proposition: Lemma ratr_sg x : ratr F (sgr x) = sgr (ratr F x).
proof: Proof. by rewrite !sgr_def fmorph_eq0 ltrq0 rmorphMn /= rmorph_sign. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop order ssralg countalg div ssrnum) mathcomp(ssrint prime archimedean)