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
  for X being BCI-Algebra_with_Condition(S) holds for x,y,z being
  Element of X holds x\y <= (x\z)*(z\y)
proof
  let X be BCI-Algebra_with_Condition(S);
  let x,y,z be Element of X;
  ((x\y)\(x\z))\(z\y) = 0.X by BCIALG_1:11;
  then (x\y)\((x\z)*(z\y)) = 0.X by Th11;
  hence thesis;
end;
