proposition: Lemma sin_ge0_pi x : 0 <= x <= pi -> 0 <= sin x.
proof: Proof. move=> xI; rewrite -cosBpihalf cos_ge0_pihalf //. by rewrite lerBrDl subrr lerBDr -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