diff -r ad6d4a14adb5 -r f03a01a18c6e src/HOL/Analysis/Bounded_Continuous_Function.thy --- a/src/HOL/Analysis/Bounded_Continuous_Function.thy Fri Apr 12 19:48:29 2019 +0200 +++ b/src/HOL/Analysis/Bounded_Continuous_Function.thy Fri Apr 12 22:09:25 2019 +0200 @@ -7,7 +7,7 @@ subsection \Definition\ -definition%important "bcontfun = {f. continuous_on UNIV f \ bounded (range f)}" +definition\<^marker>\tag important\ "bcontfun = {f. continuous_on UNIV f \ bounded (range f)}" typedef (overloaded) ('a, 'b) bcontfun ("(_ \\<^sub>C /_)" [22, 21] 21) = "bcontfun::('a::topological_space \ 'b::metric_space) set" @@ -41,7 +41,7 @@ instantiation bcontfun :: (topological_space, metric_space) metric_space begin -lift_definition%important dist_bcontfun :: "'a \\<^sub>C 'b \ 'a \\<^sub>C 'b \ real" +lift_definition\<^marker>\tag important\ dist_bcontfun :: "'a \\<^sub>C 'b \ 'a \\<^sub>C 'b \ real" is "\f g. (SUP x. dist (f x) (g x))" . definition uniformity_bcontfun :: "('a \\<^sub>C 'b \ 'a \\<^sub>C 'b) filter" @@ -175,8 +175,8 @@ subsection \Complete Space\ -instance%important bcontfun :: (metric_space, complete_space) complete_space -proof%unimportant +instance\<^marker>\tag important\ bcontfun :: (metric_space, complete_space) complete_space +proof fix f :: "nat \ ('a, 'b) bcontfun" assume "Cauchy f" \ \Cauchy equals uniform convergence\ then obtain g where "uniform_limit UNIV f g sequentially" @@ -191,9 +191,9 @@ qed -subsection%unimportant \Supremum norm for a normed vector space\ +subsection\<^marker>\tag unimportant\ \Supremum norm for a normed vector space\ -instantiation%unimportant bcontfun :: (topological_space, real_normed_vector) real_vector +instantiation\<^marker>\tag unimportant\ bcontfun :: (topological_space, real_normed_vector) real_vector begin lemma uminus_cont: "f \ bcontfun \ (\x. - f x) \ bcontfun" for f::"'a \ 'b" @@ -247,7 +247,7 @@ "bounded (range f) \ norm (f x) \ (SUP x. norm (f x))" by (auto intro!: cSUP_upper bounded_imp_bdd_above simp: bounded_norm_comp) -instantiation%unimportant bcontfun :: (topological_space, real_normed_vector) real_normed_vector +instantiation\<^marker>\tag unimportant\ bcontfun :: (topological_space, real_normed_vector) real_normed_vector begin definition norm_bcontfun :: "('a, 'b) bcontfun \ real" @@ -290,7 +290,7 @@ using dist_bound[of f 0 b] assms by (simp add: dist_norm) -subsection%unimportant \(bounded) continuous extenstion\ +subsection\<^marker>\tag unimportant\ \(bounded) continuous extenstion\ lemma integral_clamp: "integral {t0::real..clamp t0 t1 x} f =