src/HOL/Wellfounded_Relations.thy
 changeset 10213 01c2744a3786 child 11008 f7333f055ef6
```     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/HOL/Wellfounded_Relations.thy	Thu Oct 12 18:44:35 2000 +0200
1.3 @@ -0,0 +1,44 @@
1.4 +(*  Title:      HOL/Wellfounded_Relations
1.5 +    ID:         \$Id\$
1.7 +    Copyright   1995 TU Munich
1.8 +
1.9 +Derived WF relations: inverse image, lexicographic product, measure, ...
1.10 +
1.11 +The simple relational product, in which (x',y')<(x,y) iff x'<x and y'<y, is a
1.12 +subset of the lexicographic product, and therefore does not need to be defined
1.13 +separately.
1.14 +*)
1.15 +
1.16 +Wellfounded_Relations = Finite +
1.17 +
1.18 +(* actually belongs to theory Finite *)
1.19 +instance unit :: finite                  (finite_unit)
1.20 +instance "*" :: (finite,finite) finite   (finite_Prod)
1.21 +
1.22 +
1.23 +constdefs
1.24 + less_than :: "(nat*nat)set"
1.25 +"less_than == trancl pred_nat"
1.26 +
1.27 + inv_image :: "('b * 'b)set => ('a => 'b) => ('a * 'a)set"
1.28 +"inv_image r f == {(x,y). (f(x), f(y)) : r}"
1.29 +
1.30 + measure   :: "('a => nat) => ('a * 'a)set"
1.31 +"measure == inv_image less_than"
1.32 +
1.33 + lex_prod  :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set"
1.34 +               (infixr "<*lex*>" 80)
1.35 +"ra <*lex*> rb == {((a,b),(a',b')). (a,a') : ra | a=a' & (b,b') : rb}"
1.36 +
1.37 + (* finite proper subset*)
1.38 + finite_psubset  :: "('a set * 'a set) set"
1.39 +"finite_psubset == {(A,B). A < B & finite B}"
1.40 +
1.41 +(* For rec_defs where the first n parameters stay unchanged in the recursive
1.42 +   call. See While for an application.
1.43 +*)
1.44 + same_fst :: "('a => bool) => ('a => ('b * 'b)set) => (('a*'b)*('a*'b))set"
1.45 +"same_fst P R == {((x',y'),(x,y)) . x'=x & P x & (y',y) : R x}"
1.46 +
1.47 +end
```