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

theorem Th52:
  for A being set, D being a_partition of A, X being Element of D,
    f being Function of A, REAL
  holds
    eqSupport(f, X) = eqSupport(-f, X)
proof
  let A be set, D be a_partition of A, X be Element of D,
    f be Function of A, REAL;
  A1: rng f c= COMPLEX by NUMBERS:11;
  dom f = A by FUNCT_2:def 1;
  then f is Function of A, COMPLEX by FUNCT_2:2, A1;
  hence eqSupport(f,X) = eqSupport(-f,X) by Th10;
end;
