
theorem Th15:
  for x be Element of F_Rat, x1 be Rational st x <> 0.F_Rat & x1 = x
  holds x" = x1"
  proof
    let x be Element of F_Rat, x1 be Rational;
    assume A1: x <> 0.F_Rat & x1 = x;
    reconsider w = x1" as Element of F_Rat by RAT_1:def 2;
    w * x = 1.F_Rat by A1,XCMPLX_0:def 7;
    hence thesis by A1,VECTSP_1:def 10;
  end;
