src/HOL/Relation.thy
author paulson
Thu, 12 Sep 1996 10:36:06 +0200
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permissions -rw-r--r--
Simplification and tidying of definitions
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(*  Title:      Relation.thy
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1996  University of Cambridge
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*)
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Relation = Prod +
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consts
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    id          :: "('a * 'a)set"               (*the identity relation*)
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    O           :: "[('b * 'c)set, ('a * 'b)set] => ('a * 'c)set" (infixr 60)
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    trans       :: "('a * 'a)set => bool"       (*transitivity predicate*)
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    converse    :: "('a*'b) set => ('b*'a) set"
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    "^^"        :: "[('a*'b) set,'a set] => 'b set" (infixl 90)
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    Domain      :: "('a*'b) set => 'a set"
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    Range       :: "('a*'b) set => 'b set"
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defs
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    id_def        "id == {p. ? x. p = (x,x)}"
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    comp_def      "r O s == {(x,z). ? y. (x,y):s & (y,z):r}"
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    trans_def     "trans(r) == (!x y z. (x,y):r --> (y,z):r --> (x,z):r)"
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    converse_def  "converse(r) == {(y,x). (x,y):r}"
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    Domain_def    "Domain(r) == {x. ? y. (x,y):r}"
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    Range_def     "Range(r) == Domain(converse(r))"
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    Image_def     "r ^^ s == {y. ? x:s. (x,y):r}"
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end