src/HOL/Quotient.thy
 changeset 36215 88ff48884d26 parent 36123 7f877bbad5b2 child 36276 92011cc923f5
```     1.1 --- a/src/HOL/Quotient.thy	Tue Apr 20 14:55:53 2010 +0200
1.2 +++ b/src/HOL/Quotient.thy	Tue Apr 20 14:56:20 2010 +0200
1.3 @@ -585,19 +585,15 @@
1.4    assumes q1: "Quotient R1 Abs1 Rep1"
1.5    and     q2: "Quotient R2 Abs2 Rep2"
1.6    and     q3: "Quotient R3 Abs3 Rep3"
1.7 -  shows "(Rep1 ---> Abs3) (((Abs2 ---> Rep3) f) o ((Abs1 ---> Rep2) g)) = f o g"
1.8 +  shows "((Abs2 ---> Rep3) ---> (Abs1 ---> Rep2) ---> (Rep1 ---> Abs3)) op \<circ> = op \<circ>"
1.9 +  and   "(id ---> (Abs1 ---> id) ---> Rep1 ---> id) op \<circ> = op \<circ>"
1.10    using Quotient_abs_rep[OF q1] Quotient_abs_rep[OF q2] Quotient_abs_rep[OF q3]
1.11 -  unfolding o_def expand_fun_eq by simp
1.12 +  unfolding o_def expand_fun_eq by simp_all
1.13
1.14  lemma o_rsp:
1.15 -  assumes q1: "Quotient R1 Abs1 Rep1"
1.16 -  and     q2: "Quotient R2 Abs2 Rep2"
1.17 -  and     q3: "Quotient R3 Abs3 Rep3"
1.18 -  and     a1: "(R2 ===> R3) f1 f2"
1.19 -  and     a2: "(R1 ===> R2) g1 g2"
1.20 -  shows "(R1 ===> R3) (f1 o g1) (f2 o g2)"
1.21 -  using a1 a2 unfolding o_def expand_fun_eq
1.22 -  by (auto)
1.23 +  "((R2 ===> R3) ===> (R1 ===> R2) ===> (R1 ===> R3)) op \<circ> op \<circ>"
1.24 +  "(op = ===> (R1 ===> op =) ===> R1 ===> op =) op \<circ> op \<circ>"
1.25 +  unfolding fun_rel_def o_def expand_fun_eq by auto
1.26
1.27  lemma cond_prs:
1.28    assumes a: "Quotient R absf repf"
1.29 @@ -716,8 +712,8 @@
1.30  declare [[map "fun" = (fun_map, fun_rel)]]
1.31
1.32  lemmas [quot_thm] = fun_quotient
1.33 -lemmas [quot_respect] = quot_rel_rsp if_rsp
1.34 -lemmas [quot_preserve] = if_prs
1.35 +lemmas [quot_respect] = quot_rel_rsp if_rsp o_rsp
1.36 +lemmas [quot_preserve] = if_prs o_prs
1.37  lemmas [quot_equiv] = identity_equivp
1.38
1.39
```