src/HOL/Library/Formal_Power_Series.thy
changeset 56410 a14831ac3023
parent 55159 608c157d743d
child 56479 91958d4b30f7
equal deleted inserted replaced
56409:36489d77c484 56410:a14831ac3023
  3633               add: fps_const_add [symmetric] fps_const_neg [symmetric]
  3633               add: fps_const_add [symmetric] fps_const_neg [symmetric]
  3634                    fps_sin_deriv fps_cos_deriv algebra_simps)
  3634                    fps_sin_deriv fps_cos_deriv algebra_simps)
  3635   done
  3635   done
  3636 
  3636 
  3637 lemma fps_sin_even: "fps_sin (- c) = - fps_sin c"
  3637 lemma fps_sin_even: "fps_sin (- c) = - fps_sin c"
  3638   by (auto simp add: fps_eq_iff fps_sin_def)
  3638   by (auto simp add: divide_minus_left fps_eq_iff fps_sin_def)
  3639 
  3639 
  3640 lemma fps_cos_odd: "fps_cos (- c) = fps_cos c"
  3640 lemma fps_cos_odd: "fps_cos (- c) = fps_cos c"
  3641   by (auto simp add: fps_eq_iff fps_cos_def)
  3641   by (auto simp add: fps_eq_iff fps_cos_def)
  3642 
  3642 
  3643 definition "fps_tan c = fps_sin c / fps_cos c"
  3643 definition "fps_tan c = fps_sin c / fps_cos c"