src/HOL/Real_Vector_Spaces.thy
changeset 62102 877463945ce9
parent 62101 26c0a70f78a3
child 62131 1baed43f453e
equal deleted inserted replaced
62101:26c0a70f78a3 62102:877463945ce9
     6 section \<open>Vector Spaces and Algebras over the Reals\<close>
     6 section \<open>Vector Spaces and Algebras over the Reals\<close>
     7 
     7 
     8 theory Real_Vector_Spaces
     8 theory Real_Vector_Spaces
     9 imports Real Topological_Spaces
     9 imports Real Topological_Spaces
    10 begin
    10 begin
    11 
       
    12 
    11 
    13 lemma (in ordered_ab_group_add) diff_ge_0_iff_ge [simp]: "a - b \<ge> 0 \<longleftrightarrow> a \<ge> b"
    12 lemma (in ordered_ab_group_add) diff_ge_0_iff_ge [simp]: "a - b \<ge> 0 \<longleftrightarrow> a \<ge> b"
    14   by (simp add: le_diff_eq)
    13   by (simp add: le_diff_eq)
    15 
    14 
    16 subsection \<open>Locale for additive functions\<close>
    15 subsection \<open>Locale for additive functions\<close>
  1182 apply (rule abs_mult)
  1181 apply (rule abs_mult)
  1183 apply (rule abs_mult)
  1182 apply (rule abs_mult)
  1184 done
  1183 done
  1185 
  1184 
  1186 end
  1185 end
       
  1186 
       
  1187 declare uniformity_Abort[where 'a=real, code]
  1187 
  1188 
  1188 lemma dist_of_real [simp]:
  1189 lemma dist_of_real [simp]:
  1189   fixes a :: "'a::real_normed_div_algebra"
  1190   fixes a :: "'a::real_normed_div_algebra"
  1190   shows "dist (of_real x :: 'a) (of_real y) = dist x y"
  1191   shows "dist (of_real x :: 'a) (of_real y) = dist x y"
  1191 by (metis dist_norm norm_of_real of_real_diff real_norm_def)
  1192 by (metis dist_norm norm_of_real of_real_diff real_norm_def)