reserve i,j for Nat;
reserve A,B for Ring;

theorem Th8:
  for x, y be Element of B, x1, y1 be Element of A st A is Subring of B &
  x = x1 & y = y1 holds x + y = x1 + y1
  proof
    let x, y be Element of B,
    x1, y1 be Element of A;
    assume A is Subring of B; then
    the addF of A = (the addF of B) || the carrier of A by C0SP1:def 3;
    hence thesis by FUNCT_1:49,ZFMISC_1:87;
  end;
