| author | Christian Urban <urbanc@in.tum.de> |
| Sun, 26 Jun 2011 21:42:07 +0100 | |
| changeset 2903 | e26c6c728b9e |
| parent 2902 | 9c3f6a4d95d4 |
| child 2904 | eb322a392461 |
| 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 *) |
|
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" |
|
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
|
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)
|
14 |
| NotR n::"name" t::"trm" "coname" bind n in t |
|
15 |
("NotR '(_')._ _" [100,100,100] 100)
|
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16 |
| NotL c::"coname" t::"trm" "name" bind c in t |
|
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 |
|
19 |
("AndR <_>._ <_>._ _" [100,100,100,100,100] 100)
|
|
20 |
| AndL1 n::"name" t::"trm" "name" bind n in t |
|
21 |
("AndL1 '(_')._ _" [100,100,100] 100)
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22 |
| AndL2 n::"name" t::"trm" "name" bind n in t |
|
23 |
("AndL2 '(_')._ _" [100,100,100] 100)
|
|
24 |
| OrR1 c::"coname" t::"trm" "coname" bind c in t |
|
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)
|
|
28 |
| OrL n1::"name" t1::"trm" n2::"name" t2::"trm" "name" bind n1 in t1, bind n2 in t2 |
|
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 |
|
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
|
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 |
|
3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
37 |
thm trm.exhaust |
|
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
|
40 |
thm trm.fv_defs |
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3885dc2669f9
cleaned up (almost completely) the examples
Christian Urban <urbanc@in.tum.de>
parents:
2434
diff
changeset
|
41 |
thm trm.bn_defs |
|
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 |
|
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 |
|
|
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
|
49 |
lemma Abs_lst1_fcb2: |
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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
|
50 |
fixes a b :: "'a :: at" |
|
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
|
51 |
and S T :: "'b :: fs" |
|
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
|
52 |
and c::"'c::fs" |
|
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
|
53 |
assumes e: "(Abs_lst [atom a] T) = (Abs_lst [atom b] S)" |
|
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
|
54 |
and fcb1: "atom a \<sharp> f a T c" |
|
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
|
55 |
and fresh: "{atom a, atom b} \<sharp>* c"
|
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2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
56 |
and perm1: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f a T c) = f (p \<bullet> a) (p \<bullet> T) c" |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
57 |
and perm2: "\<And>p. supp p \<sharp>* c \<Longrightarrow> p \<bullet> (f b S c) = f (p \<bullet> b) (p \<bullet> S) c" |
|
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
|
58 |
shows "f a T c = f b S c" |
|
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
|
59 |
proof - |
|
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
|
60 |
have fcb2: "atom b \<sharp> f b S 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
|
61 |
using e[symmetric] |
|
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
|
62 |
apply(simp add: Abs_eq_iff2) |
|
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
|
63 |
apply(erule exE) |
|
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
|
64 |
apply(simp add: alphas) |
|
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
|
65 |
apply(rule_tac p="p" in permute_boolE) |
|
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
|
66 |
apply(simp add: fresh_eqvt) |
|
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
|
67 |
apply(subst perm2) |
|
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
|
68 |
using fresh |
|
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
|
69 |
apply(auto simp add: fresh_star_def)[1] |
|
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
|
70 |
apply(simp add: atom_eqvt) |
|
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
|
71 |
apply(rule fcb1) |
|
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
|
72 |
done |
|
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
|
73 |
have fin1: "finite (supp (f a T c))" |
|
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
|
74 |
apply(rule_tac S="supp (a, T, c)" in supports_finite) |
|
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
|
75 |
apply(simp add: supports_def) |
|
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
|
76 |
apply(simp add: fresh_def[symmetric]) |
|
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
|
77 |
apply(clarify) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
78 |
apply(subst perm1) |
|
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
|
79 |
apply(simp add: supp_swap fresh_star_def) |
|
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
|
80 |
apply(simp add: swap_fresh_fresh 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
|
81 |
apply(simp add: finite_supp) |
|
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
|
82 |
done |
|
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
|
83 |
have fin2: "finite (supp (f b S c))" |
|
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
|
84 |
apply(rule_tac S="supp (b, S, c)" in supports_finite) |
|
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
|
85 |
apply(simp add: supports_def) |
|
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
|
86 |
apply(simp add: fresh_def[symmetric]) |
|
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
|
87 |
apply(clarify) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
88 |
apply(subst perm2) |
|
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
|
89 |
apply(simp add: supp_swap fresh_star_def) |
|
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
|
90 |
apply(simp add: swap_fresh_fresh 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
|
91 |
apply(simp add: finite_supp) |
|
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
|
92 |
done |
|
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
|
93 |
obtain d::"'a::at" where fr: "atom d \<sharp> (a, b, S, T, c, f a T c, f b S c)" |
|
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
|
94 |
using obtain_fresh'[where x="(a, b, S, T, c, f a T c, f b S c)"] |
|
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
|
95 |
apply(auto simp add: finite_supp supp_Pair fin1 fin2) |
|
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
|
96 |
done |
|
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
|
97 |
have "(a \<leftrightarrow> d) \<bullet> (Abs_lst [atom a] T) = (b \<leftrightarrow> d) \<bullet> (Abs_lst [atom b] S)" |
|
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
|
98 |
apply(simp (no_asm_use) only: flip_def) |
|
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
|
99 |
apply(subst swap_fresh_fresh) |
|
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
|
100 |
apply(simp add: Abs_fresh_iff) |
|
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
|
101 |
using fr |
|
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
|
102 |
apply(simp add: Abs_fresh_iff) |
|
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
|
103 |
apply(subst swap_fresh_fresh) |
|
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
|
104 |
apply(simp add: Abs_fresh_iff) |
|
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
|
105 |
using fr |
|
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
|
106 |
apply(simp add: Abs_fresh_iff) |
|
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
|
107 |
apply(rule e) |
|
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
|
108 |
done |
|
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
|
109 |
then have "Abs_lst [atom d] ((a \<leftrightarrow> d) \<bullet> T) = Abs_lst [atom d] ((b \<leftrightarrow> d) \<bullet> S)" |
|
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
|
110 |
apply (simp add: swap_atom flip_def) |
|
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
|
111 |
done |
|
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
|
112 |
then have eq: "(a \<leftrightarrow> d) \<bullet> T = (b \<leftrightarrow> d) \<bullet> S" |
|
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
|
113 |
by (simp add: Abs1_eq_iff) |
|
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
|
114 |
have "f a T c = (a \<leftrightarrow> d) \<bullet> f a T c" |
|
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
|
115 |
unfolding flip_def |
|
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
|
116 |
apply(rule sym) |
|
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
|
117 |
apply(rule swap_fresh_fresh) |
|
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:
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diff
changeset
|
118 |
using fcb1 |
|
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
|
119 |
apply(simp) |
|
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
|
120 |
using fr |
|
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
|
121 |
apply(simp add: 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
|
122 |
done |
|
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
|
123 |
also have "... = f d ((a \<leftrightarrow> d) \<bullet> T) c" |
|
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
|
124 |
unfolding flip_def |
|
2901
754aa24006c8
did all cases, except the multiple binder case
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parents:
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diff
changeset
|
125 |
apply(subst perm1) |
|
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
|
126 |
using fresh fr |
|
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
|
127 |
apply(simp add: supp_swap 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:
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diff
changeset
|
128 |
apply(simp) |
|
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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changeset
|
129 |
done |
|
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
|
130 |
also have "... = f d ((b \<leftrightarrow> d) \<bullet> S) c" using eq by simp |
|
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
|
131 |
also have "... = (b \<leftrightarrow> d) \<bullet> f b S c" |
|
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
|
132 |
unfolding flip_def |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
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diff
changeset
|
133 |
apply(subst perm2) |
|
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
|
134 |
using fresh fr |
|
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
|
135 |
apply(simp add: supp_swap 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
|
136 |
apply(simp) |
|
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
|
137 |
done |
|
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
|
138 |
also have "... = f b S c" |
|
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
|
139 |
apply(rule flip_fresh_fresh) |
|
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
|
140 |
using fcb2 |
|
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
|
141 |
apply(simp) |
|
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
|
142 |
using fr |
|
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
|
143 |
apply(simp add: 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:
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diff
changeset
|
144 |
done |
|
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
|
145 |
finally show ?thesis by simp |
|
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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changeset
|
146 |
qed |
|
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
|
147 |
|
|
2903
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
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parents:
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changeset
|
148 |
(* |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
149 |
lemma Abs_lst_fcb2: |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
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changeset
|
150 |
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
|
151 |
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:
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diff
changeset
|
152 |
and c::"'c::fs" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
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diff
changeset
|
153 |
assumes e: "(Abs_lst as x) = (Abs_lst bs y)" |
|
e26c6c728b9e
only one of the fcb precondistions are needed (probably the same with the perm-conditions)
Christian Urban <urbanc@in.tum.de>
parents:
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diff
changeset
|
154 |
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
|
155 |
and fcb2: "(set bs) \<sharp>* f bs 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
|
156 |
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
|
157 |
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
|
158 |
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
|
159 |
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
|
160 |
shows "f as x c = f bs 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
|
161 |
*) |
|
2892
a9f3600c9ae6
Speed-up the completeness proof.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2891
diff
changeset
|
162 |
|
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
163 |
nominal_primrec |
| 2889 | 164 |
crename :: "trm \<Rightarrow> coname \<Rightarrow> coname \<Rightarrow> trm" ("_[_\<turnstile>c>_]" [100,100,100] 100)
|
165 |
where |
|
166 |
"(Ax x a)[d\<turnstile>c>e] = (if a=d then Ax x e else Ax x a)" |
|
167 |
| "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])" |
|
168 |
| "(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)" |
|
169 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (NotL <a>.M x)[d\<turnstile>c>e] = (NotL <a>.(M[d\<turnstile>c>e]) x)" |
|
170 |
| "\<lbrakk>atom a \<sharp> (d, e); atom b \<sharp> (d, e)\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c)[d\<turnstile>c>e] = |
|
171 |
(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)" |
|
172 |
| "(AndL1 (x).M y)[d\<turnstile>c>e] = AndL1 (x).(M[d\<turnstile>c>e]) y" |
|
173 |
| "(AndL2 (x).M y)[d\<turnstile>c>e] = AndL2 (x).(M[d\<turnstile>c>e]) y" |
|
174 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (OrR1 <a>.M b)[d\<turnstile>c>e] = |
|
175 |
(if b=d then OrR1 <a>.(M[d\<turnstile>c>e]) e else OrR1 <a>.(M[d\<turnstile>c>e]) b)" |
|
176 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (OrR2 <a>.M b)[d\<turnstile>c>e] = |
|
177 |
(if b=d then OrR2 <a>.(M[d\<turnstile>c>e]) e else OrR2 <a>.(M[d\<turnstile>c>e]) b)" |
|
178 |
| "(OrL (x).M (y).N z)[d\<turnstile>c>e] = OrL (x).(M[d\<turnstile>c>e]) (y).(N[d\<turnstile>c>e]) z" |
|
179 |
| "atom a \<sharp> (d, e) \<Longrightarrow> (ImpR (x).<a>.M b)[d\<turnstile>c>e] = |
|
180 |
(if b=d then ImpR (x).<a>.(M[d\<turnstile>c>e]) e else ImpR (x).<a>.(M[d\<turnstile>c>e]) b)" |
|
181 |
| "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" |
|
182 |
apply(simp only: eqvt_def) |
|
183 |
apply(simp only: crename_graph_def) |
|
184 |
apply (rule, perm_simp, rule) |
|
185 |
apply(rule TrueI) |
|
186 |
-- "covered all cases" |
|
187 |
apply(case_tac x) |
|
188 |
apply(rule_tac y="a" and c="(b, c)" in trm.strong_exhaust) |
|
|
2892
a9f3600c9ae6
Speed-up the completeness proof.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2891
diff
changeset
|
189 |
apply (simp_all add: fresh_star_def)[12] |
|
a9f3600c9ae6
Speed-up the completeness proof.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2891
diff
changeset
|
190 |
apply(metis)+ |
|
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
|
191 |
-- "compatibility" |
| 2889 | 192 |
apply(simp_all) |
|
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
|
193 |
apply(rule conjI) |
|
2892
a9f3600c9ae6
Speed-up the completeness proof.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2891
diff
changeset
|
194 |
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
|
195 |
apply(erule_tac c="(da,ea)" in Abs_lst1_fcb2) |
|
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
|
196 |
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
|
197 |
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
|
198 |
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
|
199 |
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
|
200 |
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
|
201 |
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
|
202 |
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
|
203 |
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
|
204 |
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
|
205 |
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
|
206 |
apply(elim conjE) |
|
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 (M, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
208 |
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
|
209 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
210 |
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
|
211 |
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
|
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(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
|
214 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
215 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
216 |
apply(elim conjE) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
217 |
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
|
218 |
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
|
219 |
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
|
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(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
|
222 |
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
|
223 |
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
|
224 |
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
|
225 |
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
|
226 |
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
|
227 |
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
|
228 |
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
|
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(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
|
231 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
232 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
233 |
apply(erule conjE)+ |
|
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 (N, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
235 |
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
|
236 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
237 |
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
|
238 |
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
|
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(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
|
241 |
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
|
242 |
apply(blast) |
|
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
243 |
apply(elim conjE) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
244 |
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
|
245 |
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
|
246 |
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
|
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(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
|
249 |
apply(elim conjE) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
250 |
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
|
251 |
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
|
252 |
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
|
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(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
|
255 |
apply(elim conjE) |
|
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 (M, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
257 |
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
|
258 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
259 |
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
|
260 |
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
|
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(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
|
263 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
264 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
265 |
apply(erule conjE)+ |
|
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 (M, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
267 |
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
|
268 |
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
|
269 |
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
|
270 |
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
|
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(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
|
273 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
274 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
275 |
apply(rule conjI) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
276 |
apply(erule conjE)+ |
|
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 (M, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
278 |
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
|
279 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
280 |
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
|
281 |
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
|
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(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
|
284 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
285 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
286 |
apply(erule conjE)+ |
|
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 (N, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
288 |
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
|
289 |
apply(erule Abs_lst1_fcb2) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
290 |
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
|
291 |
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
|
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(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
|
294 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
295 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
296 |
defer |
|
2899
fe290b4e508f
except for the interated binder case, finished definition in Calssical.thy
Christian Urban <urbanc@in.tum.de>
parents:
2892
diff
changeset
|
297 |
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
|
298 |
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
|
299 |
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
|
300 |
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
|
301 |
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
|
302 |
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
|
303 |
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
|
304 |
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
|
305 |
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
|
306 |
apply(blast) |
|
2901
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
307 |
apply(blast) |
|
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 (N, da, ea)") |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
309 |
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
|
310 |
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
|
311 |
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
|
312 |
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
|
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(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
|
315 |
apply(blast) |
|
754aa24006c8
did all cases, except the multiple binder case
Christian Urban <urbanc@in.tum.de>
parents:
2900
diff
changeset
|
316 |
apply(blast) |
| 2889 | 317 |
oops |
|
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
|
318 |
|
|
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
|
319 |
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
|
320 |
|
|
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
|
321 |
|
|
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
|
322 |