|
1440
|
1 |
(* Title: CLattice.thy
|
|
|
2 |
ID: $Id$
|
|
|
3 |
Author: Markus Wenzel, TU Muenchen
|
|
|
4 |
|
|
|
5 |
Complete lattices are orders with infima and suprema of arbitrary
|
|
|
6 |
subsets.
|
|
|
7 |
|
|
|
8 |
TODO:
|
|
|
9 |
derive some more well-known theorems (e.g. ex_Inf == ex_Sup)
|
|
|
10 |
*)
|
|
|
11 |
|
|
|
12 |
CLattice = Order +
|
|
|
13 |
|
|
|
14 |
axclass
|
|
2606
|
15 |
clattice < partial_order
|
|
1440
|
16 |
ex_Inf "ALL A. EX inf. is_Inf A inf"
|
|
|
17 |
ex_Sup "ALL A. EX sup. is_Sup A sup"
|
|
|
18 |
|
|
1573
|
19 |
constdefs
|
|
1440
|
20 |
Inf :: "'a::clattice set => 'a"
|
|
1573
|
21 |
"Inf A == @inf. is_Inf A inf"
|
|
1440
|
22 |
|
|
1573
|
23 |
Sup :: "'a::clattice set => 'a"
|
|
|
24 |
"Sup A == @sup. is_Sup A sup"
|
|
1440
|
25 |
|
|
|
26 |
end
|