src/HOL/Library/Quotient_List.thy
changeset 36276 92011cc923f5
parent 36216 8fb6cc6f3b94
child 36812 e090bdb4e1c5
     1.1 --- a/src/HOL/Library/Quotient_List.thy	Thu Apr 22 09:30:39 2010 +0200
     1.2 +++ b/src/HOL/Library/Quotient_List.thy	Thu Apr 22 11:55:19 2010 +0200
     1.3 @@ -271,6 +271,15 @@
     1.4    apply(simp_all)
     1.5    done
     1.6  
     1.7 +lemma list_rel_find_element:
     1.8 +  assumes a: "x \<in> set a"
     1.9 +  and b: "list_rel R a b"
    1.10 +  shows "\<exists>y. (y \<in> set b \<and> R x y)"
    1.11 +proof -
    1.12 +  have "length a = length b" using b by (rule list_rel_len)
    1.13 +  then show ?thesis using a b by (induct a b rule: list_induct2) auto
    1.14 +qed
    1.15 +
    1.16  lemma list_rel_refl:
    1.17    assumes a: "\<And>x y. R x y = (R x = R y)"
    1.18    shows "list_rel R x x"