reserve X for BCI-algebra;
reserve X1 for non empty Subset of X;
reserve A,I for Ideal of X;
reserve x,y,z for Element of X;
reserve a for Element of A;

theorem
  for x,y,z,u being Element of X st x<=y holds u\(z\x)<=u\(z\y)
proof
  let x,y,z,u be Element of X;
  assume x<=y;
  then z\y<=z\x by BCIALG_1:5;
  hence thesis by BCIALG_1:5;
end;
