proposition: Lemma index_sdprod G A B : A ><| B = G -> #|B| = #|G : A|.
proof: Proof. case/sdprodP=> [[K H -> ->] <- _ tiHK]. by rewrite indexMg -indexgI setIC tiHK indexg1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)