Implicit Types B : {set (coset_of H)}.Notation fH_G := (restrm quotm_dom_proof fH).Definition quotm := factm quotm_ker_proof nHG.Definition qisom :=
  restrm qisom_restr_proof (factm qisom_ker_proof im_qisom_proof).

(* Specifications: *)
Lemma qisomE x : qisom (coset G x) = coset H x.
Lemma val_qisom Gx : val (qisom Gx) = val Gx.
Lemma qisom_isom : isom setT setT qisom.
Lemma qisom_inj : injective qisom.