|
1606
|
1 |
(* Title: ZF/ex/Mutil
|
|
|
2 |
ID: $Id$
|
|
|
3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
|
|
|
4 |
Copyright 1996 University of Cambridge
|
|
|
5 |
|
|
|
6 |
The Mutilated Checkerboard Problem, formalized inductively
|
|
|
7 |
*)
|
|
|
8 |
|
|
1624
|
9 |
Mutil = CardinalArith +
|
|
1606
|
10 |
consts
|
|
|
11 |
domino :: i
|
|
|
12 |
evnodd :: [i,i]=>i
|
|
|
13 |
tiling :: i=>i
|
|
|
14 |
|
|
|
15 |
inductive
|
|
|
16 |
domains "domino" <= "Pow(nat*nat)"
|
|
|
17 |
intrs
|
|
|
18 |
horiz "[| i: nat; j: nat |] ==> {<i,j>, <i,succ(j)>} : domino"
|
|
|
19 |
vertl "[| i: nat; j: nat |] ==> {<i,j>, <succ(i),j>} : domino"
|
|
|
20 |
type_intrs "[empty_subsetI, cons_subsetI, PowI, SigmaI, nat_succI]"
|
|
|
21 |
|
|
|
22 |
|
|
|
23 |
defs
|
|
|
24 |
evnodd_def "evnodd(A,b) == {z:A. EX i j. z=<i,j> & (i#+j) mod 2 = b}"
|
|
|
25 |
|
|
|
26 |
inductive
|
|
|
27 |
domains "tiling(A)" <= "Pow(Union(A))"
|
|
|
28 |
intrs
|
|
|
29 |
empty "0 : tiling(A)"
|
|
|
30 |
Un "[| a: A; t: tiling(A); a Int t = 0 |] ==> a Un t : tiling(A)"
|
|
|
31 |
type_intrs "[empty_subsetI, Union_upper, Un_least, PowI]"
|
|
|
32 |
type_elims "[make_elim PowD]"
|
|
|
33 |
|
|
|
34 |
end
|