a reindex_dprod R idx (op : Monoid.com_law idx) (F : gT -> R) :
   \big[op/idx]_(g in G) F g =
      \big[op/idx]_(k in K) \big[op/idx]_(h inH) F (k * h)%g.
Proof.have /mulgmP/misomP[fM /isomP[injf im_f]] := KxH.

(* Specifications: *)
Canonical cfDprodl_rmorphism := [rmorphism of cfD
Canonical cfDprodl_lrmorphism := [lrmorphism of c
Canonical cfDprodr_additive := [additive of cfDprodr].
Proof. by rewrite cfunE /= !cfSdprod1. Qed.
Lemma cfDprodl_eq1 phi : (cfDprodl phi == 1) = (phi == 1
Lemma cfDprodr_eq1 psi : (cfDprodr psi