(* Title: HOL/ex/Mutil
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1996 University of Cambridge
The Mutilated Chess Board Problem, formalized inductively
Originator is Max Black, according to J A Robinson.
Popularized as the Mutilated Checkerboard Problem by J McCarthy
*)
Mutil = Finite +
consts
domino :: "(nat*nat)set set"
tiling :: 'a set set => 'a set set
below :: nat => nat set
evnodd :: "[(nat*nat)set, nat] => (nat*nat)set"
inductive domino
intrs
horiz "{(i, j), (i, Suc j)} : domino"
vertl "{(i, j), (Suc i, j)} : domino"
inductive "tiling A"
intrs
empty "{} : tiling A"
Un "[| a: A; t: tiling A; a Int t = {} |] ==> a Un t : tiling A"
defs
below_def "below n == nat_rec n {} insert"
evnodd_def "evnodd A b == A Int {(i,j). (i+j) mod 2 = b}"
end