Definition:Inclusion Ordered Set

Definition
Let $\struct {S, \preceq}$ be an ordered set.

$\struct {S, \preceq}$ is inclusion ordered set :
 * $\mathord\preceq = \mathord\subseteq \cap \paren {S \times S}$

That means:
 * $\forall x, y \in S: x \preceq y \iff x \subseteq y$