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 Th9:
  (ComplexFuncMult(A)).(ComplexFuncUnit(A),f) = f
proof
  now
    let x be Element of A;
    thus ((ComplexFuncMult(A)).(ComplexFuncUnit(A),f)).x= (ComplexFuncUnit(A))
    .x * f.x by Th2
      .=1r * f.x by FUNCOP_1:7
      .= f.x by COMPLEX1:def 4;
  end;
  hence thesis by FUNCT_2:63;
end;
