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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
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(*                                Checker.v                                 *)
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(*               The mutilated checkerboard problem                         *)
(*               Coq V5.10  G. Huet March 20th 1996                         *)
(* Uses second-order formalisation Constrained Resolution G. Huet July 1973 *)
(* Cf `A tough nut for proof procedures' J. McCarthy July 1964 SAIL Memo 16 *)
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Parameter Black White : Set. (* sets of black (resp. white) squares *)
Parameter BW : Black -> White. (* |Black|<=|White| in full board *)

(* Specifications: *)
Axiom BW_One_one : Injective _ _ BW.
(* finite board *)
Axiom Finite_Board : Finite Black.
Parameter Domino : White -> Black.
(* The Domino one_one map covers White *)
Axiom Domino_one_one : Injective _ _ Domino.
Theorem Domino_covers_Black : Surjective _ _ Domino.