reserve i,j for Nat;
reserve A,B for Ring;
reserve K, L for Field;

theorem Lm57:
  for x be Element of F_Complex holds
    the addF of F_Rat = (the addF of FQ_Ring(x))||RAT
  proof
    let x be Element of F_Complex;
    thus the addF of F_Rat =
      addcomplex|[:RAT,RAT:] by ZFMISC_1:96,RELAT_1:74,
         VECTSP_1:def 5,RING_3:2,GAUSSINT:13
      .= (the addF of FQ_Ring(x))||RAT by Lm56,RELAT_1:74;
  end;
