diff -r 42ec82147d83 -r 64b30e3cc6d4 src/HOL/Relation.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Relation.thy Fri May 26 18:11:47 1995 +0200 @@ -0,0 +1,27 @@ +(* Title: Relation.thy + ID: \$Id\$ + Author: Riccardo Mattolini, Dip. Sistemi e Informatica + and Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1994 Universita' di Firenze + Copyright 1993 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) + trans :: "('a * 'a)set => bool" (*transitivity predicate*) + converse :: "('a*'a) set => ('a*'a) set" + "^^" :: "[('a*'a) set,'a set] => 'a set" (infixl 90) + Domain :: "('a*'a) set => 'a set" + Range :: "('a*'a) set => 'a set" +defs + id_def "id == {p. ? x. p = (x,x)}" + comp_def (*composition of relations*) + "r O s == {xz. ? x y z. xz = (x,z) & (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) == {z. (? w:r. ? x y. w=(x,y) & z=(y,x))}" + Domain_def "Domain(r) == {z. ! x. (z=x --> (? y. (x,y):r))}" + Range_def "Range(r) == Domain(converse(r))" + Image_def "r ^^ s == {y. y:Range(r) & (? x:s. (x,y):r)}" +end