src/ZF/Constructible/MetaExists.thy
 author ballarin Thu Dec 11 18:30:26 2008 +0100 (2008-12-11) changeset 29223 e09c53289830 parent 21404 eb85850d3eb7 child 32960 69916a850301 permissions -rw-r--r--
Conversion of HOL-Main and ZF to new locales.
```     1 (*  Title:      ZF/Constructible/MetaExists.thy
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```     2     ID:         \$Id\$
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```     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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```     4 *)
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```     5
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```     6 header{*The meta-existential quantifier*}
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```     7
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```     8 theory MetaExists imports Main begin
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```     9
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```    10 text{*Allows quantification over any term having sort @{text logic}.  Used to
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```    11 quantify over classes.  Yields a proposition rather than a FOL formula.*}
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```    12
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```    13 definition
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```    14   ex :: "(('a::{}) => prop) => prop"  (binder "?? " 0) where
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```    15   "ex(P) == (!!Q. (!!x. PROP P(x) ==> PROP Q) ==> PROP Q)"
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```    16
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```    17 notation (xsymbols)
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```    18   ex  (binder "\<Or>" 0)
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```    19
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```    20 lemma meta_exI: "PROP P(x) ==> (?? x. PROP P(x))"
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```    21 proof (unfold ex_def)
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```    22   assume P: "PROP P(x)"
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```    23   fix Q
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```    24   assume PQ: "\<And>x. PROP P(x) \<Longrightarrow> PROP Q"
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```    25   from P show "PROP Q" by (rule PQ)
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```    26 qed
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```    27
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```    28 lemma meta_exE: "[| ?? x. PROP P(x);  !!x. PROP P(x) ==> PROP R |] ==> PROP R"
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```    29 proof (unfold ex_def)
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```    30   assume QPQ: "\<And>Q. (\<And>x. PROP P(x) \<Longrightarrow> PROP Q) \<Longrightarrow> PROP Q"
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```    31   assume PR: "\<And>x. PROP P(x) \<Longrightarrow> PROP R"
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```    32   from PR show "PROP R" by (rule QPQ)
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```    33 qed
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```    34
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```    35 end
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