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Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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1 |
theory Term7
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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2 |
imports "Nominal2_Atoms" "Nominal2_Eqvt" "Nominal2_Supp" "Abs" "Perm" "Fv" "Rsp" "../Attic/Prove"
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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3 |
begin
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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4 |
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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5 |
atom_decl name
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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6 |
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Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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7 |
(* example with a respectful bn function defined over the type itself *)
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Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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8 |
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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9 |
datatype rtrm7 =
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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10 |
rVr7 "name"
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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11 |
| rLm7 "name" "rtrm7" --"bind left in right"
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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12 |
| rLt7 "rtrm7" "rtrm7" --"bind (bv7 left) in (right)"
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
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13 |
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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14 |
primrec
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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15 |
rbv7
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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16 |
where
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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17 |
"rbv7 (rVr7 n) = {atom n}"
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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18 |
| "rbv7 (rLm7 n t) = rbv7 t - {atom n}"
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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19 |
| "rbv7 (rLt7 l r) = rbv7 l \<union> rbv7 r"
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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20 |
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1277
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21 |
setup {* snd o define_raw_perms (Datatype.the_info @{theory} "Term7.rtrm7") 1 *}
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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22 |
thm permute_rtrm7.simps
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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23 |
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1277
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24 |
local_setup {* snd o define_fv_alpha (Datatype.the_info @{theory} "Term7.rtrm7") [
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1270
8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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25 |
[[[]], [[(NONE, 0)], [(NONE, 0)]], [[], [(SOME @{term rbv7}, 0)]]]] *}
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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26 |
print_theorems
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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27 |
notation
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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28 |
alpha_rtrm7 ("_ \<approx>7a _" [100, 100] 100)
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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29 |
thm alpha_rtrm7.intros
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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30 |
thm fv_rtrm7.simps
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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31 |
inductive
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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32 |
alpha7 :: "rtrm7 \<Rightarrow> rtrm7 \<Rightarrow> bool" ("_ \<approx>7 _" [100, 100] 100)
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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33 |
where
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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34 |
a1: "a = b \<Longrightarrow> (rVr7 a) \<approx>7 (rVr7 b)"
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Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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35 |
| a2: "(\<exists>pi. (({atom a}, t) \<approx>gen alpha7 fv_rtrm7 pi ({atom b}, s))) \<Longrightarrow> rLm7 a t \<approx>7 rLm7 b s"
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8c3cf9f4f5f2
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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36 |
| a3: "(\<exists>pi. (((rbv7 t1), s1) \<approx>gen alpha7 fv_rtrm7 pi ((rbv7 t2), s2))) \<Longrightarrow> rLt7 t1 s1 \<approx>7 rLt7 t2 s2"
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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37 |
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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38 |
lemma "(x::name) \<noteq> y \<Longrightarrow> \<not> (alpha7 ===> op =) rbv7 rbv7"
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Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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39 |
apply simp
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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40 |
apply (rule_tac x="rLt7 (rVr7 x) (rVr7 x)" in exI)
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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41 |
apply (rule_tac x="rLt7 (rVr7 y) (rVr7 y)" in exI)
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
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42 |
apply simp
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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43 |
apply (rule a3)
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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44 |
apply (rule_tac x="(x \<leftrightarrow> y)" in exI)
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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45 |
apply (simp_all add: alpha_gen fresh_star_def)
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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46 |
apply (rule a1)
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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47 |
apply (rule refl)
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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48 |
done
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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changeset
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49 |
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8c3cf9f4f5f2
Split Terms into separate files and add them to tests.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
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50 |
end
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