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author | haftmann |

Wed, 17 Aug 2011 18:51:27 +0200 | |

changeset 44244 | 567fb5f5c639 |

parent 44235 | 85e9dad3c187 (current diff) |

parent 44243 | d58864221eef (diff) |

child 44245 | 45fb4b29c267 |

merged

--- a/src/HOL/Quotient.thy Wed Aug 17 10:03:58 2011 +0200 +++ b/src/HOL/Quotient.thy Wed Aug 17 18:51:27 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 *}