proposition: Lemma actX x a n : to x (a ^+ n) = iter n (to^~ a) x.
proof: Proof. by elim: n => [|n /= <-]; rewrite ?act1 // -actM expgSr. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient)