lemma morphim_qisom A : qisom @* (A / G) = A / H.
Lemma injm_qisom : 'injm qisom.
End EqIso.