Section Sdprodm.
Variables H K G : {group gT}.
Variables (fH : {morphism H >-> rT}) (fK : {morphism K >-> rT}).
Hypothesis eqHK_G : H ><| K = G.
Hypothesis actf : {in H & K, morph_act 'J 'J fH fK}.
Definition sdprodm :=
restrm sdprodm_sub (pprodm sdprodm_norm actf sdprodm_eqf).
Canonical sdprodm_morphism := Eval hnf in [morphism of sdprodm].

Lemma sdprodmE a b : a \in H -> b \in K -> sdprodm (a * b) = fH a * fK b.