| author | Christian Urban <urbanc@in.tum.de> |
| Mon, 25 Jan 2010 19:14:46 +0100 | |
| changeset 922 | a2589b4bc442 |
| parent 913 | b1f55dd64481 |
| child 925 | 8d51795ef54d |
| permissions | -rw-r--r-- |
|
593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
1 |
theory QuotProd |
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830b58c2fa94
decoupled QuotProd from QuotMain and also started new cleaning strategy
Christian Urban <urbanc@in.tum.de>
parents:
597
diff
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2 |
imports QuotMain |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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3 |
begin |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
4 |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
5 |
fun |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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6 |
prod_rel |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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7 |
where |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
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8 |
"prod_rel R1 R2 = (\<lambda>(a,b) (c,d). R1 a c \<and> R2 b d)" |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
9 |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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10 |
declare [[map * = (prod_fun, prod_rel)]] |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
11 |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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12 |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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lemma prod_equivp[quot_equiv]: |
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QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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14 |
assumes a: "equivp R1" |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
15 |
assumes b: "equivp R2" |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
16 |
shows "equivp (prod_rel R1 R2)" |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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unfolding equivp_reflp_symp_transp reflp_def symp_def transp_def |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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18 |
apply(auto simp add: equivp_reflp[OF a] equivp_reflp[OF b]) |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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apply(simp only: equivp_symp[OF a]) |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
20 |
apply(simp only: equivp_symp[OF b]) |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
21 |
using equivp_transp[OF a] apply blast |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
22 |
using equivp_transp[OF b] apply blast |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
23 |
done |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
24 |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
25 |
lemma prod_quotient[quot_thm]: |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
26 |
assumes q1: "Quotient R1 Abs1 Rep1" |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
27 |
assumes q2: "Quotient R2 Abs2 Rep2" |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
28 |
shows "Quotient (prod_rel R1 R2) (prod_fun Abs1 Abs2) (prod_fun Rep1 Rep2)" |
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18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
29 |
unfolding Quotient_def |
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699
aa157e957655
added maps-printout and tuned some comments
Christian Urban <urbanc@in.tum.de>
parents:
668
diff
changeset
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using q1 q2 |
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aa157e957655
added maps-printout and tuned some comments
Christian Urban <urbanc@in.tum.de>
parents:
668
diff
changeset
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31 |
apply (simp add: Quotient_abs_rep Quotient_abs_rep Quotient_rel_rep Quotient_rel_rep) |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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32 |
using Quotient_rel[OF q1] Quotient_rel[OF q2] |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
33 |
by blast |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
34 |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
35 |
lemma pair_rsp[quot_respect]: |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
36 |
assumes q1: "Quotient R1 Abs1 Rep1" |
|
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
37 |
assumes q2: "Quotient R2 Abs2 Rep2" |
|
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
38 |
shows "(R1 ===> R2 ===> prod_rel R1 R2) Pair Pair" |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
39 |
by simp |
|
593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
40 |
|
|
648
830b58c2fa94
decoupled QuotProd from QuotMain and also started new cleaning strategy
Christian Urban <urbanc@in.tum.de>
parents:
597
diff
changeset
|
41 |
lemma pair_prs[quot_preserve]: |
|
830b58c2fa94
decoupled QuotProd from QuotMain and also started new cleaning strategy
Christian Urban <urbanc@in.tum.de>
parents:
597
diff
changeset
|
42 |
assumes q1: "Quotient R1 Abs1 Rep1" |
|
830b58c2fa94
decoupled QuotProd from QuotMain and also started new cleaning strategy
Christian Urban <urbanc@in.tum.de>
parents:
597
diff
changeset
|
43 |
assumes q2: "Quotient R2 Abs2 Rep2" |
|
830b58c2fa94
decoupled QuotProd from QuotMain and also started new cleaning strategy
Christian Urban <urbanc@in.tum.de>
parents:
597
diff
changeset
|
44 |
shows "(Rep1 ---> Rep2 ---> (prod_fun Abs1 Abs2)) Pair = Pair" |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
45 |
apply(simp add: expand_fun_eq) |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
46 |
apply(simp add: Quotient_abs_rep[OF q1] Quotient_abs_rep[OF q2]) |
|
648
830b58c2fa94
decoupled QuotProd from QuotMain and also started new cleaning strategy
Christian Urban <urbanc@in.tum.de>
parents:
597
diff
changeset
|
47 |
done |
|
830b58c2fa94
decoupled QuotProd from QuotMain and also started new cleaning strategy
Christian Urban <urbanc@in.tum.de>
parents:
597
diff
changeset
|
48 |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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49 |
lemma fst_rsp[quot_respect]: |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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50 |
assumes "Quotient R1 Abs1 Rep1" |
|
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
51 |
assumes "Quotient R2 Abs2 Rep2" |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
52 |
shows "(prod_rel R1 R2 ===> R1) fst fst" |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
53 |
by simp |
|
648
830b58c2fa94
decoupled QuotProd from QuotMain and also started new cleaning strategy
Christian Urban <urbanc@in.tum.de>
parents:
597
diff
changeset
|
54 |
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|
922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
55 |
lemma fst_prs[quot_preserve]: |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
56 |
assumes q1: "Quotient R1 Abs1 Rep1" |
|
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
57 |
assumes q2: "Quotient R2 Abs2 Rep2" |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
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shows "(prod_fun Rep1 Rep2 ---> Abs1) fst = fst" |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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59 |
apply(simp add: expand_fun_eq) |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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apply(simp add: Quotient_abs_rep[OF q1]) |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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61 |
done |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
62 |
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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lemma snd_rsp[quot_respect]: |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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64 |
assumes "Quotient R1 Abs1 Rep1" |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
65 |
assumes "Quotient R2 Abs2 Rep2" |
|
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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shows "(prod_rel R1 R2 ===> R2) snd snd" |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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67 |
by simp |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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68 |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
69 |
lemma snd_prs[quot_preserve]: |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
70 |
assumes q1: "Quotient R1 Abs1 Rep1" |
|
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
71 |
assumes q2: "Quotient R2 Abs2 Rep2" |
|
922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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72 |
shows "(prod_fun Rep1 Rep2 ---> Abs2) snd = snd" |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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73 |
apply(simp add: expand_fun_eq) |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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74 |
apply(simp add: Quotient_abs_rep[OF q2]) |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
|
75 |
done |
|
593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
76 |
|
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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77 |
lemma prod_fun_id[id_simps]: |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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shows "prod_fun id id \<equiv> id" |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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79 |
by (rule eq_reflection) |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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80 |
(simp add: prod_fun_def) |
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
81 |
|
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922
a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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82 |
lemma prod_rel_eq[id_simps]: |
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a2589b4bc442
tuned proofs (mainly in QuotProd)
Christian Urban <urbanc@in.tum.de>
parents:
913
diff
changeset
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83 |
shows "prod_rel op = op = \<equiv> op =" |
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829
42b90994ac77
map and rel simps for all quotients; needed when changing the relations to aggregate ones.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
699
diff
changeset
|
84 |
apply (rule eq_reflection) |
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42b90994ac77
map and rel simps for all quotients; needed when changing the relations to aggregate ones.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
699
diff
changeset
|
85 |
apply (rule ext)+ |
|
42b90994ac77
map and rel simps for all quotients; needed when changing the relations to aggregate ones.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
699
diff
changeset
|
86 |
apply auto |
|
42b90994ac77
map and rel simps for all quotients; needed when changing the relations to aggregate ones.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
699
diff
changeset
|
87 |
done |
|
42b90994ac77
map and rel simps for all quotients; needed when changing the relations to aggregate ones.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
699
diff
changeset
|
88 |
|
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593
18eac4596ef1
QuotProd with product_quotient and a 3 respects and preserves lemmas.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
89 |
end |