An existential example of real_asymp
authorpaulson <lp15@cam.ac.uk>
Sat, 18 Oct 2025 13:14:55 +0100
changeset 83276 385e6ed1db49
parent 83275 252739089bc8
child 83277 c0f025dd8722
An existential example of real_asymp
src/HOL/Real_Asymp/Real_Asymp_Examples.thy
--- a/src/HOL/Real_Asymp/Real_Asymp_Examples.thy	Fri Oct 17 15:42:50 2025 +0100
+++ b/src/HOL/Real_Asymp/Real_Asymp_Examples.thy	Sat Oct 18 13:14:55 2025 +0100
@@ -11,6 +11,13 @@
 
 lemma "((\<lambda>x::real. exp x * (exp (1/x - exp (-x)) - exp (1/x))) \<longlongrightarrow> -1) at_top"
   by real_asymp
+
+text \<open>Also works with schematic goals!\<close>
+lemma "\<exists>L. ((\<lambda>x::real. exp x * (exp (1/x - exp (-x)) - exp (1/x))) \<longlongrightarrow> L) at_top \<and> L<0"
+  apply (intro exI conjI)
+  apply real_asymp
+  apply auto
+  done
   
 lemma "((\<lambda>x::real. exp x * (exp (1/x + exp (-x) + exp (-(x^2))) -
                      exp (1/x - exp (-exp x)))) \<longlongrightarrow> 1) at_top"