cleanup for Fun.thy:
merged Update.{thy|ML} into Fun.{thy|ML}
moved o_def from HOL.thy to Fun.thy
added Id_def to Fun.thy
moved image_compose from Set.ML to Fun.ML
moved o_apply and o_assoc from simpdata.ML to Fun.ML
moved fun_upd_same and fun_upd_other (from Map.ML) to Fun.ML
added fun_upd_twist to Fun.ML
(* Title: Relation.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1996 University of Cambridge
*)
Relation = Prod +
consts
id :: "('a * 'a)set" (*the identity relation*)
O :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
converse :: "('a*'b) set => ('b*'a) set" ("(_^-1)" [1000] 999)
"^^" :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
Domain :: "('a*'b) set => 'a set"
Range :: "('a*'b) set => 'b set"
trans :: "('a * 'a)set => bool" (*transitivity predicate*)
Univalent :: "('a * 'b)set => bool"
defs
id_def "id == {p. ? x. p = (x,x)}"
comp_def "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
converse_def "r^-1 == {(y,x). (x,y):r}"
Domain_def "Domain(r) == {x. ? y. (x,y):r}"
Range_def "Range(r) == Domain(r^-1)"
Image_def "r ^^ s == {y. ? x:s. (x,y):r}"
trans_def "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
Univalent_def "Univalent r == !x y. (x,y):r --> (!z. (x,z):r --> y=z)"
end