| author | haftmann |
| Fri, 12 Oct 2007 08:25:48 +0200 | |
| changeset 24996 | ebd5f4cc7118 |
| parent 16417 | 9bc16273c2d4 |
| child 41589 | bbd861837ebc |
| permissions | -rw-r--r-- |
|
14620
1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
1 |
(* Title: HOL/Import/MakeEqual.thy |
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1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
2 |
ID: $Id$ |
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1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
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Author: Sebastian Skalberg (TU Muenchen) |
|
1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
4 |
*) |
|
1be590fd2422
Minor cleanup of headers and some speedup of the HOL4 import.
skalberg
parents:
14516
diff
changeset
|
5 |
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| 16417 | 6 |
theory MakeEqual imports Main |
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uses "shuffler.ML" begin |
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setup Shuffler.setup |
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lemma conj_norm [shuffle_rule]: "(A & B ==> PROP C) == ([| A ; B |] ==> PROP C)" |
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proof |
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assume "A & B ==> PROP C" A B |
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thus "PROP C" |
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by auto |
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next |
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assume "[| A; B |] ==> PROP C" "A & B" |
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thus "PROP C" |
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by auto |
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qed |
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lemma imp_norm [shuffle_rule]: "(Trueprop (A --> B)) == (A ==> B)" |
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proof |
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assume "A --> B" A |
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thus B .. |
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next |
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assume "A ==> B" |
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thus "A --> B" |
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by auto |
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qed |
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lemma all_norm [shuffle_rule]: "(Trueprop (ALL x. P x)) == (!!x. P x)" |
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proof |
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fix x |
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assume "ALL x. P x" |
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thus "P x" .. |
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next |
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assume "!!x. P x" |
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thus "ALL x. P x" |
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.. |
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qed |
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lemma ex_norm [shuffle_rule]: "(EX x. P x ==> PROP Q) == (!!x. P x ==> PROP Q)" |
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proof |
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fix x |
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assume ex: "EX x. P x ==> PROP Q" |
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assume "P x" |
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hence "EX x. P x" .. |
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with ex show "PROP Q" . |
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next |
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assume allx: "!!x. P x ==> PROP Q" |
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assume "EX x. P x" |
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hence p: "P (SOME x. P x)" |
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.. |
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from allx |
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have "P (SOME x. P x) ==> PROP Q" |
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. |
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with p |
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show "PROP Q" |
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by auto |
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qed |
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lemma eq_norm [shuffle_rule]: "Trueprop (t = u) == (t == u)" |
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proof |
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assume "t = u" |
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thus "t == u" by simp |
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next |
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assume "t == u" |
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thus "t = u" |
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by simp |
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qed |
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end |