diff -r 8c240fdeffcb -r 5840724b1d71 src/HOL/Analysis/Nonnegative_Lebesgue_Integration.thy --- a/src/HOL/Analysis/Nonnegative_Lebesgue_Integration.thy Sun Sep 23 21:49:31 2018 +0200 +++ b/src/HOL/Analysis/Nonnegative_Lebesgue_Integration.thy Mon Sep 24 14:30:09 2018 +0200 @@ -279,7 +279,7 @@ lemmas simple_function_add[intro, simp] = simple_function_compose2[where h="(+)"] and simple_function_diff[intro, simp] = simple_function_compose2[where h="(-)"] and simple_function_uminus[intro, simp] = simple_function_compose[where g="uminus"] - and simple_function_mult[intro, simp] = simple_function_compose2[where h="( * )"] + and simple_function_mult[intro, simp] = simple_function_compose2[where h="(*)"] and simple_function_div[intro, simp] = simple_function_compose2[where h="(/)"] and simple_function_inverse[intro, simp] = simple_function_compose[where g="inverse"] and simple_function_max[intro, simp] = simple_function_compose2[where h=max] @@ -760,7 +760,7 @@ using assms by (intro simple_function_partition) auto also have "\ = (\y\(\x. (f x, indicator A x::ennreal))`space M. if snd y = 1 then fst y * emeasure M (f -` {fst y} \ space M \ A) else 0)" - by (auto simp: indicator_def split: if_split_asm intro!: arg_cong2[where f="( * )"] arg_cong2[where f=emeasure] sum.cong) + by (auto simp: indicator_def split: if_split_asm intro!: arg_cong2[where f="(*)"] arg_cong2[where f=emeasure] sum.cong) also have "\ = (\y\(\x. (f x, 1::ennreal))`A. fst y * emeasure M (f -` {fst y} \ space M \ A))" using assms by (subst sum.If_cases) (auto intro!: simple_functionD(1) simp: eq) also have "\ = (\y\fst`(\x. (f x, 1::ennreal))`A. y * emeasure M (f -` {y} \ space M \ A))"