src/HOL/Analysis/Change_Of_Vars.thy
changeset 71189 954ee5acaae0
parent 71172 575b3a818de5
child 71192 a8ccea88b725
equal deleted inserted replaced
71181:8331063570d6 71189:954ee5acaae0
  3386   with True show ?thesis
  3386   with True show ?thesis
  3387     by (auto simp: absolutely_integrable_on_def integrable_negligible integral_negligible)
  3387     by (auto simp: absolutely_integrable_on_def integrable_negligible integral_negligible)
  3388 next
  3388 next
  3389   case False
  3389   case False
  3390   then obtain h where h: "\<And>x. x \<in> S \<Longrightarrow> h (g x) = x" "linear h"
  3390   then obtain h where h: "\<And>x. x \<in> S \<Longrightarrow> h (g x) = x" "linear h"
  3391     using assms det_nz_iff_inj linear_injective_isomorphism by blast
  3391     using assms det_nz_iff_inj linear_injective_isomorphism by metis
  3392   show ?thesis
  3392   show ?thesis
  3393   proof (rule has_absolute_integral_change_of_variables_invertible)
  3393   proof (rule has_absolute_integral_change_of_variables_invertible)
  3394     show "(g has_derivative g) (at x within S)" for x
  3394     show "(g has_derivative g) (at x within S)" for x
  3395       by (simp add: assms linear_imp_has_derivative)
  3395       by (simp add: assms linear_imp_has_derivative)
  3396     show "continuous_on (g ` S) h"
  3396     show "continuous_on (g ` S) h"