src/HOL/Quotient.thy
changeset 47626 f7b1034cb9ce
parent 47579 28f6f4ad69bf
child 48891 c0eafbd55de3
     1.1 --- a/src/HOL/Quotient.thy	Fri Apr 20 15:30:13 2012 +0200
     1.2 +++ b/src/HOL/Quotient.thy	Fri Apr 20 15:34:33 2012 +0200
     1.3 @@ -34,21 +34,6 @@
     1.4    shows "((op =) OOO R) = R"
     1.5    by (auto simp add: fun_eq_iff)
     1.6  
     1.7 -subsection {* set map (vimage) and set relation *}
     1.8 -
     1.9 -definition "set_rel R xs ys \<equiv> \<forall>x y. R x y \<longrightarrow> x \<in> xs \<longleftrightarrow> y \<in> ys"
    1.10 -
    1.11 -lemma set_rel_eq:
    1.12 -  "set_rel op = = op ="
    1.13 -  by (subst fun_eq_iff, subst fun_eq_iff) (simp add: set_eq_iff set_rel_def)
    1.14 -
    1.15 -lemma set_rel_equivp:
    1.16 -  assumes e: "equivp R"
    1.17 -  shows "set_rel R xs ys \<longleftrightarrow> xs = ys \<and> (\<forall>x y. x \<in> xs \<longrightarrow> R x y \<longrightarrow> y \<in> xs)"
    1.18 -  unfolding set_rel_def
    1.19 -  using equivp_reflp[OF e]
    1.20 -  by auto (metis, metis equivp_symp[OF e])
    1.21 -
    1.22  subsection {* Quotient Predicate *}
    1.23  
    1.24  definition
    1.25 @@ -799,7 +784,6 @@
    1.26    id_o
    1.27    o_id
    1.28    eq_comp_r
    1.29 -  set_rel_eq
    1.30    vimage_id
    1.31  
    1.32  text {* Translation functions for the lifting process. *}