| author | Christian Urban <urbanc@in.tum.de> |
| Mon, 27 Jun 2011 22:51:42 +0100 | |
| changeset 2911 | 567967bc94cc |
| parent 2910 | ae6455351572 |
| child 2913 | bc86f5c3bc65 |
| permissions | -rw-r--r-- |
|
1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
1 |
theory Classical |
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2454
9ffee4eb1ae1
renamed NewParser to Nominal2
Christian Urban <urbanc@in.tum.de>
parents:
2436
diff
changeset
|
2 |
imports "../Nominal2" |
|
1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
3 |
begin |
|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
4 |
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2617
e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
5 |
(* example from Urban's PhD *) |
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1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
6 |
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|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
7 |
atom_decl name |
|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
8 |
atom_decl coname |
|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
9 |
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|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
10 |
nominal_datatype trm = |
| 2889 | 11 |
Ax "name" "coname" |
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2891
304dfe6cc83a
the simplifier can simplify "sort (atom a)" if a is a concrete atom type declared with atom_decl
Christian Urban <urbanc@in.tum.de>
parents:
2889
diff
changeset
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12 |
| Cut c::"coname" t1::"trm" n::"name" t2::"trm" bind n in t1, bind c in t2 |
| 2889 | 13 |
("Cut <_>._ '(_')._" [100,100,100,100] 100)
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14 |
| NotR n::"name" t::"trm" "coname" bind n in t |
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15 |
("NotR '(_')._ _" [100,100,100] 100)
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16 |
| NotL c::"coname" t::"trm" "name" bind c in t |
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17 |
("NotL <_>._ _" [100,100,100] 100)
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18 |
| AndR c1::"coname" t1::"trm" c2::"coname" t2::"trm" "coname" bind c1 in t1, bind c2 in t2 |
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19 |
("AndR <_>._ <_>._ _" [100,100,100,100,100] 100)
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20 |
| AndL1 n::"name" t::"trm" "name" bind n in t |
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21 |
("AndL1 '(_')._ _" [100,100,100] 100)
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22 |
| AndL2 n::"name" t::"trm" "name" bind n in t |
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23 |
("AndL2 '(_')._ _" [100,100,100] 100)
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24 |
| OrR1 c::"coname" t::"trm" "coname" bind c in t |
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25 |
("OrR1 <_>._ _" [100,100,100] 100)
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26 |
| OrR2 c::"coname" t::"trm" "coname" bind c in t |
|
27 |
("OrR2 <_>._ _" [100,100,100] 100)
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28 |
| OrL n1::"name" t1::"trm" n2::"name" t2::"trm" "name" bind n1 in t1, bind n2 in t2 |
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29 |
("OrL '(_')._ '(_')._ _" [100,100,100,100,100] 100)
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30 |
| ImpL c::"coname" t1::"trm" n::"name" t2::"trm" "name" bind c in t1, bind n in t2 |
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31 |
("ImpL <_>._ '(_')._ _" [100,100,100,100,100] 100)
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2902
9c3f6a4d95d4
another change to the fcb2; this is needed in order to get all proofs through in Lambda.thy
Christian Urban <urbanc@in.tum.de>
parents:
2901
diff
changeset
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32 |
| ImpR n::"name" c::"coname" t::"trm" "coname" bind n c in t |
| 2889 | 33 |
("ImpR '(_').<_>._ _" [100,100,100,100] 100)
|
|
1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
34 |
|
|
2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
35 |
thm trm.distinct |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
36 |
thm trm.induct |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
37 |
thm trm.exhaust |
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2617
e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
38 |
thm trm.strong_exhaust |
|
e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
39 |
thm trm.strong_exhaust[simplified] |
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2436
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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40 |
thm trm.fv_defs |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
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41 |
thm trm.bn_defs |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
42 |
thm trm.perm_simps |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
43 |
thm trm.eq_iff |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
44 |
thm trm.fv_bn_eqvt |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
45 |
thm trm.size_eqvt |
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2617
e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
46 |
thm trm.supp |
|
e44551d067e6
properly exported strong exhaust theorem; cleaned up some examples
Christian Urban <urbanc@in.tum.de>
parents:
2454
diff
changeset
|
47 |
thm trm.supp[simplified] |
|
1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
48 |
|
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2903
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
49 |
lemma Abs_lst_fcb2: |
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e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
50 |
fixes as bs :: "atom list" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
51 |
and x y :: "'b :: fs" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
52 |
and c::"'c::fs" |
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2911
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
53 |
assumes eq: "[as]lst. x = [bs]lst. y" |
|
2903
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
54 |
and fcb1: "(set as) \<sharp>* f as x c" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
55 |
and fresh1: "set as \<sharp>* c" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
56 |
and fresh2: "set bs \<sharp>* c" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
57 |
and perm1: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f as x c) = f (p \<bullet> as) (p \<bullet> x) c" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
58 |
and perm2: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f bs y c) = f (p \<bullet> bs) (p \<bullet> y) c" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
2902
diff
changeset
|
59 |
shows "f as x c = f bs y c" |
|
2909
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
60 |
proof - |
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2911
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
61 |
have "supp (as, x, c) supports (f as x c)" |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
62 |
unfolding supports_def fresh_def[symmetric] |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
63 |
by (simp add: fresh_Pair perm1 fresh_star_def supp_swap swap_fresh_fresh) |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
64 |
then have fin1: "finite (supp (f as x c))" |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
65 |
by (auto intro: supports_finite simp add: finite_supp) |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
66 |
have "supp (bs, y, c) supports (f bs y c)" |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
67 |
unfolding supports_def fresh_def[symmetric] |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
68 |
by (simp add: fresh_Pair perm2 fresh_star_def supp_swap swap_fresh_fresh) |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
69 |
then have fin2: "finite (supp (f bs y c))" |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
70 |
by (auto intro: supports_finite simp add: finite_supp) |
|
2909
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
71 |
obtain q::"perm" where |
|
2911
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
72 |
fr1: "(q \<bullet> (set as)) \<sharp>* (x, c, f as x c, f bs y c)" and |
|
2909
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
73 |
fr2: "supp q \<sharp>* Abs_lst as x" and |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
74 |
inc: "supp q \<subseteq> (set as) \<union> q \<bullet> (set as)" |
|
2911
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
75 |
using at_set_avoiding3[where xs="set as" and c="(x, c, f as x c, f bs y c)" and x="[as]lst. x"] |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
76 |
fin1 fin2 |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
77 |
by (auto simp add: supp_Pair finite_supp Abs_fresh_star dest: fresh_star_supp_conv) |
|
2909
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
78 |
have "Abs_lst (q \<bullet> as) (q \<bullet> x) = q \<bullet> Abs_lst as x" by simp |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
79 |
also have "\<dots> = Abs_lst as x" |
|
2911
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
80 |
by (simp only: fr2 perm_supp_eq) |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
81 |
finally have "Abs_lst (q \<bullet> as) (q \<bullet> x) = Abs_lst bs y" using eq by simp |
|
2909
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
82 |
then obtain r::perm where |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
83 |
qq1: "q \<bullet> x = r \<bullet> y" and |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
84 |
qq2: "q \<bullet> as = r \<bullet> bs" and |
|
2911
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
85 |
qq3: "supp r \<subseteq> (q \<bullet> (set as)) \<union> set bs" |
|
2909
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
86 |
apply(drule_tac sym) |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
87 |
apply(simp only: Abs_eq_iff2 alphas) |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
88 |
apply(erule exE) |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
89 |
apply(erule conjE)+ |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
90 |
apply(drule_tac x="p" in meta_spec) |
|
2911
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
91 |
apply(simp add: set_eqvt) |
|
2909
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
92 |
apply(blast) |
|
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
93 |
done |
|
2911
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
94 |
have "(set as) \<sharp>* f as x c" by (rule fcb1) |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
95 |
then have "q \<bullet> ((set as) \<sharp>* f as x c)" |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
96 |
by (simp add: permute_bool_def) |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
97 |
then have "set (q \<bullet> as) \<sharp>* f (q \<bullet> as) (q \<bullet> x) c" |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
98 |
apply(simp add: fresh_star_eqvt set_eqvt) |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
99 |
apply(subst (asm) perm1) |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
100 |
using inc fresh1 fr1 |
|
567967bc94cc
streamlined the fcb-proof and made fcb1 a special case of fcb
Christian Urban <urbanc@in.tum.de>
parents:
2910
diff
changeset
|
101 |
apply(auto simp add: fresh_star_def fresh_Pair) |
|
2909
de5c9a0040ec
fcb for multible (list) binders; at the moment all of them have to have the same sort (at-class); this should also work for set binders, but not yet for restriction.
Christian Urban <urbanc@in.tum.de>
parents:
2904
diff
changeset
|
102 |
done |
|
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|
103 |
then have "set (r \<bullet> bs) \<sharp>* f (r \<bullet> bs) (r \<bullet> y) c" using qq1 qq2 by simp |
|
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|
104 |
then have "r \<bullet> ((set bs) \<sharp>* f bs y c)" |
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|
105 |
apply(simp add: fresh_star_eqvt set_eqvt) |
|
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|
106 |
apply(subst (asm) perm2[symmetric]) |
|
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|
107 |
using qq3 fresh2 fr1 |
|
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|
108 |
apply(auto simp add: set_eqvt fresh_star_def fresh_Pair) |
|
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|
109 |
done |
|
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|
110 |
then have fcb2: "(set bs) \<sharp>* f bs y c" by (simp add: permute_bool_def) |
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changeset
|
111 |
have "f as x c = q \<bullet> (f as x c)" |
|
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|
112 |
apply(rule perm_supp_eq[symmetric]) |
|
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|
113 |
using inc fcb1 fr1 by (auto simp add: fresh_star_def) |
|
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|
114 |
also have "\<dots> = f (q \<bullet> as) (q \<bullet> x) c" |
|
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115 |
apply(rule perm1) |
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116 |
using inc fresh1 fr1 by (auto simp add: fresh_star_def) |
|
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117 |
also have "\<dots> = f (r \<bullet> bs) (r \<bullet> y) c" using qq1 qq2 by simp |
|
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|
118 |
also have "\<dots> = r \<bullet> (f bs y c)" |
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119 |
apply(rule perm2[symmetric]) |
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120 |
using qq3 fresh2 fr1 by (auto simp add: fresh_star_def) |
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|
121 |
also have "... = f bs y c" |
|
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|
122 |
apply(rule perm_supp_eq) |
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|
123 |
using qq3 fr1 fcb2 by (auto simp add: fresh_star_def) |
|
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|
124 |
finally show ?thesis by simp |
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|
125 |
qed |
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|
126 |
|
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|
127 |
lemma Abs_lst1_fcb2: |
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|
128 |
fixes a b :: "atom" |
|
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|
129 |
and x y :: "'b :: fs" |
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130 |
and c::"'c :: fs" |
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131 |
assumes e: "(Abs_lst [a] x) = (Abs_lst [b] y)" |
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132 |
and fcb1: "a \<sharp> f a x c" |
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|
133 |
and fresh: "{a, b} \<sharp>* c"
|
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|
134 |
and perm1: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f a x c) = f (p \<bullet> a) (p \<bullet> x) c" |
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|
135 |
and perm2: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f b y c) = f (p \<bullet> b) (p \<bullet> y) c" |
|
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|
136 |
shows "f a x c = f b y c" |
|
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|
137 |
using e |
|
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|
138 |
apply(drule_tac Abs_lst_fcb2[where c="c" and f="\<lambda>(as::atom list) . f (hd as)"]) |
|
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|
139 |
apply(simp_all) |
|
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|
140 |
using fcb1 fresh perm1 perm2 |
|
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|
141 |
apply(simp_all add: fresh_star_def) |
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|
142 |
done |
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|
143 |
|
|
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equality of lst_binder and a few helper lemmas
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|
144 |
lemma supp_zero_perm_zero: |
|
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|
145 |
shows "supp (p :: perm) = {} \<longleftrightarrow> p = 0"
|
|
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|
146 |
by (metis supp_perm_singleton supp_zero_perm) |
|
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|
147 |
|
|
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equality of lst_binder and a few helper lemmas
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|
148 |
lemma permute_atom_list_id: |
|
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|
149 |
shows "p \<bullet> l = l \<longleftrightarrow> supp p \<inter> set l = {}"
|
|
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|
150 |
by (induct l) (auto simp add: supp_Nil supp_perm) |
|
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changeset
|
151 |
|
|
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equality of lst_binder and a few helper lemmas
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|
152 |
lemma Abs_lst_binder_length: |
|
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|
153 |
shows "[xs]lst. T = [ys]lst. S \<Longrightarrow> length xs = length ys" |
|
eb322a392461
equality of lst_binder and a few helper lemmas
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parents:
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changeset
|
154 |
by (auto simp add: Abs_eq_iff alphas length_eqvt[symmetric] permute_pure) |
|
eb322a392461
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parents:
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changeset
|
155 |
|
|
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equality of lst_binder and a few helper lemmas
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parents:
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|
156 |
lemma Abs_lst_binder_eq: |
|
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changeset
|
157 |
shows "Abs_lst l T = Abs_lst l S \<longleftrightarrow> T = S" |
|
eb322a392461
equality of lst_binder and a few helper lemmas
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parents:
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changeset
|
158 |
by (rule, simp_all add: Abs_eq_iff2 alphas) |
|
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parents:
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changeset
|
159 |
(metis fresh_star_zero inf_absorb1 permute_atom_list_id supp_perm_eq |
|
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parents:
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|
160 |
supp_zero_perm_zero) |
|
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parents:
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|
161 |
|
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
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|
162 |
nominal_primrec |
| 2889 | 163 |
crename :: "trm \<Rightarrow> coname \<Rightarrow> coname \<Rightarrow> trm" ("_[_\<turnstile>c>_]" [100,100,100] 100)
|
164 |
where |
|
165 |
"(Ax x a)[d\<turnstile>c>e] = (if a=d then Ax x e else Ax x a)" |
|
166 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (Cut <a>.M (x).N)[d\<turnstile>c>e] = Cut <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e])" |
|
167 |
| "(NotR (x).M a)[d\<turnstile>c>e] = (if a=d then NotR (x).(M[d\<turnstile>c>e]) e else NotR (x).(M[d\<turnstile>c>e]) a)" |
|
168 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (NotL <a>.M x)[d\<turnstile>c>e] = (NotL <a>.(M[d\<turnstile>c>e]) x)" |
|
169 |
| "\<lbrakk>atom a \<sharp> (d, e); atom b \<sharp> (d, e)\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c)[d\<turnstile>c>e] = |
|
170 |
(if c=d then AndR <a>.(M[d\<turnstile>c>e]) <b>.(N[d \<turnstile>c>e]) e else AndR <a>.(M[d\<turnstile>c>e]) <b>.(N[d\<turnstile>c>e]) c)" |
|
171 |
| "(AndL1 (x).M y)[d\<turnstile>c>e] = AndL1 (x).(M[d\<turnstile>c>e]) y" |
|
172 |
| "(AndL2 (x).M y)[d\<turnstile>c>e] = AndL2 (x).(M[d\<turnstile>c>e]) y" |
|
173 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (OrR1 <a>.M b)[d\<turnstile>c>e] = |
|
174 |
(if b=d then OrR1 <a>.(M[d\<turnstile>c>e]) e else OrR1 <a>.(M[d\<turnstile>c>e]) b)" |
|
175 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (OrR2 <a>.M b)[d\<turnstile>c>e] = |
|
176 |
(if b=d then OrR2 <a>.(M[d\<turnstile>c>e]) e else OrR2 <a>.(M[d\<turnstile>c>e]) b)" |
|
177 |
| "(OrL (x).M (y).N z)[d\<turnstile>c>e] = OrL (x).(M[d\<turnstile>c>e]) (y).(N[d\<turnstile>c>e]) z" |
|
178 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (ImpR (x).<a>.M b)[d\<turnstile>c>e] = |
|
179 |
(if b=d then ImpR (x).<a>.(M[d\<turnstile>c>e]) e else ImpR (x).<a>.(M[d\<turnstile>c>e]) b)" |
|
180 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (ImpL <a>.M (x).N y)[d\<turnstile>c>e] = ImpL <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e]) y" |
|
181 |
apply(simp only: eqvt_def) |
|
182 |
apply(simp only: crename_graph_def) |
|
183 |
apply (rule, perm_simp, rule) |
|
184 |
apply(rule TrueI) |
|
185 |
-- "covered all cases" |
|
186 |
apply(case_tac x) |
|
187 |
apply(rule_tac y="a" and c="(b, c)" in trm.strong_exhaust) |
|
|
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Speed-up the completeness proof.
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parents:
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|
188 |
apply (simp_all add: fresh_star_def)[12] |
|
a9f3600c9ae6
Speed-up the completeness proof.
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parents:
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changeset
|
189 |
apply(metis)+ |
|
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the simplifier can simplify "sort (atom a)" if a is a concrete atom type declared with atom_decl
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|
190 |
-- "compatibility" |
| 2889 | 191 |
apply(simp_all) |
|
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the simplifier can simplify "sort (atom a)" if a is a concrete atom type declared with atom_decl
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changeset
|
192 |
apply(rule conjI) |
|
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Speed-up the completeness proof.
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|
193 |
apply(elim conjE) |
|
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an alternative FCB for Abs_lst1; seems simpler but not as simple as I thought; not sure whether it generalises to multiple binders.
Christian Urban <urbanc@in.tum.de>
parents:
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diff
changeset
|
194 |
apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2) |
|
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304dfe6cc83a
the simplifier can simplify "sort (atom a)" if a is a concrete atom type declared with atom_decl
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|
195 |
apply(simp add: Abs_fresh_iff) |
|
2900
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an alternative FCB for Abs_lst1; seems simpler but not as simple as I thought; not sure whether it generalises to multiple binders.
Christian Urban <urbanc@in.tum.de>
parents:
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diff
changeset
|
196 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
d66430c7c4f1
an alternative FCB for Abs_lst1; seems simpler but not as simple as I thought; not sure whether it generalises to multiple binders.
Christian Urban <urbanc@in.tum.de>
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diff
changeset
|
197 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
d66430c7c4f1
an alternative FCB for Abs_lst1; seems simpler but not as simple as I thought; not sure whether it generalises to multiple binders.
Christian Urban <urbanc@in.tum.de>
parents:
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diff
changeset
|
198 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
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parents:
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diff
changeset
|
199 |
apply(elim conjE) |
|
2900
d66430c7c4f1
an alternative FCB for Abs_lst1; seems simpler but not as simple as I thought; not sure whether it generalises to multiple binders.
Christian Urban <urbanc@in.tum.de>
parents:
2899
diff
changeset
|
200 |
apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
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parents:
2892
diff
changeset
|
201 |
apply(simp add: Abs_fresh_iff) |
|
2900
d66430c7c4f1
an alternative FCB for Abs_lst1; seems simpler but not as simple as I thought; not sure whether it generalises to multiple binders.
Christian Urban <urbanc@in.tum.de>
parents:
2899
diff
changeset
|
202 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
d66430c7c4f1
an alternative FCB for Abs_lst1; seems simpler but not as simple as I thought; not sure whether it generalises to multiple binders.
Christian Urban <urbanc@in.tum.de>
parents:
2899
diff
changeset
|
203 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
d66430c7c4f1
an alternative FCB for Abs_lst1; seems simpler but not as simple as I thought; not sure whether it generalises to multiple binders.
Christian Urban <urbanc@in.tum.de>
parents:
2899
diff
changeset
|
204 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
205 |
apply(elim conjE) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
206 |
apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
207 |
apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
208 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
209 |
apply(simp add: Abs_fresh_iff) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
210 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
211 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
212 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
213 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
214 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
215 |
apply(elim conjE) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
216 |
apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
217 |
apply(simp add: Abs_fresh_iff) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
218 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
219 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
220 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
221 |
apply(rule conjI) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
222 |
apply(elim conjE) |
|
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
223 |
apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)") |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
224 |
apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
225 |
apply(erule Abs_lst1_fcb2) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
226 |
apply(simp add: Abs_fresh_iff) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
227 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
228 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
229 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
230 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
231 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
232 |
apply(erule conjE)+ |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
233 |
apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
234 |
apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
235 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
236 |
apply(simp add: Abs_fresh_iff) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
237 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
238 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
239 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
240 |
apply(blast) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
241 |
apply(blast) |
|
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
242 |
apply(elim conjE) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
243 |
apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
244 |
apply(simp add: Abs_fresh_iff) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
245 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
246 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
247 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
248 |
apply(elim conjE) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
249 |
apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
250 |
apply(simp add: Abs_fresh_iff) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
251 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
252 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
253 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
254 |
apply(elim conjE) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
255 |
apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
256 |
apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
257 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
258 |
apply(simp add: Abs_fresh_iff) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
259 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
260 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
261 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
262 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
263 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
264 |
apply(erule conjE)+ |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
265 |
apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
266 |
apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
267 |
apply(erule Abs_lst1_fcb2) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
268 |
apply(simp add: Abs_fresh_iff) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
269 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
270 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
271 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
272 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
273 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
274 |
apply(rule conjI) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
275 |
apply(erule conjE)+ |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
276 |
apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
277 |
apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
278 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
279 |
apply(simp add: Abs_fresh_iff) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
280 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
281 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
282 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
283 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
284 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
285 |
apply(erule conjE)+ |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
286 |
apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
287 |
apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
288 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
289 |
apply(simp add: Abs_fresh_iff) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
290 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
291 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
292 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
293 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
294 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
295 |
defer |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
296 |
apply(erule conjE)+ |
|
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
297 |
apply(rule conjI) |
|
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
298 |
apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)") |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
299 |
apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
300 |
apply(erule Abs_lst1_fcb2) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
301 |
apply(simp add: Abs_fresh_iff) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
302 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
303 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
304 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
305 |
apply(blast) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
306 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
307 |
apply(subgoal_tac "eqvt_at crename_sumC (N, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
308 |
apply(subgoal_tac "eqvt_at crename_sumC (Na, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
309 |
apply(erule Abs_lst1_fcb2) |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
310 |
apply(simp add: Abs_fresh_iff) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
311 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
312 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
313 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
314 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
315 |
apply(blast) |
|
2910
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
316 |
apply(subgoal_tac "eqvt_at crename_sumC (M, da, ea)") |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
317 |
apply(subgoal_tac "eqvt_at crename_sumC (Ma, da, ea)") |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
318 |
apply(erule conjE)+ |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
319 |
apply(erule Abs_lst_fcb2) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
320 |
apply(simp add: Abs_fresh_star) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
321 |
apply(simp add: Abs_fresh_star) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
322 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
323 |
apply(simp add: fresh_at_base fresh_star_def fresh_Pair) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
324 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
325 |
apply(simp add: eqvt_at_def atom_eqvt fresh_star_Pair perm_supp_eq) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
326 |
apply(blast) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
327 |
apply(blast) |
|
ae6455351572
completed proof in Classical; the fcb lemma works for any list of atoms (despite what was written earlier)
Christian Urban <urbanc@in.tum.de>
parents:
2909
diff
changeset
|
328 |
done |
|
1792
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
329 |
|
|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
330 |
end |
|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
331 |
|
|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
332 |
|
|
c29a139410d2
properly separated the example from my PhD and gave the correct alpha-equivalence relation (according to the paper)
Christian Urban <urbanc@in.tum.de>
parents:
diff
changeset
|
333 |