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 Th12:
  (ComplexFuncExtMult(A)).[1r,f] = f
proof
  now
    let x be Element of A;
    thus ((ComplexFuncExtMult(A)).[1r,f]).x = 1r*(f.x) by Th4
      .= f.x by COMPLEX1:def 4;
  end;
  hence thesis by FUNCT_2:63;
end;
