proposition: Lemma morphim_sdprodm A B : A \subset H -> B \subset K -> sdprodm @* (A * B) = fH @* A * fK @* B.
proof: Proof. move=> sAH sBK; rewrite morphim_restrm /= (setIidPr _) ?morphim_pprodm //. by case/sdprodP: eqHK_G => _ <- _ _; apply: mulgSS. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)