diff -r d2be0579a2c8 -r 1fe0ec14a90a src/HOL/Analysis/Path_Connected.thy --- a/src/HOL/Analysis/Path_Connected.thy Thu Dec 21 18:11:24 2017 +0100 +++ b/src/HOL/Analysis/Path_Connected.thy Thu Dec 21 19:09:18 2017 +0100 @@ -8262,10 +8262,10 @@ by (meson Topological_Spaces.connected_continuous_image \connected S\ homeomorphism_cont1 homeomorphism_of_subsets homhj hull_subset top_greatest) have hUS: "h ` U \ h ` S" by (meson homeomorphism_imp_open_map homeomorphism_of_subsets homhj hull_subset opeS opeU open_UNIV openin_open_eq) - have op: "openin (subtopology euclidean (affine hull S)) U \ open (h ` U)" for U + have opn: "openin (subtopology euclidean (affine hull S)) U \ open (h ` U)" for U using homeomorphism_imp_open_map [OF homhj] by simp have "open (h ` U)" "open (h ` S)" - by (auto intro: opeS opeU openin_trans op) + by (auto intro: opeS opeU openin_trans opn) then obtain f g where hom: "homeomorphism (h ` T) (h ` T) f g" and f: "\x. x \ h ` K \ f x \ h ` U" and sub: "{x. \ (f x = x \ g x = x)} \ h ` S"