reserve D,D1,D2 for non empty set,
        d,d1,d2 for XFinSequence of D,
        n,k,i,j for Nat;
reserve A,B for object,
        v for Element of (n+k)-tuples_on {A,B},
        f,g for FinSequence;

theorem Th18:
  A = B or n <= k implies DominatedElection(A,n,B,k) is empty
proof
  assume A1:A=B or n <=k;
  assume DominatedElection(A,n,B,k) is non empty;
  then consider f be object such that
A2: f in DominatedElection(A,n,B,k);
  f in  Election(A,n,B,k) by A2;
  then reconsider f as Element of (n+k)-tuples_on {A,B};
  f is A,n,B,k-dominated-election by A2,Def3;
  hence thesis by Th13,Th14,A1;
end;
