src/HOL/Analysis/Norm_Arith.thy
changeset 67962 0acdcd8f4ba1
parent 66453 cc19f7ca2ed6
child 68607 67bb59e49834
equal deleted inserted replaced
67961:9c31678d2139 67962:0acdcd8f4ba1
   129   mult_1_left
   129   mult_1_left
   130   mult_1_right
   130   mult_1_right
   131 
   131 
   132 ML_file "normarith.ML"
   132 ML_file "normarith.ML"
   133 
   133 
   134 method_setup norm = \<open>
   134 method_setup%important norm = \<open>
   135   Scan.succeed (SIMPLE_METHOD' o NormArith.norm_arith_tac)
   135   Scan.succeed (SIMPLE_METHOD' o NormArith.norm_arith_tac)
   136 \<close> "prove simple linear statements about vector norms"
   136 \<close> "prove simple linear statements about vector norms"
   137 
   137 
   138 
   138 
   139 text \<open>Hence more metric properties.\<close>
   139 text \<open>Hence more metric properties.\<close>
   140 
   140 
   141 lemma dist_triangle_add:
   141 lemma%important dist_triangle_add:
   142   fixes x y x' y' :: "'a::real_normed_vector"
   142   fixes x y x' y' :: "'a::real_normed_vector"
   143   shows "dist (x + y) (x' + y') \<le> dist x x' + dist y y'"
   143   shows "dist (x + y) (x' + y') \<le> dist x x' + dist y y'"
   144   by norm
   144   by norm
   145 
   145 
   146 lemma dist_triangle_add_half:
   146 lemma dist_triangle_add_half: