diff -r b8dee46d778a -r 0e42be14f136 src/HOL/Relation.thy --- a/src/HOL/Relation.thy Thu Oct 21 19:00:25 1999 +0200 +++ b/src/HOL/Relation.thy Fri Oct 22 17:04:19 1999 +0200 @@ -6,21 +6,20 @@ Relation = Prod + -consts - 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) - -defs - comp_def "r O s == {(x,z). ? y. (x,y):s & (y,z):r}" - converse_def "r^-1 == {(y,x). (x,y):r}" - Image_def "r ^^ s == {y. ? x:s. (x,y):r}" - constdefs - Id :: "('a * 'a)set" (*the identity relation*) - "Id == {p. ? x. p = (x,x)}" + converse :: "('a*'b) set => ('b*'a) set" ("(_^-1)" [1000] 999) + "r^-1 == {(y,x). (x,y):r}" + + comp :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr "O" 60) + "r O s == {(x,z). ? y. (x,y):s & (y,z):r}" - diag :: "'a set => ('a * 'a)set" + Image :: "[('a*'b) set,'a set] => 'b set" (infixl "^^" 90) + "r ^^ s == {y. ? x:s. (x,y):r}" + + Id :: "('a * 'a)set" (*the identity relation*) + "Id == {p. ? x. p = (x,x)}" + + diag :: "'a set => ('a * 'a)set" (*diagonal: identity over a set*) "diag(A) == UN x:A. {(x,x)}" Domain :: "('a*'b) set => 'a set"