author | wenzelm |
Mon, 17 Feb 1997 17:23:14 +0100 | |
changeset 2652 | 024654b75919 |
parent 2637 | e9b203f854ae |
child 2891 | d8f254ad1ab9 |
permissions | -rw-r--r-- |
1465 | 1 |
(* Title: Relation.ML |
1128
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2 |
ID: $Id$ |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
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3 |
Authors: Lawrence C Paulson, Cambridge University Computer Laboratory |
84cf16192e03
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paulson
parents:
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4 |
Copyright 1996 University of Cambridge |
1128
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5 |
*) |
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Trancl is now based on Relation which used to be in Integ.
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parents:
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6 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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7 |
open Relation; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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8 |
|
64b30e3cc6d4
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9 |
(** Identity relation **) |
64b30e3cc6d4
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10 |
|
64b30e3cc6d4
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11 |
goalw Relation.thy [id_def] "(a,a) : id"; |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
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|
12 |
by (Fast_tac 1); |
1128
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Trancl is now based on Relation which used to be in Integ.
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13 |
qed "idI"; |
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parents:
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14 |
|
64b30e3cc6d4
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parents:
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15 |
val major::prems = goalw Relation.thy [id_def] |
64b30e3cc6d4
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parents:
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16 |
"[| p: id; !!x.[| p = (x,x) |] ==> P \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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17 |
\ |] ==> P"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
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18 |
by (rtac (major RS CollectE) 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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19 |
by (etac exE 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
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20 |
by (eresolve_tac prems 1); |
64b30e3cc6d4
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parents:
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21 |
qed "idE"; |
64b30e3cc6d4
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22 |
|
64b30e3cc6d4
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23 |
goalw Relation.thy [id_def] "(a,b):id = (a=b)"; |
1754
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
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24 |
by (Fast_tac 1); |
1128
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25 |
qed "pair_in_id_conv"; |
1694 | 26 |
Addsimps [pair_in_id_conv]; |
1128
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27 |
|
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Trancl is now based on Relation which used to be in Integ.
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28 |
|
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29 |
(** Composition of two relations **) |
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30 |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
31 |
goalw Relation.thy [comp_def] |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
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|
32 |
"!!r s. [| (a,b):s; (b,c):r |] ==> (a,c) : r O s"; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
33 |
by (Fast_tac 1); |
1128
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34 |
qed "compI"; |
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35 |
|
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36 |
(*proof requires higher-level assumptions or a delaying of hyp_subst_tac*) |
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37 |
val prems = goalw Relation.thy [comp_def] |
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parents:
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38 |
"[| xz : r O s; \ |
64b30e3cc6d4
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39 |
\ !!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.
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parents:
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40 |
\ |] ==> P"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
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41 |
by (cut_facts_tac prems 1); |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
42 |
by (REPEAT (eresolve_tac [CollectE, splitE, exE, conjE] 1 |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
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43 |
ORELSE ares_tac prems 1)); |
1128
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Trancl is now based on Relation which used to be in Integ.
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44 |
qed "compE"; |
64b30e3cc6d4
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45 |
|
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46 |
val prems = goal Relation.thy |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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47 |
"[| (a,c) : r O s; \ |
64b30e3cc6d4
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48 |
\ !!y. [| (a,y):s; (y,c):r |] ==> P \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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49 |
\ |] ==> P"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
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50 |
by (rtac compE 1); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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51 |
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.
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52 |
qed "compEpair"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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53 |
|
1754
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
changeset
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54 |
AddIs [compI, idI]; |
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
changeset
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55 |
AddSEs [compE, idE]; |
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
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|
56 |
|
1128
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Trancl is now based on Relation which used to be in Integ.
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57 |
goal Relation.thy "!!r s. [| r'<=r; s'<=s |] ==> (r' O s') <= (r O s)"; |
1754
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
changeset
|
58 |
by (Fast_tac 1); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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59 |
qed "comp_mono"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
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60 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
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|
61 |
goal Relation.thy |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
62 |
"!!r s. [| s <= A Times B; r <= B Times C |] ==> (r O s) <= A Times C"; |
1754
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
changeset
|
63 |
by (Fast_tac 1); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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|
64 |
qed "comp_subset_Sigma"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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65 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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66 |
(** Natural deduction for trans(r) **) |
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67 |
|
64b30e3cc6d4
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parents:
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68 |
val prems = goalw Relation.thy [trans_def] |
64b30e3cc6d4
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parents:
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|
69 |
"(!! 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.
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parents:
diff
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|
70 |
by (REPEAT (ares_tac (prems@[allI,impI]) 1)); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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71 |
qed "transI"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
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|
72 |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
73 |
goalw Relation.thy [trans_def] |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
74 |
"!!r. [| trans(r); (a,b):r; (b,c):r |] ==> (a,c):r"; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
75 |
by (Fast_tac 1); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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76 |
qed "transD"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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77 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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|
78 |
(** Natural deduction for converse(r) **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
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parents:
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79 |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
80 |
goalw Relation.thy [converse_def] "!!a b r. ((a,b):converse r) = ((b,a):r)"; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
81 |
by (Simp_tac 1); |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
82 |
qed "converse_iff"; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
83 |
|
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
84 |
AddIffs [converse_iff]; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
85 |
|
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
86 |
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
|
87 |
by (Simp_tac 1); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
88 |
qed "converseI"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
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|
89 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
90 |
goalw Relation.thy [converse_def] "!!a b r. (a,b) : converse(r) ==> (b,a) : r"; |
1754
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
changeset
|
91 |
by (Fast_tac 1); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
92 |
qed "converseD"; |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
93 |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
94 |
(*More general than converseD, as it "splits" the member of the relation*) |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
95 |
qed_goalw "converseE" Relation.thy [converse_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
96 |
"[| yx : converse(r); \ |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
97 |
\ !!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
|
98 |
\ |] ==> P" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
99 |
(fn [major,minor]=> |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
100 |
[ (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
|
101 |
(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
|
102 |
(assume_tac 1) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
103 |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
104 |
AddSEs [converseE]; |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
105 |
|
1605 | 106 |
goalw Relation.thy [converse_def] "converse(converse R) = R"; |
2031 | 107 |
by (Fast_tac 1); |
1605 | 108 |
qed "converse_converse"; |
109 |
||
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
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|
110 |
(** Domain **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
111 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
112 |
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
|
113 |
"a: Domain(r) = (EX y. (a,y): r)" |
1754
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
changeset
|
114 |
(fn _=> [ (Fast_tac 1) ]); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
115 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
116 |
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
|
117 |
(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
|
118 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
119 |
qed_goal "DomainE" Relation.thy |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
120 |
"[| 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
|
121 |
(fn prems=> |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
122 |
[ (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
|
123 |
(REPEAT (ares_tac prems 1)) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
124 |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
125 |
AddIs [DomainI]; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
126 |
AddSEs [DomainE]; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
127 |
|
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
128 |
(** Range **) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
129 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
130 |
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
|
131 |
(fn _ => [ (etac (converseI RS DomainI) 1) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
132 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
133 |
qed_goalw "RangeE" Relation.thy [Range_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
134 |
"[| 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
|
135 |
(fn major::prems=> |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
136 |
[ (rtac (major RS DomainE) 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
137 |
(resolve_tac prems 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
138 |
(etac converseD 1) ]); |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
139 |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
140 |
AddIs [RangeI]; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
141 |
AddSEs [RangeE]; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
142 |
|
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
143 |
(*** Image of a set under a relation ***) |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
144 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
145 |
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
|
146 |
"b : r^^A = (? x:A. (x,b):r)" |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
147 |
(fn _ => [ Fast_tac 1 ]); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
148 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
149 |
qed_goal "Image_singleton_iff" Relation.thy |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
150 |
"(b : r^^{a}) = ((a,b):r)" |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
151 |
(fn _ => [ rtac (Image_iff RS trans) 1, |
1754
852093aeb0ab
Replaced fast_tac by Fast_tac (which uses default claset)
berghofe
parents:
1694
diff
changeset
|
152 |
Fast_tac 1 ]); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
153 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
154 |
qed_goalw "ImageI" Relation.thy [Image_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
155 |
"!!a b r. [| (a,b): r; a:A |] ==> b : r^^A" |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
156 |
(fn _ => [ (Fast_tac 1)]); |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
157 |
|
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
158 |
qed_goalw "ImageE" Relation.thy [Image_def] |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
159 |
"[| 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
|
160 |
(fn major::prems=> |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
161 |
[ (rtac (major RS CollectE) 1), |
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
162 |
(Step_tac 1), |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
163 |
(rtac (hd prems) 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
164 |
(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
|
165 |
|
1985
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
166 |
AddIs [ImageI]; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
167 |
AddSEs [ImageE]; |
84cf16192e03
Tidied many proofs, using AddIffs to let equivalences take
paulson
parents:
1842
diff
changeset
|
168 |
|
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
169 |
qed_goal "Image_subset" Relation.thy |
1642 | 170 |
"!!A B r. r <= A Times B ==> r^^C <= B" |
1128
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
171 |
(fn _ => |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
172 |
[ (rtac subsetI 1), |
64b30e3cc6d4
Trancl is now based on Relation which used to be in Integ.
nipkow
parents:
diff
changeset
|
173 |
(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
|
174 |
|
1694 | 175 |
goal Relation.thy "R O id = R"; |
2637
e9b203f854ae
reflecting my recent changes of the simplifier and classical reasoner
oheimb
parents:
2031
diff
changeset
|
176 |
by (fast_tac (!claset addbefore split_all_tac) 1); |
1694 | 177 |
qed "R_O_id"; |
178 |
||
179 |
goal Relation.thy "id O R = R"; |
|
2637
e9b203f854ae
reflecting my recent changes of the simplifier and classical reasoner
oheimb
parents:
2031
diff
changeset
|
180 |
by (fast_tac (!claset addbefore split_all_tac) 1); |
1694 | 181 |
qed "id_O_R"; |
182 |
||
183 |
Addsimps [R_O_id,id_O_R]; |