proposition: Lemma sgr_id x : sg (sg x) = sg x.
proof: Proof. by rewrite !(fun_if sg) !sgrE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(ssrAC div fintype path bigop order finset fingroup) mathcomp(ssralg poly)