Partial order relation $\leq$

1. reflexivity: $\forall x \in X: x \leq x$;
2. antisymmetry: $\forall x, y \in X: x \leq y, y \leq x \implies x = y$;
3. transitivity: $\forall x,y,z \in X: x \leq y, y \leq z \implies x \leq z$.