src/HOL/Relation.thy

 Relation = Prod +
 consts
     id          :: "('a * 'a)set"               (*the identity relation*)
     O           :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
     trans       :: "('a * 'a)set => bool"       (*transitivity predicate*)
-    converse    :: "('a*'b) set => ('b*'a) set"
+    inverse    :: "('a*'b) set => ('b*'a) set"     ("(_^-1)" [1000] 1000)
     "^^"        :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
     Domain      :: "('a*'b) set => 'a set"
     Range       :: "('a*'b) set => 'b set"
 defs
     id_def        "id == {p. ? x. p = (x,x)}"
     comp_def      "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
     trans_def     "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
-    converse_def  "converse(r) == {(y,x). (x,y):r}"
+    inverse_def   "r^-1 == {(y,x). (x,y):r}"
     Domain_def    "Domain(r) == {x. ? y. (x,y):r}"
-    Range_def     "Range(r) == Domain(converse(r))"
+    Range_def     "Range(r) == Domain(r^-1)"
     Image_def     "r ^^ s == {y. ? x:s. (x,y):r}"
 end