src/HOL/Import/MakeEqual.thy
 author nipkow Mon Jan 30 21:49:41 2012 +0100 (2012-01-30) changeset 46372 6fa9cdb8b850 parent 41589 bbd861837ebc permissions -rw-r--r--
```     1 (*  Title:      HOL/Import/MakeEqual.thy
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```     2     Author:     Sebastian Skalberg, TU Muenchen
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```     3 *)
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```     4
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```     5 theory MakeEqual imports Main
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```     6   uses "shuffler.ML" begin
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```     7
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```     8 setup Shuffler.setup
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```     9
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```    10 lemma conj_norm [shuffle_rule]: "(A & B ==> PROP C) == ([| A ; B |] ==> PROP C)"
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```    11 proof
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```    12   assume "A & B ==> PROP C" A B
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```    13   thus "PROP C"
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```    14     by auto
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```    15 next
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```    16   assume "[| A; B |] ==> PROP C" "A & B"
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```    17   thus "PROP C"
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```    18     by auto
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```    19 qed
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```    20
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```    21 lemma imp_norm [shuffle_rule]: "(Trueprop (A --> B)) == (A ==> B)"
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```    22 proof
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```    23   assume "A --> B" A
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```    24   thus B ..
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```    25 next
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```    26   assume "A ==> B"
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```    27   thus "A --> B"
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```    28     by auto
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```    29 qed
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```    30
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```    31 lemma all_norm [shuffle_rule]: "(Trueprop (ALL x. P x)) == (!!x. P x)"
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```    32 proof
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```    33   fix x
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```    34   assume "ALL x. P x"
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```    35   thus "P x" ..
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```    36 next
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```    37   assume "!!x. P x"
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```    38   thus "ALL x. P x"
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```    39     ..
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```    40 qed
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```    41
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```    42 lemma ex_norm [shuffle_rule]: "(EX x. P x ==> PROP Q) == (!!x. P x ==> PROP Q)"
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```    43 proof
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```    44   fix x
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```    45   assume ex: "EX x. P x ==> PROP Q"
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```    46   assume "P x"
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```    47   hence "EX x. P x" ..
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```    48   with ex show "PROP Q" .
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```    49 next
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```    50   assume allx: "!!x. P x ==> PROP Q"
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```    51   assume "EX x. P x"
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```    52   hence p: "P (SOME x. P x)"
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```    53     ..
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```    54   from allx
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```    55   have "P (SOME x. P x) ==> PROP Q"
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```    56     .
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```    57   with p
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```    58   show "PROP Q"
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```    59     by auto
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```    60 qed
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```    61
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```    62 lemma eq_norm [shuffle_rule]: "Trueprop (t = u) == (t == u)"
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```    63 proof
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```    64   assume "t = u"
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```    65   thus "t == u" by simp
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```    66 next
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```    67   assume "t == u"
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```    68   thus "t = u"
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```    69     by simp
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```    70 qed
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```    71
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```    72 end
```