(* Title : Lubs.thy
ID : $Id$
Author : Jacques D. Fleuriot
Copyright : 1998 University of Cambridge
Description : Upper bounds, lubs definitions
suggested by James Margetson
*)
Lubs = Set +
consts
"*<=" :: ['a set, 'a] => bool (infixl 70)
"<=*" :: ['a, 'a set] => bool (infixl 70)
constdefs
leastP :: ['a =>bool,'a] => bool
"leastP P x == (P x & x <=* Collect P)"
isLub :: ['a set, 'a set, 'a] => bool
"isLub R S x == leastP (isUb R S) x"
isUb :: ['a set, 'a set, 'a] => bool
"isUb R S x == S *<= x & x: R"
ubs :: ['a set, 'a set] => 'a set
"ubs R S == Collect (isUb R S)"
defs
setle_def
"S *<= x == (ALL y: S. y <= x)"
setge_def
"x <=* S == (ALL y: S. x <= y)"
end