--- a/src/HOL/Quotient.thy Wed Aug 17 18:05:31 2011 +0200
+++ b/src/HOL/Quotient.thy Wed Aug 17 18:52:21 2011 +0200
@@ -643,10 +643,18 @@
have "Collect (R (SOME x. x \<in> Rep a)) = (Rep a)" by (metis some_collect rep_prop)
then show "Abs (Collect (R (SOME x. x \<in> Rep a))) = a" using rep_inverse by auto
have "R r r \<Longrightarrow> R s s \<Longrightarrow> Abs (Collect (R r)) = Abs (Collect (R s)) \<longleftrightarrow> R r = R s"
- by (metis Collect_def abs_inverse)
+ proof -
+ assume "R r r" and "R s s"
+ then have "Abs (Collect (R r)) = Abs (Collect (R s)) \<longleftrightarrow> Collect (R r) = Collect (R s)"
+ by (metis abs_inverse)
+ also have "Collect (R r) = Collect (R s) \<longleftrightarrow> (\<lambda>A x. x \<in> A) (Collect (R r)) = (\<lambda>A x. x \<in> A) (Collect (R s))"
+ by rule simp_all
+ finally show "Abs (Collect (R r)) = Abs (Collect (R s)) \<longleftrightarrow> R r = R s" by simp
+ qed
then show "R r s \<longleftrightarrow> R r r \<and> R s s \<and> (Abs (Collect (R r)) = Abs (Collect (R s)))"
using equivp[simplified part_equivp_def] by metis
qed
+
end
subsection {* ML setup *}