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 Th12:
  A <> B implies card Election(A,n,B,k) = (n+k) choose n
proof
  assume
A1: A<>B;
  thus card Election(A,n,B,k) = card Choose(Seg (n+k),n,A,B) by Th10
         .= card Seg (n+k) choose n by A1,CARD_FIN:16
         .= (n+k) choose n by FINSEQ_1:57;
end;
