(* Title: HOL/Induct/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 = Main +
consts tiling :: "'a set set => 'a set set"
inductive "tiling A"
intrs
empty "{} : tiling A"
Un "[| a: A; t: tiling A; a <= -t |] ==> a Un t : tiling A"
consts domino :: "(nat*nat)set set"
inductive domino
intrs
horiz "{(i, j), (i, Suc j)} : domino"
vertl "{(i, j), (Suc i, j)} : domino"
constdefs
below :: "nat => nat set"
"below n == {i. i<n}"
colored :: "nat => (nat*nat)set"
"colored b == {(i,j). (i+j) mod #2 = b}"
end