src/HOL/Complex.thy
changeset 58740 cb9d84d3e7f2
parent 58709 efdc6c533bd3
child 58889 5b7a9633cfa8
equal deleted inserted replaced
58739:cf78e16caa3a 58740:cb9d84d3e7f2
   731       by (simp_all add: complex_eq_iff)
   731       by (simp_all add: complex_eq_iff)
   732     hence cos: "cos d = 1" unfolding d_def cos_diff by simp
   732     hence cos: "cos d = 1" unfolding d_def cos_diff by simp
   733     moreover from cos have "sin d = 0" by (rule cos_one_sin_zero)
   733     moreover from cos have "sin d = 0" by (rule cos_one_sin_zero)
   734     ultimately have "d = 0"
   734     ultimately have "d = 0"
   735       unfolding sin_zero_iff
   735       unfolding sin_zero_iff
   736       by (auto simp add: numeral_2_eq_2 less_Suc_eq elim!: evenE)
   736       by (auto elim!: evenE dest!: less_2_cases)
   737     thus "a = x" unfolding d_def by simp
   737     thus "a = x" unfolding d_def by simp
   738   qed (simp add: assms del: Re_sgn Im_sgn)
   738   qed (simp add: assms del: Re_sgn Im_sgn)
   739   with `z \<noteq> 0` show "arg z = x"
   739   with `z \<noteq> 0` show "arg z = x"
   740     unfolding arg_def by simp
   740     unfolding arg_def by simp
   741 qed
   741 qed