equal
deleted
inserted
replaced
1352 |
1352 |
1353 lemma continuous_on_inverse_ennreal[continuous_intros]: |
1353 lemma continuous_on_inverse_ennreal[continuous_intros]: |
1354 fixes f :: "'a::topological_space \<Rightarrow> ennreal" |
1354 fixes f :: "'a::topological_space \<Rightarrow> ennreal" |
1355 shows "continuous_on A f \<Longrightarrow> continuous_on A (\<lambda>x. inverse (f x))" |
1355 shows "continuous_on A f \<Longrightarrow> continuous_on A (\<lambda>x. inverse (f x))" |
1356 proof (transfer fixing: A) |
1356 proof (transfer fixing: A) |
1357 show "pred_fun (\<lambda>_. True) (op \<le> 0) f \<Longrightarrow> continuous_on A (\<lambda>x. inverse (f x))" if "continuous_on A f" |
1357 show "pred_fun top (op \<le> 0) f \<Longrightarrow> continuous_on A (\<lambda>x. inverse (f x))" if "continuous_on A f" |
1358 for f :: "'a \<Rightarrow> ereal" |
1358 for f :: "'a \<Rightarrow> ereal" |
1359 using continuous_on_compose2[OF continuous_on_inverse_ereal that] by (auto simp: subset_eq) |
1359 using continuous_on_compose2[OF continuous_on_inverse_ereal that] by (auto simp: subset_eq) |
1360 qed |
1360 qed |
1361 |
1361 |
1362 instance ennreal :: topological_comm_monoid_add |
1362 instance ennreal :: topological_comm_monoid_add |