equal
deleted
inserted
replaced
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 |