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"
proof (induct xs)
case Nil thus ?case by auto
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
So, one might consider to replace the current lemma list_size_pointwise
by the stronger version list_size_pointwise'.
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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