diff -r 5eb932e604a2 -r eab6ce8368fa src/HOL/Analysis/Bochner_Integration.thy --- a/src/HOL/Analysis/Bochner_Integration.thy Wed Jan 10 15:21:49 2018 +0100 +++ b/src/HOL/Analysis/Bochner_Integration.thy Wed Jan 10 15:25:09 2018 +0100 @@ -497,7 +497,7 @@ have "ennreal (norm (?s - ?t)) = norm (simple_bochner_integral M (\x. s x - t x))" using s t by (subst simple_bochner_integral_diff) auto also have "\ \ simple_bochner_integral M (\x. norm (s x - t x))" - using simple_bochner_integrable_compose2[of "op -" M "s" "t"] s t + using simple_bochner_integrable_compose2[of "(-)" M "s" "t"] s t by (auto intro!: simple_bochner_integral_norm_bound) also have "\ = (\\<^sup>+x. norm (s x - t x) \M)" using simple_bochner_integrable_compose2[of "\x y. norm (x - y)" M "s" "t"] s t @@ -1855,7 +1855,7 @@ have sf[measurable]: "\i. simple_function M (s' i)" unfolding s'_def using s(1) - by (intro simple_function_compose2[where h="op *\<^sub>R"] simple_function_indicator) auto + by (intro simple_function_compose2[where h="( *\<^sub>R)"] simple_function_indicator) auto { fix i have "\z. {y. s' i z = y \ y \ s' i ` space M \ y \ 0 \ z \ space M} = @@ -2282,7 +2282,7 @@ shows "integrable (density M g) f \ integrable M (\x. g x *\<^sub>R f x)" unfolding integrable_iff_bounded using nn apply (simp add: nn_integral_density less_top[symmetric]) - apply (intro arg_cong2[where f="op ="] refl nn_integral_cong_AE) + apply (intro arg_cong2[where f="(=)"] refl nn_integral_cong_AE) apply (auto simp: ennreal_mult) done