src/HOL/Analysis/Bounded_Continuous_Function.thy
changeset 78890 d8045bc0544e
parent 71172 575b3a818de5
child 80914 d97fdabd9e2b
equal deleted inserted replaced
78889:88eb92a52f9b 78890:d8045bc0544e
   242 instance
   242 instance
   243   by standard (auto intro!: bcontfun_eqI simp: algebra_simps)
   243   by standard (auto intro!: bcontfun_eqI simp: algebra_simps)
   244 
   244 
   245 end
   245 end
   246 
   246 
   247 lemma bounded_norm_le_SUP_norm:
       
   248   "bounded (range f) \<Longrightarrow> norm (f x) \<le> (SUP x. norm (f x))"
       
   249   by (auto intro!: cSUP_upper bounded_imp_bdd_above simp: bounded_norm_comp)
       
   250 
       
   251 instantiation\<^marker>\<open>tag unimportant\<close> bcontfun :: (topological_space, real_normed_vector) real_normed_vector
   247 instantiation\<^marker>\<open>tag unimportant\<close> bcontfun :: (topological_space, real_normed_vector) real_normed_vector
   252 begin
   248 begin
   253 
   249 
   254 definition norm_bcontfun :: "('a, 'b) bcontfun \<Rightarrow> real"
   250 definition norm_bcontfun :: "('a, 'b) bcontfun \<Rightarrow> real"
   255   where "norm_bcontfun f = dist f 0"
   251   where "norm_bcontfun f = dist f 0"