# HG changeset patch # User wenzelm # Date 1548795400 -3600 # Node ID 9a3b4cca6d0ba2e324ab2c37c10c265b1c152662 # Parent facaf96cd79eb40630e90c12758c7613022270f3 eliminated suspicious Unicode; diff -r facaf96cd79e -r 9a3b4cca6d0b src/HOL/Analysis/Abstract_Topology_2.thy --- a/src/HOL/Analysis/Abstract_Topology_2.thy Tue Jan 29 13:54:43 2019 +0100 +++ b/src/HOL/Analysis/Abstract_Topology_2.thy Tue Jan 29 21:56:40 2019 +0100 @@ -864,7 +864,7 @@ T \ S \ continuous_on S r \ r ` S = T \ (\x \ T. r x = x)" by (force simp: retraction_def) -lemma retractionE: \ \yields properties normalized wrt. simp – less likely to loop\ +lemma retractionE: \ \yields properties normalized wrt. simp -- less likely to loop\ assumes "retraction S T r" obtains "T = r ` S" "r ` S \ S" "continuous_on S r" "\x. x \ S \ r (r x) = r x" proof (rule that) @@ -879,7 +879,7 @@ using that by auto qed -lemma retract_ofE: \ \yields properties normalized wrt. simp – less likely to loop\ +lemma retract_ofE: \ \yields properties normalized wrt. simp -- less likely to loop\ assumes "T retract_of S" obtains r where "T = r ` S" "r ` S \ S" "continuous_on S r" "\x. x \ S \ r (r x) = r x" proof -