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 Th13:
  f is A,n,B,k-dominated-election implies A <> B
proof
  assume
A1: f is A,n,B,k-dominated-election;
  then reconsider f as Element of (n+k)-tuples_on {A,B};
  len f+1 >= len f by NAT_1:13;
  then f| (len f+1 ) = f by FINSEQ_1:58;
  then card (f"{A}) > card (f"{B}) by A1;
  hence thesis;
end;
