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(* Title: ZF/ex/Mutil
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ID: $Id$
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1996 University of Cambridge
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The Mutilated Checkerboard Problem, formalized inductively
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Really needs only CardinalArith, not AC, as sets are finite
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*)
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Mutil = Cardinal_AC +
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consts
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domino :: i
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evnodd :: [i,i]=>i
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tiling :: i=>i
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inductive
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domains "domino" <= "Pow(nat*nat)"
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intrs
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horiz "[| i: nat; j: nat |] ==> {<i,j>, <i,succ(j)>} : domino"
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vertl "[| i: nat; j: nat |] ==> {<i,j>, <succ(i),j>} : domino"
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type_intrs "[empty_subsetI, cons_subsetI, PowI, SigmaI, nat_succI]"
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defs
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evnodd_def "evnodd(A,b) == {z:A. EX i j. z=<i,j> & (i#+j) mod 2 = b}"
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inductive
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domains "tiling(A)" <= "Pow(Union(A))"
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intrs
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empty "0 : tiling(A)"
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Un "[| a: A; t: tiling(A); a Int t = 0 |] ==> a Un t : tiling(A)"
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type_intrs "[empty_subsetI, Union_upper, Un_least, PowI]"
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type_elims "[make_elim PowD]"
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end
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