src/HOL/WF_Rel.thy
 author paulson Thu Sep 23 13:06:31 1999 +0200 (1999-09-23) changeset 7584 5be4bb8e4e3f parent 3296 2ee6c397003d child 8262 08ad0a986db2 permissions -rw-r--r--
1 (*  Title:      HOL/WF_Rel
2     ID:         \$Id\$
6 Derived WF relations: inverse image, lexicographic product, measure, ...
8 The simple relational product, in which (x',y')<(x,y) iff x'<x and y'<y, is a
9 subset of the lexicographic product, and therefore does not need to be defined
10 separately.
11 *)
13 WF_Rel = Finite +
14 consts
15   less_than :: "(nat*nat)set"
16   inv_image :: "('b * 'b)set => ('a => 'b) => ('a * 'a)set"
17   measure   :: "('a => nat) => ('a * 'a)set"
18   "**"      :: "[('a*'a)set, ('b*'b)set] => (('a*'b)*('a*'b))set" (infixl 70)
19   finite_psubset  :: "('a set * 'a set) set"
22 defs
23   less_than_def "less_than == trancl pred_nat"
25   inv_image_def "inv_image r f == {(x,y). (f(x), f(y)) : r}"
27   measure_def   "measure == inv_image less_than"
29   lex_prod_def  "ra**rb == {p. ? a a' b b'.
30                                 p = ((a,b),(a',b')) &
31                                ((a,a') : ra | a=a' & (b,b') : rb)}"
33   (* finite proper subset*)
34   finite_psubset_def "finite_psubset == {(A,B). A < B & finite B}"
35 end