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

theorem Lm58:
  for x be Element of F_Complex holds
    the multF of F_Rat = (the multF of FQ_Ring(x))||RAT
proof
  let x be Element of F_Complex;
   thus the multF of F_Rat
     = multcomplex|[:RAT,RAT:] by ZFMISC_1:96,RELAT_1:74,
      VECTSP_1:def 5,RING_3:3,GAUSSINT:13
    .= (the multF of FQ_Ring(x))||RAT by Lm56,RELAT_1:74;
end;
