src/HOL/Relation.thy
changeset 8703 816d8f6513be
parent 8268 722074b93cdd
child 10212 33fe2d701ddd
equal deleted inserted replaced
8702:78b7010db847 8703:816d8f6513be
    27 
    27 
    28   Range  :: "('a*'b) set => 'b set"
    28   Range  :: "('a*'b) set => 'b set"
    29     "Range(r) == Domain(r^-1)"
    29     "Range(r) == Domain(r^-1)"
    30 
    30 
    31   refl   :: "['a set, ('a*'a) set] => bool" (*reflexivity over a set*)
    31   refl   :: "['a set, ('a*'a) set] => bool" (*reflexivity over a set*)
    32     "refl A r == r <= A Times A & (ALL x: A. (x,x) : r)"
    32     "refl A r == r <= A <*> A & (ALL x: A. (x,x) : r)"
    33 
    33 
    34   sym    :: "('a*'a) set=>bool"             (*symmetry predicate*)
    34   sym    :: "('a*'a) set=>bool"             (*symmetry predicate*)
    35     "sym(r) == ALL x y. (x,y): r --> (y,x): r"
    35     "sym(r) == ALL x y. (x,y): r --> (y,x): r"
    36 
    36 
    37   antisym:: "('a * 'a)set => bool"          (*antisymmetry predicate*)
    37   antisym:: "('a * 'a)set => bool"          (*antisymmetry predicate*)