author huffman Tue, 17 Apr 2007 03:13:38 +0200 changeset 22722 704de05715b4 parent 22721 d9be18bd7a28 child 22723 a3a856313bcf
lemma isCont_inv_fun is same as isCont_inverse_function
```--- a/src/HOL/Hyperreal/Transcendental.thy	Tue Apr 17 00:55:00 2007 +0200
+++ b/src/HOL/Hyperreal/Transcendental.thy	Tue Apr 17 03:13:38 2007 +0200
@@ -2244,21 +2244,7 @@
shows "[| 0 < d; \<forall>z. \<bar>z - x\<bar> \<le> d --> g(f(z)) = z;
\<forall>z. \<bar>z - x\<bar> \<le> d --> isCont f z |]
==> isCont g (f x)"
-apply (simp (no_asm) add: isCont_iff LIM_def)
-apply safe
-apply (drule_tac ?d1.0 = r in real_lbound_gt_zero)
-apply (assumption, safe)
-apply (subgoal_tac "\<forall>z. \<bar>z - x\<bar> \<le> e --> (g (f z) = z) ")
-prefer 2 apply force
-apply (subgoal_tac "\<forall>z. \<bar>z - x\<bar> \<le> e --> isCont f z")
-prefer 2 apply force
-apply (drule_tac d = e in isCont_inj_range)
-prefer 2 apply (assumption, assumption, safe)
-apply (rule_tac x = ea in exI, auto)
-apply (drule_tac x = "f (x) + xa" and P = "%y. \<bar>y - f x\<bar> \<le> ea \<longrightarrow> (\<exists>z. \<bar>z - x\<bar> \<le> e \<and> f z = y)" in spec)
-apply auto
-apply (drule sym, auto)
-done
+by (rule isCont_inverse_function)

lemma isCont_inv_fun_inv:
fixes f g :: "real \<Rightarrow> real"```