author | Christian Urban <urbanc@in.tum.de> |
Sat, 04 Sep 2010 06:23:31 +0800 | |
changeset 2468 | 7b1470b55936 |
parent 2464 | f4eba60cbd69 |
child 2473 | a3711f07449b |
permissions | -rw-r--r-- |
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
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parents:
1773
diff
changeset
|
1 |
theory SingleLet |
2454
9ffee4eb1ae1
renamed NewParser to Nominal2
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|
2 |
imports "../Nominal2" |
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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3 |
begin |
c69d9fb16785
Move Ex1 and Ex2 out of Test
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parents:
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|
4 |
|
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
5 |
atom_decl name |
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
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6 |
|
2436
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parents:
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|
7 |
declare [[STEPS = 100]] |
2294
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properly exported bn_descr
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parents:
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8 |
|
2436
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parents:
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|
9 |
nominal_datatype single_let: trm = |
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
10 |
Var "name" |
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
11 |
| App "trm" "trm" |
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parents:
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12 |
| Lam x::"name" t::"trm" bind x in t |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
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parents:
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13 |
| Let a::"assg" t::"trm" bind "bn a" in t |
2424
621ebd8b13c4
changed parser so that the binding mode is indicated as "bind (list)", "bind (set)" or "bind (res)"; if only "bind" is given, then bind (list) is assumed as default
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parents:
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14 |
| Foo x::"name" y::"name" t::"trm" t1::"trm" t2::"trm" bind (set) x in y t t1 t2 |
2296 | 15 |
| Bar x::"name" y::"name" t::"trm" bind y x in t x y |
2316 | 16 |
| Baz x::"name" t1::"trm" t2::"trm" bind x in t1, bind x in t2 |
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
17 |
and assg = |
2320
d835a2771608
prove that alpha implies alpha_bn (needed for rsp proofs)
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parents:
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18 |
As "name" x::"name" t::"trm" bind x in t |
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
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19 |
binder |
2464
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parents:
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|
20 |
bn::"assg \<Rightarrow> atom list" |
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
21 |
where |
2464
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Christian Urban <urbanc@in.tum.de>
parents:
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|
22 |
"bn (As x y t) = [atom x]" |
1911
60b5c61d3de2
renamed Ex1.thy to SingleLet.thy
Christian Urban <urbanc@in.tum.de>
parents:
1773
diff
changeset
|
23 |
|
2448 | 24 |
|
2436
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parents:
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25 |
thm single_let.distinct |
3885dc2669f9
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parents:
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|
26 |
thm single_let.induct |
3885dc2669f9
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parents:
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27 |
thm single_let.exhaust |
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
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28 |
thm single_let.fv_defs |
3885dc2669f9
cleaned up (almost completely) the examples
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parents:
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29 |
thm single_let.bn_defs |
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
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30 |
thm single_let.perm_simps |
3885dc2669f9
cleaned up (almost completely) the examples
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parents:
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|
31 |
thm single_let.eq_iff |
3885dc2669f9
cleaned up (almost completely) the examples
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parents:
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32 |
thm single_let.fv_bn_eqvt |
3885dc2669f9
cleaned up (almost completely) the examples
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parents:
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|
33 |
thm single_let.size_eqvt |
2448 | 34 |
thm single_let.supports |
2450
217ef3e4282e
added proofs for fsupp properties
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parents:
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35 |
thm single_let.fsupp |
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updated to new Isabelle
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parents:
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36 |
|
2461
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some experiments with support
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parents:
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|
37 |
lemma test2: |
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some experiments with support
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parents:
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38 |
assumes "fv_trm t = supp t" |
86028b2016bd
some experiments with support
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parents:
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|
39 |
shows "\<forall>p. fv_trm (p \<bullet> t) = supp (p \<bullet> t)" |
2464
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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40 |
apply(rule allI) |
f4eba60cbd69
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Christian Urban <urbanc@in.tum.de>
parents:
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41 |
apply(rule_tac p="-p" in permute_boolE) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
42 |
apply(perm_simp add: single_let.fv_bn_eqvt permute_minus_cancel) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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changeset
|
43 |
apply(rule assms) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
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parents:
2461
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|
44 |
done |
2461
86028b2016bd
some experiments with support
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parents:
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|
45 |
|
86028b2016bd
some experiments with support
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parents:
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46 |
|
2361 | 47 |
lemma supp_fv: |
2461
86028b2016bd
some experiments with support
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parents:
2454
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changeset
|
48 |
"fv_trm t = supp t \<and> fv_assg as = supp as \<and> fv_bn as = {a. infinite {b. \<not>alpha_bn ((a \<rightleftharpoons> b) \<bullet> as) as}}" |
2448 | 49 |
apply(rule single_let.induct) |
2464
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Christian Urban <urbanc@in.tum.de>
parents:
2461
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changeset
|
50 |
apply(simp_all (no_asm_use) only: single_let.fv_defs)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
51 |
apply(simp_all (no_asm_use) only: supp_def)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
52 |
apply(simp_all (no_asm_use) only: single_let.perm_simps)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
53 |
apply(simp_all (no_asm_use) only: single_let.eq_iff)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
54 |
apply(simp_all (no_asm_use) only: de_Morgan_conj)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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changeset
|
55 |
apply(simp_all (no_asm_use) only: Collect_disj_eq)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
56 |
apply(simp_all (no_asm_use) only: finite_Un)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
57 |
apply(simp_all (no_asm_use) only: de_Morgan_conj)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
58 |
apply(simp_all (no_asm_use) only: Collect_disj_eq)[2] |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
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|
59 |
apply(simp) |
2461
86028b2016bd
some experiments with support
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parents:
2454
diff
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|
60 |
--" 1 " |
2464
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
61 |
apply(simp only: single_let.fv_defs supp_Pair[symmetric]) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
62 |
apply(simp only: supp_abs(3)[symmetric]) |
2461
86028b2016bd
some experiments with support
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
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|
63 |
apply(simp (no_asm) only: supp_def) |
2464
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
64 |
apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
65 |
apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
66 |
apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject) |
2461
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parents:
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67 |
apply(drule test2) |
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parents:
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68 |
apply(simp only:) |
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parents:
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69 |
-- " 2 " |
86028b2016bd
some experiments with support
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parents:
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70 |
apply(erule conjE)+ |
2464
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made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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71 |
apply(simp only: single_let.fv_defs supp_Pair[symmetric]) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
72 |
apply(simp only: supp_abs(3)[symmetric]) |
2448 | 73 |
apply(simp (no_asm) only: supp_def) |
2464
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
74 |
apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
75 |
apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
76 |
apply(simp only: de_Morgan_conj Collect_disj_eq finite_Un) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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changeset
|
77 |
apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
78 |
apply(drule test2) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
79 |
apply(simp only:) |
f4eba60cbd69
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parents:
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|
80 |
-- " 3 " |
f4eba60cbd69
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Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
81 |
apply(simp only: single_let.fv_defs supp_Pair[symmetric]) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
82 |
apply(simp only: supp_abs(1)[symmetric]) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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changeset
|
83 |
apply(simp (no_asm) only: supp_def) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
84 |
apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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changeset
|
85 |
apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
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changeset
|
86 |
apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject) |
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some experiments with support
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parents:
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|
87 |
apply(drule test2)+ |
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parents:
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|
88 |
apply(simp only: supp_Pair Un_assoc conj_assoc) |
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some experiments with support
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parents:
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|
89 |
-- " Bar " |
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parents:
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|
90 |
apply(simp only: single_let.fv_defs supp_Pair[symmetric]) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
91 |
apply(simp only: supp_abs(3)[symmetric]) |
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parents:
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|
92 |
apply(simp (no_asm) only: supp_def) |
2464
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made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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|
93 |
apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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|
94 |
apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
95 |
apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
96 |
apply(drule test2)+ |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
97 |
apply(simp only: supp_Pair Un_assoc conj_assoc) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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|
98 |
-- " Baz " |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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|
99 |
apply(simp only: single_let.fv_defs supp_Pair[symmetric]) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
100 |
apply(simp only: supp_abs(3)[symmetric]) |
2461
86028b2016bd
some experiments with support
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parents:
2454
diff
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|
101 |
apply(simp (no_asm) only: supp_def) |
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Christian Urban <urbanc@in.tum.de>
parents:
2461
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|
102 |
apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
103 |
apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
104 |
apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject) |
f4eba60cbd69
made the fv-definition aggree more with alpha (needed in the support proofs)
Christian Urban <urbanc@in.tum.de>
parents:
2461
diff
changeset
|
105 |
apply(simp only: de_Morgan_conj Collect_disj_eq finite_Un) |
f4eba60cbd69
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106 |
apply(drule test2)+ |
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107 |
apply(simp only: supp_Pair Un_assoc conj_assoc) |
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108 |
-- "last" |
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|
109 |
apply(rule conjI) |
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110 |
apply(simp only: single_let.fv_defs supp_Pair[symmetric]) |
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|
111 |
apply(simp only: supp_abs(3)[symmetric]) |
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112 |
apply(simp (no_asm) only: supp_def) |
2464
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113 |
apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt) |
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114 |
apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff) |
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115 |
apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject) |
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116 |
apply(simp only: de_Morgan_conj Collect_disj_eq finite_Un) |
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117 |
apply(drule test2)+ |
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118 |
apply(simp only: supp_Pair Un_assoc conj_assoc) |
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119 |
-- "other case" |
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120 |
apply(simp only: single_let.fv_defs supp_Pair[symmetric]) |
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121 |
apply(simp only: supp_abs(3)[symmetric]) |
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122 |
apply(simp (no_asm) only: supp_def) |
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123 |
apply(perm_simp add: single_let.perm_simps single_let.fv_bn_eqvt) |
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|
124 |
apply(simp (no_asm) only: single_let.eq_iff Abs_eq_iff) |
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125 |
apply(simp only: alphas prod_alpha_def prod_fv.simps prod_rel.simps permute_prod_def prod.recs prod.cases prod.inject) |
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126 |
apply(simp only: de_Morgan_conj Collect_disj_eq finite_Un)? |
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127 |
apply(drule test2)+ |
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128 |
apply(simp only: supp_Pair Un_assoc conj_assoc) |
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|
129 |
done |
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some experiments with support
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130 |
|
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131 |
|
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132 |
|
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some experiments with support
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133 |
|
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134 |
|
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|
135 |
text {* *} |
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|
136 |
|
2448 | 137 |
(* |
2365 | 138 |
consts perm_bn_trm :: "perm \<Rightarrow> trm \<Rightarrow> trm" |
139 |
consts perm_bn_assg :: "perm \<Rightarrow> assg \<Rightarrow> assg" |
|
140 |
||
141 |
lemma y: |
|
142 |
"perm_bn_trm p (Var x) = (Var x)" |
|
143 |
"perm_bn_trm p (App t1 t2) = (App t1 t2)" |
|
144 |
"perm_bn_trm p (" |
|
145 |
||
146 |
||
2361 | 147 |
|
2336
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|
148 |
typ trm |
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|
149 |
typ assg |
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|
150 |
|
1911
60b5c61d3de2
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|
151 |
thm trm_assg.fv |
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|
152 |
thm trm_assg.supp |
2024
d974059827ad
Equivariance fails for single let?
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diff
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|
153 |
thm trm_assg.eq_iff |
1911
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|
154 |
thm trm_assg.bn |
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|
155 |
thm trm_assg.perm |
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|
156 |
thm trm_assg.induct |
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|
157 |
thm trm_assg.inducts |
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|
158 |
thm trm_assg.distinct |
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|
159 |
ML {* Sign.of_sort @{theory} (@{typ trm}, @{sort fs}) *} |
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|
160 |
*) |
2024
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Equivariance fails for single let?
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|
161 |
|
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|
162 |
|
2064
2725853f43b9
solved the problem with equivariance by first eta-normalising the goal
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|
163 |
|
1596
c69d9fb16785
Move Ex1 and Ex2 out of Test
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|
164 |
end |
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Move Ex1 and Ex2 out of Test
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|
165 |
|
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Move Ex1 and Ex2 out of Test
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|
166 |
|
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Move Ex1 and Ex2 out of Test
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|
167 |