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
  Election(A,n,A,0) = {n|-> A}
proof
A1: {A,A}={A} by ENUMSET1:29;
  thus Election(A,n,A,0) c= {n|-> A}
  proof
    let x be object;
    assume
A2:   x in Election(A,n,A,0);
    then reconsider v=x as Element of (n+0)-tuples_on {A} by ENUMSET1:29;
A3:   card (v"{A})=n by A2,Def1;
A4:   len v =n by CARD_1:def 7;
    per cases;
      suppose rng v={};
        then v = {}-->{A};
        then v = n|->A by A3;
        hence thesis by TARSKI:def 1;
      end;
      suppose rng v <>{};
        then v = (dom v)--> A by ZFMISC_1:33,FUNCOP_1:9;
        then v = n|->A by A4,FINSEQ_1:def 3;
        hence thesis by TARSKI:def 1;
      end;
  end;
  A in {A} by TARSKI:def 1;
  then reconsider nA=n|->A as Element of n-tuples_on {A,A} by A1,FINSEQ_2:112;
  nA"{A} = Seg n by FUNCOP_1:15;
  then card (nA"{A})=n by FINSEQ_1:57;
  then nA in Election(A,n,A,0) by Def1;
  hence thesis by ZFMISC_1:31;
end;
