src/HOL/Multivariate_Analysis/Norm_Arith.thy
changeset 47108 2a1953f0d20d
parent 44516 d9a496ae5d9d
child 48112 b1240319ef15
equal deleted inserted replaced
47107:35807a5d8dc2 47108:2a1953f0d20d
   102   fixes x :: "'a::real_normed_vector" shows
   102   fixes x :: "'a::real_normed_vector" shows
   103   "x = y \<longleftrightarrow> norm (x - y) \<le> 0"
   103   "x = y \<longleftrightarrow> norm (x - y) \<le> 0"
   104   "x \<noteq> y \<longleftrightarrow> \<not> (norm (x - y) \<le> 0)"
   104   "x \<noteq> y \<longleftrightarrow> \<not> (norm (x - y) \<le> 0)"
   105   using norm_ge_zero[of "x - y"] by auto
   105   using norm_ge_zero[of "x - y"] by auto
   106 
   106 
       
   107 lemmas arithmetic_simps =
       
   108   arith_simps
       
   109   add_numeral_special
       
   110   add_neg_numeral_special
       
   111   add_0_left
       
   112   add_0_right
       
   113   mult_zero_left
       
   114   mult_zero_right
       
   115   mult_1_left
       
   116   mult_1_right
       
   117 
   107 use "normarith.ML"
   118 use "normarith.ML"
   108 
   119 
   109 method_setup norm = {* Scan.succeed (SIMPLE_METHOD' o NormArith.norm_arith_tac)
   120 method_setup norm = {* Scan.succeed (SIMPLE_METHOD' o NormArith.norm_arith_tac)
   110 *} "prove simple linear statements about vector norms"
   121 *} "prove simple linear statements about vector norms"
   111 
   122