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

theorem
  for A being Order, f1, f2 being finite-support Function of A, REAL holds
    eqSumOf f1 = eqSumOf f2 implies f1 = f2
proof
  let A be Order;
  let f1, f2 be finite-support Function of A, REAL;
  assume A1: eqSumOf f1 = eqSumOf f2;
  thus f1 = (eqSumOf f2)*(proj A) by A1, Th61
    .= f2 by Th61;
end;
