proposition: Lemma irr_modeX n : {in 'Z(G), {morph irr_mode : x / (x ^+ n)%g >-> x ^+ n}}.
proof: Proof. elim: n => [|n IHn] x Zx; first exact: irr_mode1. by rewrite expgS irr_modeM ?groupX // exprS IHn. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv finset fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup matrix mxalgebra) mathcomp(mxpoly)