src/HOL/Relation.thy
 changeset 7014 11ee650edcd2 parent 6806 43c081a0858d child 7912 0e42be14f136
```     1.1 --- a/src/HOL/Relation.thy	Fri Jul 16 12:02:06 1999 +0200
1.2 +++ b/src/HOL/Relation.thy	Fri Jul 16 12:09:48 1999 +0200
1.3 @@ -7,14 +7,14 @@
1.4  Relation = Prod +
1.5
1.6  consts
1.7 -  O           :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
1.8 -  converse    :: "('a*'b) set => ('b*'a) set"     ("(_^-1)" [1000] 999)
1.9 -  "^^"        :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
1.10 +  O            :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
1.11 +  converse     :: "('a*'b) set => ('b*'a) set"     ("(_^-1)" [1000] 999)
1.12 +  "^^"         :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
1.13
1.14  defs
1.15 -  comp_def      "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
1.16 -  converse_def  "r^-1 == {(y,x). (x,y):r}"
1.17 -  Image_def     "r ^^ s == {y. ? x:s. (x,y):r}"
1.18 +  comp_def         "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
1.19 +  converse_def     "r^-1 == {(y,x). (x,y):r}"
1.20 +  Image_def        "r ^^ s == {y. ? x:s. (x,y):r}"
1.21
1.22  constdefs
1.23    Id     :: "('a * 'a)set"                 (*the identity relation*)
1.24 @@ -44,6 +44,9 @@
1.25    Univalent :: "('a * 'b)set => bool"
1.26      "Univalent r == !x y. (x,y):r --> (!z. (x,z):r --> y=z)"
1.27
1.28 +  fun_rel_comp :: "['a => 'b, ('b * 'c) set] => ('a => 'c) set"
1.29 +    "fun_rel_comp f R == {g. !x. (f x, g x) : R}"
1.30 +
1.31  syntax
1.32    reflexive :: "('a * 'a)set => bool"       (*reflexivity over a type*)
1.33
```