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

theorem Lm56:
  for x be Element of F_Complex holds
  [:RAT,RAT:] c= [:FQ(x),FQ(x):] & [:FQ(x),FQ(x):] c= [:COMPLEX,COMPLEX:]
  proof
    let x be Element of F_Complex;
A1: the carrier of F_Rat c= the carrier of FQ_Ring(x) by Lm48;
A2: FQ(x) c= the carrier of F_Complex;
    FQ(x) c= COMPLEX by A2,COMPLFLD:def 1;
    hence thesis by A1,ZFMISC_1:96;
  end;
