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 Th14:
  f is A,n,B,k-dominated-election implies n > k
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
A2: f| (len f+1) = f by FINSEQ_1:58;
A3: A<>B by A1,Th13;
A4: card (f"{A}) = n by A1,Def1;
  card (f"{B}) = k by A1,A3,Th11;
  hence thesis by A2,A1,A4;
end;
