src/HOL/Relation.thy
 changeset 7912 0e42be14f136 parent 7014 11ee650edcd2 child 8268 722074b93cdd
```     1.1 --- a/src/HOL/Relation.thy	Thu Oct 21 19:00:25 1999 +0200
1.2 +++ b/src/HOL/Relation.thy	Fri Oct 22 17:04:19 1999 +0200
1.3 @@ -6,21 +6,20 @@
1.4
1.5  Relation = Prod +
1.6
1.7 -consts
1.8 -  O            :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
1.9 -  converse     :: "('a*'b) set => ('b*'a) set"     ("(_^-1)" [1000] 999)
1.10 -  "^^"         :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
1.11 -
1.12 -defs
1.13 -  comp_def         "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
1.14 -  converse_def     "r^-1 == {(y,x). (x,y):r}"
1.15 -  Image_def        "r ^^ s == {y. ? x:s. (x,y):r}"
1.16 -
1.17  constdefs
1.18 -  Id     :: "('a * 'a)set"                 (*the identity relation*)
1.19 -      "Id == {p. ? x. p = (x,x)}"
1.20 +  converse :: "('a*'b) set => ('b*'a) set"               ("(_^-1)" [1000] 999)
1.21 +    "r^-1 == {(y,x). (x,y):r}"
1.22 +
1.23 +  comp  :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set"  (infixr "O" 60)
1.24 +    "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
1.25
1.26 -  diag   :: "'a set => ('a * 'a)set"
1.27 +  Image :: "[('a*'b) set,'a set] => 'b set"                (infixl "^^" 90)
1.28 +    "r ^^ s == {y. ? x:s. (x,y):r}"
1.29 +
1.30 +  Id    :: "('a * 'a)set"                            (*the identity relation*)
1.31 +    "Id == {p. ? x. p = (x,x)}"
1.32 +
1.33 +  diag  :: "'a set => ('a * 'a)set"          (*diagonal: identity over a set*)
1.34      "diag(A) == UN x:A. {(x,x)}"
1.35
1.36    Domain :: "('a*'b) set => 'a set"
```