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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
1 |
theory Term5
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
2 |
imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs" "Perm" "Fv" "Rsp" "../Attic/Prove"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
3 |
begin
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
4 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
5 |
atom_decl name
|
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
6 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
7 |
datatype rtrm5 =
|
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
8 |
rVr5 "name"
|
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
9 |
| rAp5 "rtrm5" "rtrm5"
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
10 |
| rLt5 "rlts" "rtrm5" --"bind (bv5 lts) in (rtrm5)"
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
11 |
and rlts =
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
12 |
rLnil
|
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
13 |
| rLcons "name" "rtrm5" "rlts"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
14 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
15 |
primrec
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
16 |
rbv5
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
17 |
where
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
18 |
"rbv5 rLnil = {}"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
19 |
| "rbv5 (rLcons n t ltl) = {atom n} \<union> (rbv5 ltl)"
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
20 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
21 |
|
1277
|
22 |
setup {* snd o define_raw_perms (Datatype.the_info @{theory} "Term5.rtrm5") 2 *}
|
1270
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
23 |
print_theorems
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
24 |
|
1288
|
25 |
|
1277
|
26 |
local_setup {* snd o define_fv_alpha (Datatype.the_info @{theory} "Term5.rtrm5") [
|
1288
|
27 |
[ [],
|
|
28 |
[],
|
|
29 |
[(SOME @{term rbv5}, 0, 1)] ],
|
|
30 |
[ [],
|
|
31 |
[]] ] *}
|
1270
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
32 |
print_theorems
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
33 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
34 |
(* Alternate version with additional binding of name in rlts in rLcons *)
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
35 |
(*local_setup {* snd o define_fv_alpha "Term5.rtrm5" [
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
36 |
[[[]], [[], []], [[(SOME @{term rbv5}, 0)], [(SOME @{term rbv5}, 0)]]], [[], [[(NONE,0)], [], [(NONE,0)]]] ] *}
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
37 |
print_theorems*)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
38 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
39 |
notation
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
40 |
alpha_rtrm5 ("_ \<approx>5 _" [100, 100] 100) and
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
41 |
alpha_rlts ("_ \<approx>l _" [100, 100] 100)
|
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
42 |
thm alpha_rtrm5_alpha_rlts.intros
|
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
43 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
44 |
local_setup {* (fn ctxt => snd (Local_Theory.note ((@{binding alpha5_inj}, []), (build_alpha_inj @{thms alpha_rtrm5_alpha_rlts.intros} @{thms rtrm5.distinct rtrm5.inject rlts.distinct rlts.inject} @{thms alpha_rtrm5.cases alpha_rlts.cases} ctxt)) ctxt)) *}
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
45 |
thm alpha5_inj
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
46 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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|
47 |
lemma rbv5_eqvt[eqvt]:
|
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
48 |
"pi \<bullet> (rbv5 x) = rbv5 (pi \<bullet> x)"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
49 |
apply (induct x)
|
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
50 |
apply (simp_all add: eqvts atom_eqvt)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
51 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
52 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
53 |
lemma fv_rtrm5_rlts_eqvt[eqvt]:
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
|
54 |
"pi \<bullet> (fv_rtrm5 x) = fv_rtrm5 (pi \<bullet> x)"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
55 |
"pi \<bullet> (fv_rlts l) = fv_rlts (pi \<bullet> l)"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
56 |
apply (induct x and l)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
57 |
apply (simp_all add: eqvts atom_eqvt)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
58 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
59 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
60 |
lemma alpha5_eqvt:
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
61 |
"xa \<approx>5 y \<Longrightarrow> (x \<bullet> xa) \<approx>5 (x \<bullet> y)"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
62 |
"xb \<approx>l ya \<Longrightarrow> (x \<bullet> xb) \<approx>l (x \<bullet> ya)"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
63 |
apply (induct rule: alpha_rtrm5_alpha_rlts.inducts)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
64 |
apply (simp_all add: alpha5_inj)
|
1288
|
65 |
sorry
|
1270
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
66 |
|
1288
|
67 |
lemma alpha5_equivp:
|
|
68 |
"equivp alpha_rtrm5"
|
|
69 |
"equivp alpha_rlts"
|
|
70 |
sorry
|
1270
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
71 |
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
72 |
quotient_type
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
73 |
trm5 = rtrm5 / alpha_rtrm5
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
74 |
and
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
75 |
lts = rlts / alpha_rlts
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
76 |
by (auto intro: alpha5_equivp)
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
77 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
78 |
local_setup {*
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
79 |
(fn ctxt => ctxt
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
80 |
|> snd o (Quotient_Def.quotient_lift_const ("Vr5", @{term rVr5}))
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
81 |
|> snd o (Quotient_Def.quotient_lift_const ("Ap5", @{term rAp5}))
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
82 |
|> snd o (Quotient_Def.quotient_lift_const ("Lt5", @{term rLt5}))
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
83 |
|> snd o (Quotient_Def.quotient_lift_const ("Lnil", @{term rLnil}))
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
84 |
|> snd o (Quotient_Def.quotient_lift_const ("Lcons", @{term rLcons}))
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
85 |
|> snd o (Quotient_Def.quotient_lift_const ("fv_trm5", @{term fv_rtrm5}))
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
86 |
|> snd o (Quotient_Def.quotient_lift_const ("fv_lts", @{term fv_rlts}))
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
87 |
|> snd o (Quotient_Def.quotient_lift_const ("bv5", @{term rbv5})))
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
88 |
*}
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
89 |
print_theorems
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
90 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
91 |
lemma alpha5_rfv:
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
92 |
"(t \<approx>5 s \<Longrightarrow> fv_rtrm5 t = fv_rtrm5 s)"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
93 |
"(l \<approx>l m \<Longrightarrow> fv_rlts l = fv_rlts m)"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
94 |
apply(induct rule: alpha_rtrm5_alpha_rlts.inducts)
|
1288
|
95 |
apply(simp_all)
|
|
96 |
apply(simp add: alpha_gen)
|
|
97 |
apply(erule conjE)+
|
|
98 |
apply(erule exE)
|
|
99 |
apply(erule conjE)+
|
|
100 |
apply(simp_all)
|
1270
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
101 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
102 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
103 |
lemma bv_list_rsp:
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
104 |
shows "x \<approx>l y \<Longrightarrow> rbv5 x = rbv5 y"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
105 |
apply(induct rule: alpha_rtrm5_alpha_rlts.inducts(2))
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
106 |
apply(simp_all)
|
1288
|
107 |
apply(clarify)
|
|
108 |
apply simp
|
1270
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
109 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
110 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
111 |
lemma [quot_respect]:
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
112 |
"(alpha_rlts ===> op =) fv_rlts fv_rlts"
|
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
113 |
"(alpha_rtrm5 ===> op =) fv_rtrm5 fv_rtrm5"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
114 |
"(alpha_rlts ===> op =) rbv5 rbv5"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
115 |
"(op = ===> alpha_rtrm5) rVr5 rVr5"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
116 |
"(alpha_rtrm5 ===> alpha_rtrm5 ===> alpha_rtrm5) rAp5 rAp5"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
117 |
"(alpha_rlts ===> alpha_rtrm5 ===> alpha_rtrm5) rLt5 rLt5"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
118 |
"(op = ===> alpha_rtrm5 ===> alpha_rlts ===> alpha_rlts) rLcons rLcons"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
119 |
"(op = ===> alpha_rtrm5 ===> alpha_rtrm5) permute permute"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
120 |
"(op = ===> alpha_rlts ===> alpha_rlts) permute permute"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
121 |
apply (simp_all add: alpha5_inj alpha5_rfv alpha5_eqvt bv_list_rsp)
|
1288
|
122 |
apply (clarify)
|
1270
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
123 |
apply (rule_tac x="0" in exI) apply (simp add: fresh_star_def fresh_zero_perm alpha_gen alpha5_rfv)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
124 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
125 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
126 |
lemma
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
127 |
shows "(alpha_rlts ===> op =) rbv5 rbv5"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
128 |
by (simp add: bv_list_rsp)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
129 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
130 |
lemmas trm5_lts_inducts = rtrm5_rlts.inducts[quot_lifted]
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
131 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
132 |
instantiation trm5 and lts :: pt
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
133 |
begin
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
134 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
135 |
quotient_definition
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
136 |
"permute_trm5 :: perm \<Rightarrow> trm5 \<Rightarrow> trm5"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
137 |
is
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
138 |
"permute :: perm \<Rightarrow> rtrm5 \<Rightarrow> rtrm5"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
139 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
140 |
quotient_definition
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
141 |
"permute_lts :: perm \<Rightarrow> lts \<Rightarrow> lts"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
142 |
is
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
143 |
"permute :: perm \<Rightarrow> rlts \<Rightarrow> rlts"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
144 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
145 |
instance by default
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
146 |
(simp_all add: permute_rtrm5_permute_rlts_zero[quot_lifted] permute_rtrm5_permute_rlts_append[quot_lifted])
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
147 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
148 |
end
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
149 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
150 |
lemmas
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
151 |
permute_trm5_lts = permute_rtrm5_permute_rlts.simps[quot_lifted]
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
152 |
and alpha5_INJ = alpha5_inj[unfolded alpha_gen, quot_lifted, folded alpha_gen]
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
153 |
and bv5[simp] = rbv5.simps[quot_lifted]
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
154 |
and fv_trm5_lts[simp] = fv_rtrm5_fv_rlts.simps[quot_lifted]
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
155 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
156 |
lemma lets_ok:
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
157 |
"(Lt5 (Lcons x (Vr5 x) Lnil) (Vr5 x)) = (Lt5 (Lcons y (Vr5 y) Lnil) (Vr5 y))"
|
1288
|
158 |
apply (simp add: alpha5_INJ)
|
1270
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
159 |
apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
|
1288
|
160 |
apply (simp_all add: alpha_gen)
|
1270
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
161 |
apply (simp add: permute_trm5_lts fresh_star_def)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
162 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
163 |
|
1286
|
164 |
lemma lets_ok3:
|
1288
|
165 |
"x \<noteq> y \<Longrightarrow>
|
|
166 |
(Lt5 (Lcons x (Ap5 (Vr5 y) (Vr5 x)) (Lcons y (Vr5 y) Lnil)) (Ap5 (Vr5 x) (Vr5 y))) \<noteq>
|
|
167 |
(Lt5 (Lcons y (Ap5 (Vr5 x) (Vr5 y)) (Lcons x (Vr5 x) Lnil)) (Ap5 (Vr5 x) (Vr5 y)))"
|
|
168 |
apply (simp add: permute_trm5_lts alpha_gen alpha5_INJ)
|
1286
|
169 |
done
|
1270
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
170 |
|
1288
|
171 |
|
1270
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
172 |
lemma lets_not_ok1:
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
173 |
"x \<noteq> y \<Longrightarrow> (Lt5 (Lcons x (Vr5 x) (Lcons y (Vr5 y) Lnil)) (Ap5 (Vr5 x) (Vr5 y))) \<noteq>
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
174 |
(Lt5 (Lcons y (Vr5 x) (Lcons x (Vr5 y) Lnil)) (Ap5 (Vr5 x) (Vr5 y)))"
|
1288
|
175 |
apply (simp add: alpha5_INJ alpha_gen)
|
1270
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
176 |
apply (simp add: permute_trm5_lts fresh_star_def alpha5_INJ(5) alpha5_INJ(2) alpha5_INJ(1))
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
177 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
178 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
179 |
lemma distinct_helper:
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
180 |
shows "\<not>(rVr5 x \<approx>5 rAp5 y z)"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
181 |
apply auto
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
182 |
apply (erule alpha_rtrm5.cases)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
183 |
apply (simp_all only: rtrm5.distinct)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
184 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
185 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
186 |
lemma distinct_helper2:
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
187 |
shows "(Vr5 x) \<noteq> (Ap5 y z)"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
188 |
by (lifting distinct_helper)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
189 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
190 |
lemma lets_nok:
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
191 |
"x \<noteq> y \<Longrightarrow> x \<noteq> z \<Longrightarrow> z \<noteq> y \<Longrightarrow>
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
192 |
(Lt5 (Lcons x (Ap5 (Vr5 z) (Vr5 z)) (Lcons y (Vr5 z) Lnil)) (Ap5 (Vr5 x) (Vr5 y))) \<noteq>
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
193 |
(Lt5 (Lcons y (Vr5 z) (Lcons x (Ap5 (Vr5 z) (Vr5 z)) Lnil)) (Ap5 (Vr5 x) (Vr5 y)))"
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
194 |
apply (simp only: alpha5_INJ(3) alpha5_INJ(5) alpha_gen permute_trm5_lts fresh_star_def)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
195 |
apply (simp add: distinct_helper2)
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
196 |
done
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
197 |
|
8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
198 |
end
|