diff -r ff00ad5dc03a -r b34551d94934 src/HOL/Library/Multiset.thy --- a/src/HOL/Library/Multiset.thy Wed Sep 16 23:48:35 2015 +0200 +++ b/src/HOL/Library/Multiset.thy Thu Sep 17 15:47:24 2015 +0200 @@ -1408,14 +1408,14 @@ proof (rule properties_for_sort_key) from mset_equal show "mset ys = mset xs" by simp - from `sorted (map f ys)` + from \sorted (map f ys)\ show "sorted (map f ys)" . show "[x\ys . f k = f x] = [x\xs . f k = f x]" if "k \ set ys" for k proof - from mset_equal have set_equal: "set xs = set ys" by (rule mset_eq_setD) with that have "insert k (set ys) = set ys" by auto - with `inj_on f (set xs)` have inj: "inj_on f (insert k (set ys))" + with \inj_on f (set xs)\ have inj: "inj_on f (insert k (set ys))" by (simp add: set_equal) from inj have "[x\ys . f k = f x] = filter (HOL.eq k) ys" by (auto intro!: inj_on_filter_key_eq)