proposition: Lemma trace_rot n (lc : colseq) : trace (rot n lc) = rot n (trace lc).
proof: Proof. elim: n => [|n IHn]; first by rewrite !rot0. have [le_le_c | lt_n_le] := leqP (size lc) n. by rewrite !rot_oversize ?size_trace // ltnW. by rewrite -add1n !rotD ?size_trace // -IHn -!urtrace_trace -urtrace_rot. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype)