author | nipkow |
Wed, 07 Feb 1996 12:22:32 +0100 | |
changeset 1481 | 03f096efa26d |
parent 1465 | 5d7a7e439cec |
child 1552 | 6f71b5d46700 |
permissions | -rw-r--r-- |
1465 | 1 |
(* Title: Relation.ML |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
2 |
ID: $Id$ |
1465 | 3 |
Authors: Riccardo Mattolini, Dip. Sistemi e Informatica |
4 |
Lawrence C Paulson, Cambridge University Computer Laboratory |
|
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
5 |
Copyright 1994 Universita' di Firenze |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
6 |
Copyright 1993 University of Cambridge |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
7 |
*) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
8 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
9 |
val RSLIST = curry (op MRS); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
10 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
11 |
open Relation; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
12 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
13 |
(** Identity relation **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
14 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
15 |
goalw Relation.thy [id_def] "(a,a) : id"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
16 |
by (rtac CollectI 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
17 |
by (rtac exI 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
18 |
by (rtac refl 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
19 |
qed "idI"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
20 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
21 |
val major::prems = goalw Relation.thy [id_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
22 |
"[| p: id; !!x.[| p = (x,x) |] ==> P \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
23 |
\ |] ==> P"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
24 |
by (rtac (major RS CollectE) 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
25 |
by (etac exE 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
26 |
by (eresolve_tac prems 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
27 |
qed "idE"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
28 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
29 |
goalw Relation.thy [id_def] "(a,b):id = (a=b)"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
30 |
by(fast_tac prod_cs 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
31 |
qed "pair_in_id_conv"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
32 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
33 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
34 |
(** Composition of two relations **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
35 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
36 |
val prems = goalw Relation.thy [comp_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
37 |
"[| (a,b):s; (b,c):r |] ==> (a,c) : r O s"; |
1454
d0266c81a85e
Streamlined defs in Relation and added new intro/elim rules to do with
nipkow
parents:
1264
diff
changeset
|
38 |
by (fast_tac (prod_cs addIs prems) 1); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
39 |
qed "compI"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
40 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
41 |
(*proof requires higher-level assumptions or a delaying of hyp_subst_tac*) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
42 |
val prems = goalw Relation.thy [comp_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
43 |
"[| xz : r O s; \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
44 |
\ !!x y z. [| xz = (x,z); (x,y):s; (y,z):r |] ==> P \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
45 |
\ |] ==> P"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
46 |
by (cut_facts_tac prems 1); |
1454
d0266c81a85e
Streamlined defs in Relation and added new intro/elim rules to do with
nipkow
parents:
1264
diff
changeset
|
47 |
by (REPEAT (eresolve_tac [CollectE, splitE, exE, conjE] 1 ORELSE ares_tac prems 1)); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
48 |
qed "compE"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
49 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
50 |
val prems = goal Relation.thy |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
51 |
"[| (a,c) : r O s; \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
52 |
\ !!y. [| (a,y):s; (y,c):r |] ==> P \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
53 |
\ |] ==> P"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
54 |
by (rtac compE 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
55 |
by (REPEAT (ares_tac prems 1 ORELSE eresolve_tac [Pair_inject,ssubst] 1)); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
56 |
qed "compEpair"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
57 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
58 |
val comp_cs = prod_cs addIs [compI, idI] addSEs [compE, idE]; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
59 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
60 |
goal Relation.thy "!!r s. [| r'<=r; s'<=s |] ==> (r' O s') <= (r O s)"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
61 |
by (fast_tac comp_cs 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
62 |
qed "comp_mono"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
63 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
64 |
goal Relation.thy |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
65 |
"!!r s. [| s <= Sigma A (%x.B); r <= Sigma B (%x.C) |] ==> \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
66 |
\ (r O s) <= Sigma A (%x.C)"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
67 |
by (fast_tac comp_cs 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
68 |
qed "comp_subset_Sigma"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
69 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
70 |
(** Natural deduction for trans(r) **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
71 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
72 |
val prems = goalw Relation.thy [trans_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
73 |
"(!! x y z. [| (x,y):r; (y,z):r |] ==> (x,z):r) ==> trans(r)"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
74 |
by (REPEAT (ares_tac (prems@[allI,impI]) 1)); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
75 |
qed "transI"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
76 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
77 |
val major::prems = goalw Relation.thy [trans_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
78 |
"[| trans(r); (a,b):r; (b,c):r |] ==> (a,c):r"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
79 |
by (cut_facts_tac [major] 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
80 |
by (fast_tac (HOL_cs addIs prems) 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
81 |
qed "transD"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
82 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
83 |
(** Natural deduction for converse(r) **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
84 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
85 |
goalw Relation.thy [converse_def] "!!a b r. (a,b):r ==> (b,a):converse(r)"; |
1264
3eb91524b938
added local simpsets; removed IOA from 'make test'
clasohm
parents:
1128
diff
changeset
|
86 |
by (Simp_tac 1); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
87 |
qed "converseI"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
88 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
89 |
goalw Relation.thy [converse_def] "!!a b r. (a,b) : converse(r) ==> (b,a) : r"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
90 |
by (fast_tac comp_cs 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
91 |
qed "converseD"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
92 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
93 |
qed_goalw "converseE" Relation.thy [converse_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
94 |
"[| yx : converse(r); \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
95 |
\ !!x y. [| yx=(y,x); (x,y):r |] ==> P \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
96 |
\ |] ==> P" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
97 |
(fn [major,minor]=> |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
98 |
[ (rtac (major RS CollectE) 1), |
1454
d0266c81a85e
Streamlined defs in Relation and added new intro/elim rules to do with
nipkow
parents:
1264
diff
changeset
|
99 |
(REPEAT (eresolve_tac [splitE, bexE,exE, conjE, minor] 1)), |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
100 |
(assume_tac 1) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
101 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
102 |
val converse_cs = comp_cs addSIs [converseI] |
1465 | 103 |
addSEs [converseD,converseE]; |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
104 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
105 |
(** Domain **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
106 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
107 |
qed_goalw "Domain_iff" Relation.thy [Domain_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
108 |
"a: Domain(r) = (EX y. (a,y): r)" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
109 |
(fn _=> [ (fast_tac comp_cs 1) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
110 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
111 |
qed_goal "DomainI" Relation.thy "!!a b r. (a,b): r ==> a: Domain(r)" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
112 |
(fn _ => [ (etac (exI RS (Domain_iff RS iffD2)) 1) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
113 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
114 |
qed_goal "DomainE" Relation.thy |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
115 |
"[| a : Domain(r); !!y. (a,y): r ==> P |] ==> P" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
116 |
(fn prems=> |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
117 |
[ (rtac (Domain_iff RS iffD1 RS exE) 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
118 |
(REPEAT (ares_tac prems 1)) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
119 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
120 |
(** Range **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
121 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
122 |
qed_goalw "RangeI" Relation.thy [Range_def] "!!a b r.(a,b): r ==> b : Range(r)" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
123 |
(fn _ => [ (etac (converseI RS DomainI) 1) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
124 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
125 |
qed_goalw "RangeE" Relation.thy [Range_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
126 |
"[| b : Range(r); !!x. (x,b): r ==> P |] ==> P" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
127 |
(fn major::prems=> |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
128 |
[ (rtac (major RS DomainE) 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
129 |
(resolve_tac prems 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
130 |
(etac converseD 1) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
131 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
132 |
(*** Image of a set under a relation ***) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
133 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
134 |
qed_goalw "Image_iff" Relation.thy [Image_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
135 |
"b : r^^A = (? x:A. (x,b):r)" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
136 |
(fn _ => [ fast_tac (comp_cs addIs [RangeI]) 1 ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
137 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
138 |
qed_goal "Image_singleton_iff" Relation.thy |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
139 |
"(b : r^^{a}) = ((a,b):r)" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
140 |
(fn _ => [ rtac (Image_iff RS trans) 1, |
1465 | 141 |
fast_tac comp_cs 1 ]); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
142 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
143 |
qed_goalw "ImageI" Relation.thy [Image_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
144 |
"!!a b r. [| (a,b): r; a:A |] ==> b : r^^A" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
145 |
(fn _ => [ (REPEAT (ares_tac [CollectI,RangeI,bexI] 1)), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
146 |
(resolve_tac [conjI ] 1), |
1465 | 147 |
(rtac RangeI 1), |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
148 |
(REPEAT (fast_tac set_cs 1))]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
149 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
150 |
qed_goalw "ImageE" Relation.thy [Image_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
151 |
"[| b: r^^A; !!x.[| (x,b): r; x:A |] ==> P |] ==> P" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
152 |
(fn major::prems=> |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
153 |
[ (rtac (major RS CollectE) 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
154 |
(safe_tac set_cs), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
155 |
(etac RangeE 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
156 |
(rtac (hd prems) 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
157 |
(REPEAT (etac bexE 1 ORELSE ares_tac prems 1)) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
158 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
159 |
qed_goal "Image_subset" Relation.thy |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
160 |
"!!A B r. r <= Sigma A (%x.B) ==> r^^C <= B" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
161 |
(fn _ => |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
162 |
[ (rtac subsetI 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
163 |
(REPEAT (eresolve_tac [asm_rl, ImageE, subsetD RS SigmaD2] 1)) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
164 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
165 |
val rel_cs = converse_cs addSIs [converseI] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
166 |
addIs [ImageI, DomainI, RangeI] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
167 |
addSEs [ImageE, DomainE, RangeE]; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
168 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
169 |
val rel_eq_cs = rel_cs addSIs [equalityI]; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
170 |
|
1264
3eb91524b938
added local simpsets; removed IOA from 'make test'
clasohm
parents:
1128
diff
changeset
|
171 |
Addsimps [pair_in_id_conv]; |