| author | Christian Urban <urbanc@in.tum.de> |
| Thu, 31 May 2012 12:01:01 +0100 | |
| changeset 3181 | ca162f0a7957 |
| parent 2456 | 5e76af0a51f9 |
| permissions | -rw-r--r-- |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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1 |
theory FSet_ballbex |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
2 |
imports "../../../Nominal/FSet" |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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3 |
begin |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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4 |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
5 |
notation |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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6 |
list_eq (infix "\<approx>" 50) |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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7 |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
8 |
lemma test: |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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"\<forall>xs \<in> (\<lambda>xs. memb x xs). memb x (y # xs)" |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
10 |
apply (simp add: memb_def) |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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apply (metis mem_def) |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
12 |
done |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
13 |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
14 |
thm test[quot_lifted] |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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15 |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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lemma "\<forall>xs \<in> (\<lambda>xs. x |\<in>| xs). x |\<in>| finsert y xs" |
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No need to unfold mem_def with rsp/prs (requires new isabelle).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2441
diff
changeset
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17 |
unfolding Ball_def |
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5e76af0a51f9
No need to unfold mem_def with rsp/prs (requires new isabelle).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2441
diff
changeset
|
18 |
by (lifting test[unfolded Ball_def]) |
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2441
fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
19 |
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2456
5e76af0a51f9
No need to unfold mem_def with rsp/prs (requires new isabelle).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2441
diff
changeset
|
20 |
ML {* Quotient_Tacs.lifted @{context} [@{typ "'a fset"}] @{thms Ball_def Bex_def} @{thm test}*}
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2441
fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
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21 |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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lemma test2: |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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"\<exists>xs \<in> (\<lambda>xs. xs \<approx> []). xs \<approx> []" |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
24 |
apply (rule_tac x="[]" in bexI) |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
25 |
apply (auto simp add: mem_def) |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
26 |
done |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
28 |
thm test2[quot_lifted] |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
29 |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
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lemma "\<exists>xs \<in> (\<lambda>xs. xs = {||}). xs = {||}"
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2456
5e76af0a51f9
No need to unfold mem_def with rsp/prs (requires new isabelle).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2441
diff
changeset
|
31 |
unfolding Bex_def |
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5e76af0a51f9
No need to unfold mem_def with rsp/prs (requires new isabelle).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2441
diff
changeset
|
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by (lifting test2[unfolded Bex_def]) |
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2441
fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
33 |
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2456
5e76af0a51f9
No need to unfold mem_def with rsp/prs (requires new isabelle).
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
2441
diff
changeset
|
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ML {* Quotient_Tacs.lifted @{context} [@{typ "'a fset"}] @{thms Bex_def} @{thm test2}*}
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2441
fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
35 |
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fc3e8f79e698
Ball Bex can be lifted after unfolding.
Cezary Kaliszyk <kaliszyk@in.tum.de>
parents:
diff
changeset
|
36 |
end |