src/HOL/Library/Quotient_List.thy
changeset 39302 d7728f65b353
parent 39198 f967a16dfcdd
child 40032 5f78dfb2fa7d
     1.1 --- a/src/HOL/Library/Quotient_List.thy	Mon Sep 13 08:43:48 2010 +0200
     1.2 +++ b/src/HOL/Library/Quotient_List.thy	Mon Sep 13 11:13:15 2010 +0200
     1.3 @@ -19,7 +19,7 @@
     1.4  
     1.5  lemma map_id[id_simps]:
     1.6    shows "map id = id"
     1.7 -  apply(simp add: ext_iff)
     1.8 +  apply(simp add: fun_eq_iff)
     1.9    apply(rule allI)
    1.10    apply(induct_tac x)
    1.11    apply(simp_all)
    1.12 @@ -92,7 +92,7 @@
    1.13  lemma cons_prs[quot_preserve]:
    1.14    assumes q: "Quotient R Abs Rep"
    1.15    shows "(Rep ---> (map Rep) ---> (map Abs)) (op #) = (op #)"
    1.16 -  by (simp only: ext_iff fun_map_def cons_prs_aux[OF q])
    1.17 +  by (simp only: fun_eq_iff fun_map_def cons_prs_aux[OF q])
    1.18       (simp)
    1.19  
    1.20  lemma cons_rsp[quot_respect]:
    1.21 @@ -122,7 +122,7 @@
    1.22    and     b: "Quotient R2 abs2 rep2"
    1.23    shows "((abs1 ---> rep2) ---> (map rep1) ---> (map abs2)) map = map"
    1.24    and   "((abs1 ---> id) ---> map rep1 ---> id) map = map"
    1.25 -  by (simp_all only: ext_iff fun_map_def map_prs_aux[OF a b])
    1.26 +  by (simp_all only: fun_eq_iff fun_map_def map_prs_aux[OF a b])
    1.27       (simp_all add: Quotient_abs_rep[OF a])
    1.28  
    1.29  lemma map_rsp[quot_respect]:
    1.30 @@ -148,7 +148,7 @@
    1.31    assumes a: "Quotient R1 abs1 rep1"
    1.32    and     b: "Quotient R2 abs2 rep2"
    1.33    shows "((abs1 ---> abs2 ---> rep2) ---> (map rep1) ---> rep2 ---> abs2) foldr = foldr"
    1.34 -  by (simp only: ext_iff fun_map_def foldr_prs_aux[OF a b])
    1.35 +  by (simp only: fun_eq_iff fun_map_def foldr_prs_aux[OF a b])
    1.36       (simp)
    1.37  
    1.38  lemma foldl_prs_aux:
    1.39 @@ -162,7 +162,7 @@
    1.40    assumes a: "Quotient R1 abs1 rep1"
    1.41    and     b: "Quotient R2 abs2 rep2"
    1.42    shows "((abs1 ---> abs2 ---> rep1) ---> rep1 ---> (map rep2) ---> abs1) foldl = foldl"
    1.43 -  by (simp only: ext_iff fun_map_def foldl_prs_aux[OF a b])
    1.44 +  by (simp only: fun_eq_iff fun_map_def foldl_prs_aux[OF a b])
    1.45       (simp)
    1.46  
    1.47  lemma list_all2_empty:
    1.48 @@ -231,7 +231,7 @@
    1.49  lemma[quot_preserve]:
    1.50    assumes a: "Quotient R abs1 rep1"
    1.51    shows "((abs1 ---> abs1 ---> id) ---> map rep1 ---> map rep1 ---> id) list_all2 = list_all2"
    1.52 -  apply (simp add: ext_iff)
    1.53 +  apply (simp add: fun_eq_iff)
    1.54    apply clarify
    1.55    apply (induct_tac xa xb rule: list_induct2')
    1.56    apply (simp_all add: Quotient_abs_rep[OF a])
    1.57 @@ -244,7 +244,7 @@
    1.58  
    1.59  lemma list_all2_eq[id_simps]:
    1.60    shows "(list_all2 (op =)) = (op =)"
    1.61 -  unfolding ext_iff
    1.62 +  unfolding fun_eq_iff
    1.63    apply(rule allI)+
    1.64    apply(induct_tac x xa rule: list_induct2')
    1.65    apply(simp_all)