Re: [isabelle] list_size_pointwise



Is anyone already changing this to the stronger version right now?

Otherwise I would tackle this change this evening, in two hours from now.

Lukas


On 08/30/2011 11:52 AM, Lawrence Paulson wrote:
I agree. The current version is unnecessarily week.
Larry Paulson


On 30 Aug 2011, at 10:44, René Thiemann wrote:

Dear all,

when looking at the thm in Libary List

lemma list_size_pointwise: assumes "!! x. x : set xs ==>  f x<  g x"
  shows "list_size f xs<= list_size g xs"

I was wondering why the strict inequality is used in the assumption. Indeed,
the lemma also holds in its stronger version where only<= is used in the assumption.

lemma list_size_pointwise': assumes "\<And>  x. x \<in>  set xs \<Longrightarrow>  f x \<le>  g x"
  shows "list_size f xs \<le>  list_size g xs"
  using assms
proof (induct xs)
  case Nil thus ?case by auto
next
  case (Cons x xs)
  have "list_size f xs \<le>  list_size g xs"
    by (rule Cons(1), insert Cons(2), auto)
  with Cons(2)[of x]
  show ?case by auto
qed

So, one might consider to replace the current lemma list_size_pointwise
by the stronger version list_size_pointwise'.

Cheers,
René
--
René Thiemann                    mailto:rene.thiemann at uibk.ac.at
Computational Logic Group        http://cl-informatik.uibk.ac.at/~thiemann/
Institute of Computer Science    phone: +43 512 507-6434
University of Innsbruck









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