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 ElectionEmpty:
  k>0 implies Election(A,n,A,k) is empty
proof
  assume
A1:  k>0;
  assume Election(A,n,A,k) is non empty;
  then consider v be object such that
A2:  v in Election(A,n,A,k);
  reconsider v as Element of (n+k)-tuples_on {A} by A2,ENUMSET1:29;
A3:  card dom v =(n+k) by CARD_1:def 7;
  v"(rng v) c= v"{A} by RELAT_1:143;
  then v"{A} = dom v by RELAT_1:134,132;
  then n+k = n by A3,Def1,A2;
  hence contradiction by A1;
end;
