diff -r d3d2b78b1c19 -r a8cc904a6820 src/HOL/Complex.thy --- a/src/HOL/Complex.thy Fri Oct 19 10:46:42 2012 +0200 +++ b/src/HOL/Complex.thy Fri Oct 19 15:12:52 2012 +0200 @@ -141,7 +141,7 @@ instance by intro_classes (simp_all add: complex_mult_def - right_distrib left_distrib right_diff_distrib left_diff_distrib + distrib_left distrib_right right_diff_distrib left_diff_distrib complex_inverse_def complex_divide_def power2_eq_square add_divide_distrib [symmetric] complex_eq_iff) @@ -206,9 +206,9 @@ proof fix a b :: real and x y :: complex show "scaleR a (x + y) = scaleR a x + scaleR a y" - by (simp add: complex_eq_iff right_distrib) + by (simp add: complex_eq_iff distrib_left) show "scaleR (a + b) x = scaleR a x + scaleR b x" - by (simp add: complex_eq_iff left_distrib) + by (simp add: complex_eq_iff distrib_right) show "scaleR a (scaleR b x) = scaleR (a * b) x" by (simp add: complex_eq_iff mult_assoc) show "scaleR 1 x = x" @@ -297,7 +297,7 @@ (simp add: real_sqrt_sum_squares_triangle_ineq) show "norm (scaleR r x) = \r\ * norm x" by (induct x) - (simp add: power_mult_distrib right_distrib [symmetric] real_sqrt_mult) + (simp add: power_mult_distrib distrib_left [symmetric] real_sqrt_mult) show "norm (x * y) = norm x * norm y" by (induct x, induct y) (simp add: real_sqrt_mult [symmetric] power2_eq_square algebra_simps) @@ -730,7 +730,7 @@ unfolding z b_def rcis_def using `r \ 0` by (simp add: of_real_def sgn_scaleR sgn_if, simp add: cis_def) have cis_2pi_nat: "\n. cis (2 * pi * real_of_nat n) = 1" - by (induct_tac n, simp_all add: right_distrib cis_mult [symmetric], + by (induct_tac n, simp_all add: distrib_left cis_mult [symmetric], simp add: cis_def) have cis_2pi_int: "\x. cis (2 * pi * real_of_int x) = 1" by (case_tac x rule: int_diff_cases,