1.1 --- a/src/HOL/Lim.thy Fri Aug 19 10:46:54 2011 -0700
1.2 +++ b/src/HOL/Lim.thy Fri Aug 19 11:49:53 2011 -0700
1.3 @@ -419,9 +419,13 @@
1.4 shows "\<lbrakk>isCont f a; isCont g a; g a \<noteq> 0\<rbrakk> \<Longrightarrow> isCont (\<lambda>x. f x / g x) a"
1.5 unfolding isCont_def by (rule tendsto_divide)
1.6
1.7 +lemma isCont_tendsto_compose:
1.8 + "\<lbrakk>isCont g l; (f ---> l) F\<rbrakk> \<Longrightarrow> ((\<lambda>x. g (f x)) ---> g l) F"
1.9 + unfolding isCont_def by (rule tendsto_compose)
1.10 +
1.11 lemma isCont_LIM_compose:
1.12 "\<lbrakk>isCont g l; f -- a --> l\<rbrakk> \<Longrightarrow> (\<lambda>x. g (f x)) -- a --> g l"
1.13 - unfolding isCont_def by (rule LIM_compose)
1.14 + by (rule isCont_tendsto_compose) (* TODO: delete? *)
1.15
1.16 lemma metric_isCont_LIM_compose2:
1.17 assumes f [unfolded isCont_def]: "isCont f a"