reserve X for non empty BCIStr_1;
reserve d for Element of X;
reserve n,m,k for Nat;
reserve f for sequence of  the carrier of X;

theorem Th12:
  for X being BCI-Algebra_with_Condition(S) holds for x,y being
  Element of X holds y <= x*(y\x)
proof
  let X be BCI-Algebra_with_Condition(S);
  let x,y be Element of X;
  (y\x)\(y\x) = 0.X by BCIALG_1:def 5;
  then y\x <= (y\x);
  hence thesis by Lm2;
end;
