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 Th8:
  (ComplexFuncMult(A)).(f,(ComplexFuncMult(A)).(g,h)) = (
  ComplexFuncMult(A)).((ComplexFuncMult(A)).(f,g),h)
proof
  now
    let x be Element of A;
    thus ((ComplexFuncMult(A)).(f,(ComplexFuncMult(A)).(g,h))).x = f.x * ((
    ComplexFuncMult(A)).(g,h)).x by Th2
      .= f.x * (g.x * h.x) by Th2
      .= (f.x * g.x) * h.x
      .= ((ComplexFuncMult(A)).(f,g)).x * h.x by Th2
      .= ((ComplexFuncMult(A)).((ComplexFuncMult(A)).(f,g),h)).x by Th2;
  end;
  hence thesis by FUNCT_2:63;
end;
