proposition: Lemma cos_coeff'E x n : cos_coeff' x n = cos_coeff x n.*2.
proof: Proof. rewrite /cos_coeff' /cos_coeff /= odd_double /= mul1r -2!mulrA; congr (_ * _). by rewrite (half_bit_double n false). 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