src/HOL/Complex/Complex.thy
changeset 24520 40b220403257
parent 24506 020db6ec334a
child 25502 9200b36280c0
equal deleted inserted replaced
24519:5c435b2ea137 24520:40b220403257
   322        (simp add: power_mult_distrib right_distrib [symmetric] real_sqrt_mult)
   322        (simp add: power_mult_distrib right_distrib [symmetric] real_sqrt_mult)
   323   show "norm (x * y) = norm x * norm y"
   323   show "norm (x * y) = norm x * norm y"
   324     by (induct x, induct y)
   324     by (induct x, induct y)
   325        (simp add: real_sqrt_mult [symmetric] power2_eq_square ring_simps)
   325        (simp add: real_sqrt_mult [symmetric] power2_eq_square ring_simps)
   326   show "sgn x = x /\<^sub>R cmod x" by(simp add: complex_sgn_def)
   326   show "sgn x = x /\<^sub>R cmod x" by(simp add: complex_sgn_def)
   327 qed (* FIXME junk *) (rule refl)+
   327 qed
   328 
   328 
   329 lemma cmod_unit_one [simp]: "cmod (Complex (cos a) (sin a)) = 1"
   329 lemma cmod_unit_one [simp]: "cmod (Complex (cos a) (sin a)) = 1"
   330 by simp
   330 by simp
   331 
   331 
   332 lemma cmod_complex_polar [simp]:
   332 lemma cmod_complex_polar [simp]: