proposition: Lemma prods_reducesE u v : reduces u v -> 's_[u] = 's_[v].
proof: Proof. Proof using. move/reducesP => [x] [i] [y] [->{u} ->{v}]. by rewrite !big_cat big_cons !big_seq1 /= eltr2 mul1g. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(fingroup perm morphism presentation) mathcomp(ssralg poly ssrint) permcomp tools permuted combclass congr