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;
