reserve X,Z for set;
reserve x,y,z for object;
reserve A,B,C for Subset of X;

theorem Th55:
  for A being Preorder,
    f being finite-support Function of A, REAL
  holds
    eqSumOf -f = -eqSumOf f
proof
  let A be Preorder;
  let f being finite-support Function of A, REAL;
  reconsider D = the carrier of QuotientOrder(A)
    as a_partition of the carrier of A by Th47;
  thus eqSumOf -f = D eqSumOf -f by Def15
    .= -(D eqSumOf f) by Th54
    .= -eqSumOf f by Def15;
end;
