reserve x1,x2,z for set;
reserve A,B for non empty set;
reserve f,g,h for Element of Funcs(A,COMPLEX);
reserve a,b for Complex;

theorem Th6:
  (ComplexFuncAdd(A)).(f,(ComplexFuncAdd(A)).(g,h)) = (
  ComplexFuncAdd(A)).((ComplexFuncAdd(A)).(f,g),h)
proof
  now
    let x be Element of A;
    thus ((ComplexFuncAdd(A)).(f,(ComplexFuncAdd(A)).(g,h))).x = f.x + ((
    ComplexFuncAdd(A)).(g,h)).x by Th1
      .= f.x + (g.x + h.x) by Th1
      .= (f.x + g.x) + h.x
      .= ((ComplexFuncAdd(A)).(f,g)).x + h.x by Th1
      .= ((ComplexFuncAdd(A)).((ComplexFuncAdd(A)).(f,g),h)).x by Th1;
  end;
  hence thesis by FUNCT_2:63;
end;
