src/HOL/Import/MakeEqual.thy
 author haftmann Mon Jan 30 08:20:56 2006 +0100 (2006-01-30) changeset 18851 9502ce541f01 parent 16417 9bc16273c2d4 child 41589 bbd861837ebc permissions -rw-r--r--
```     1 (*  Title:      HOL/Import/MakeEqual.thy
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```     2     ID:         \$Id\$
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```     3     Author:     Sebastian Skalberg (TU Muenchen)
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```     4 *)
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```     5
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```     6 theory MakeEqual imports Main
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```     7   uses "shuffler.ML" begin
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```     8
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```     9 setup Shuffler.setup
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```    10
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```    11 lemma conj_norm [shuffle_rule]: "(A & B ==> PROP C) == ([| A ; B |] ==> PROP C)"
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```    12 proof
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```    13   assume "A & B ==> PROP C" A B
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```    14   thus "PROP C"
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```    15     by auto
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```    16 next
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```    17   assume "[| A; B |] ==> PROP C" "A & B"
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```    18   thus "PROP C"
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```    19     by auto
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```    20 qed
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```    21
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```    22 lemma imp_norm [shuffle_rule]: "(Trueprop (A --> B)) == (A ==> B)"
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```    23 proof
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```    24   assume "A --> B" A
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```    25   thus B ..
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```    26 next
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```    27   assume "A ==> B"
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```    28   thus "A --> B"
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```    29     by auto
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```    30 qed
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```    31
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```    32 lemma all_norm [shuffle_rule]: "(Trueprop (ALL x. P x)) == (!!x. P x)"
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```    33 proof
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```    34   fix x
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```    35   assume "ALL x. P x"
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```    36   thus "P x" ..
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```    37 next
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```    38   assume "!!x. P x"
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```    39   thus "ALL x. P x"
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```    40     ..
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```    41 qed
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```    42
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```    43 lemma ex_norm [shuffle_rule]: "(EX x. P x ==> PROP Q) == (!!x. P x ==> PROP Q)"
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```    44 proof
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```    45   fix x
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```    46   assume ex: "EX x. P x ==> PROP Q"
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```    47   assume "P x"
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```    48   hence "EX x. P x" ..
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```    49   with ex show "PROP Q" .
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```    50 next
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```    51   assume allx: "!!x. P x ==> PROP Q"
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```    52   assume "EX x. P x"
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```    53   hence p: "P (SOME x. P x)"
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```    54     ..
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```    55   from allx
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```    56   have "P (SOME x. P x) ==> PROP Q"
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```    57     .
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```    58   with p
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```    59   show "PROP Q"
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```    60     by auto
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```    61 qed
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```    62
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```    63 lemma eq_norm [shuffle_rule]: "Trueprop (t = u) == (t == u)"
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```    64 proof
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```    65   assume "t = u"
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```    66   thus "t == u" by simp
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```    67 next
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```    68   assume "t == u"
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```    69   thus "t = u"
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```    70     by simp
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```    71 qed
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```    72
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```    73 end
```