proposition: Lemma quotient_coprime_sdprod : K ><| H = G -> coprime #|K| #|H| -> (K / M) ><| (H / M) = G / M.
proof: Proof. exact: morphim_coprime_sdprod. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)