diff -r 070703d83cfe -r cec875dcc59e src/HOL/Topological_Spaces.thy --- a/src/HOL/Topological_Spaces.thy Mon May 22 12:01:05 2023 +0200 +++ b/src/HOL/Topological_Spaces.thy Tue May 23 12:31:23 2023 +0100 @@ -1319,17 +1319,6 @@ subsubsection \Subsequence (alternative definition, (e.g. Hoskins)\ -lemma strict_mono_Suc_iff: "strict_mono f \ (\n. f n < f (Suc n))" -proof (intro iffI strict_monoI) - assume *: "\n. f n < f (Suc n)" - fix m n :: nat assume "m < n" - thus "f m < f n" - by (induction rule: less_Suc_induct) (use * in auto) -qed (auto simp: strict_mono_def) - -lemma strict_mono_add: "strict_mono (\n::'a::linordered_semidom. n + k)" - by (auto simp: strict_mono_def) - text \For any sequence, there is a monotonic subsequence.\ lemma seq_monosub: fixes s :: "nat \ 'a::linorder"