proposition: Lemma morphim_sdprodml A : A \subset H -> sdprodm @* A = fH @* A.
proof: Proof. by move=> sHA; rewrite -{1}(mulg1 A) morphim_sdprodm ?sub1G // morphim1 mulg1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)