src/HOL/Wellfounded_Relations.thy
 author paulson Wed Jul 25 13:13:01 2001 +0200 (2001-07-25) changeset 11451 8abfb4f7bd02 parent 11136 e34e7f6d9b57 child 11454 7514e5e21cb8 permissions -rw-r--r--
partial restructuring to reduce dependence on Axiom of Choice
```     1 (*  Title:      HOL/Wellfounded_Relations
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```     2     ID:         \$Id\$
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```     3     Author:     Konrad Slind
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```     4     Copyright   1995 TU Munich
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```     5
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```     6 Derived WF relations: inverse image, lexicographic product, measure, ...
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```     7
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```     8 The simple relational product, in which (x',y')<(x,y) iff x'<x and y'<y, is a
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```     9 subset of the lexicographic product, and therefore does not need to be defined
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```    10 separately.
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```    11 *)
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```    12
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```    13 Wellfounded_Relations = Finite + Hilbert_Choice +
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```    14
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```    15 (* logically belongs in Finite.thy, but the theorems are proved in Finite.ML *)
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```    16 instance unit :: finite                  (finite_unit)
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```    17 instance "*" :: (finite,finite) finite   (finite_Prod)
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```    18
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```    19
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```    20 constdefs
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```    21  less_than :: "(nat*nat)set"
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```    22 "less_than == trancl pred_nat"
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```    23
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```    24  measure   :: "('a => nat) => ('a * 'a)set"
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```    25 "measure == inv_image less_than"
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```    26
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```    27  lex_prod  :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set"
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```    28                (infixr "<*lex*>" 80)
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```    29 "ra <*lex*> rb == {((a,b),(a',b')). (a,a') : ra | a=a' & (b,b') : rb}"
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```    30
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```    31  (* finite proper subset*)
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```    32  finite_psubset  :: "('a set * 'a set) set"
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```    33 "finite_psubset == {(A,B). A < B & finite B}"
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```    34
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```    35 (* For rec_defs where the first n parameters stay unchanged in the recursive
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```    36    call. See Library/While_Combinator.thy for an application.
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```    37 *)
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```    38  same_fst :: "('a => bool) => ('a => ('b * 'b)set) => (('a*'b)*('a*'b))set"
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```    39 "same_fst P R == {((x',y'),(x,y)) . x'=x & P x & (y',y) : R x}"
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```    40
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```    41 end
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