proposition: Lemma reindex_dprod R idx (op : Monoid.com_law idx) (F : gT -> R) : \big[op/idx]_(g in G) F g = \big[op/idx]_(k in K) \big[op/idx]_(h in H) F (k * h)%g.
proof: Proof. have /mulgmP/misomP[fM /isomP[injf im_f]] := KxH. rewrite pair_big_dep -im_f morphimEdom big_imset; last exact/injmP. by apply: eq_big => [][x y]; rewrite ?inE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient finalg action gproduct) mathcomp(zmodp commutator cyclic center pgroup sylow) mathcomp(matrix vector falgebra ssrnum algC algnum) mathcomp(archimedean)