equal
deleted
inserted
replaced
300 lemma interval_integral_reflect: |
300 lemma interval_integral_reflect: |
301 "(LBINT x=a..b. f x) = (LBINT x=-b..-a. f (-x))" |
301 "(LBINT x=a..b. f x) = (LBINT x=-b..-a. f (-x))" |
302 proof (induct a b rule: linorder_wlog) |
302 proof (induct a b rule: linorder_wlog) |
303 case (sym a b) then show ?case |
303 case (sym a b) then show ?case |
304 by (auto simp add: interval_lebesgue_integral_def interval_integrable_endpoints_reverse |
304 by (auto simp add: interval_lebesgue_integral_def interval_integrable_endpoints_reverse |
305 split: split_if_asm) |
305 split: if_split_asm) |
306 next |
306 next |
307 case (le a b) then show ?case |
307 case (le a b) then show ?case |
308 unfolding interval_lebesgue_integral_def |
308 unfolding interval_lebesgue_integral_def |
309 by (subst set_integral_reflect) |
309 by (subst set_integral_reflect) |
310 (auto simp: interval_lebesgue_integrable_def einterval_iff |
310 (auto simp: interval_lebesgue_integrable_def einterval_iff |