--- a/src/HOL/Quotient_Examples/FSet.thy Tue Apr 03 23:49:24 2012 +0200
+++ b/src/HOL/Quotient_Examples/FSet.thy Wed Apr 04 15:15:48 2012 +0900
@@ -140,7 +140,7 @@
next
assume a: "(list_all2 R OOO op \<approx>) r s"
then have b: "map Abs r \<approx> map Abs s"
- proof (elim pred_compE)
+ proof (elim relcomppE)
fix b ba
assume c: "list_all2 R r b"
assume d: "b \<approx> ba"
@@ -165,11 +165,11 @@
have y: "list_all2 R (map Rep (map Abs s)) s"
by (fact rep_abs_rsp_left[OF list_quotient3[OF q], OF list_all2_refl'[OF e, of s]])
have c: "(op \<approx> OO list_all2 R) (map Rep (map Abs r)) s"
- by (rule pred_compI) (rule b, rule y)
+ by (rule relcomppI) (rule b, rule y)
have z: "list_all2 R r (map Rep (map Abs r))"
by (fact rep_abs_rsp[OF list_quotient3[OF q], OF list_all2_refl'[OF e, of r]])
then show "(list_all2 R OOO op \<approx>) r s"
- using a c pred_compI by simp
+ using a c relcomppI by simp
qed
qed
@@ -360,7 +360,7 @@
quotient_definition
"concat_fset :: ('a fset) fset \<Rightarrow> 'a fset"
is concat
-proof (elim pred_compE)
+proof (elim relcomppE)
fix a b ba bb
assume a: "list_all2 op \<approx> a ba"
with list_symp [OF list_eq_symp] have a': "list_all2 op \<approx> ba a" by (rule sympE)
@@ -397,9 +397,9 @@
lemma Cons_rsp2 [quot_respect]:
shows "(op \<approx> ===> list_all2 op \<approx> OOO op \<approx> ===> list_all2 op \<approx> OOO op \<approx>) Cons Cons"
apply (auto intro!: fun_relI)
- apply (rule_tac b="x # b" in pred_compI)
+ apply (rule_tac b="x # b" in relcomppI)
apply auto
- apply (rule_tac b="x # ba" in pred_compI)
+ apply (rule_tac b="x # ba" in relcomppI)
apply auto
done
@@ -453,7 +453,7 @@
assumes "(R1 ===> R2 ===> R3) C C" and "(R4 ===> R5 ===> R6) C C"
shows "(R1 OOO R4 ===> R2 OOO R5 ===> R3 OOO R6) C C"
by (auto intro!: fun_relI)
- (metis (full_types) assms fun_relE pred_compI)
+ (metis (full_types) assms fun_relE relcomppI)
lemma append_rsp2 [quot_respect]:
"(list_all2 op \<approx> OOO op \<approx> ===> list_all2 op \<approx> OOO op \<approx> ===> list_all2 op \<approx> OOO op \<approx>) append append"
@@ -479,7 +479,7 @@
by (induct y ya rule: list_induct2')
(simp_all, metis apply_rsp' list_eq_def)
show "(list_all2 op \<approx> OOO op \<approx>) (map f xa) (map f' ya)"
- by (metis a b c list_eq_def pred_compI)
+ by (metis a b c list_eq_def relcomppI)
qed
lemma map_prs2 [quot_preserve]: