proposition: Lemma sin_gt0_pi x : 0 < x < pi -> 0 < sin x.
proof: Proof. move=> xI; rewrite -cosBpihalf cos_gt0_pihalf //. by rewrite ltrBrDl subrr ltrBDr -mulr2n -[_ *+ 2]mulr_natr divfK. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) reals ereal nsatz_realtype signed topology normedtype landau sequences derive realfun exp