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

theorem Lm53:
  In(-1.F_Rat,F_Complex) = -1.F_Complex
  proof
    1.F_Complex + In(-1.F_Rat,F_Complex)
      = In(1.F_Rat,F_Complex) + In(-1.F_Rat,F_Complex) by Lm5,Th3
     .= In(0.F_Rat,F_Complex)
     .= 0.F_Complex by Lm5,Th3;
    hence thesis by RLVECT_1:def 10;
  end;
