## Non-strict partial order

### Set

 context $X$
 definiendum $\le\ \in\ \mathrm{it}$

The relation $\le$ is an order relation if it's in the intersection of all reflexive, all anti-symmetric and all transitive relation. Hence

 context $\le\ \in\ \mathrm{Rel}(X)$ $x,y,z \in X$
 postulate $x \le x$ postulate $x\le y\ \land\ y\le x \implies (x=y)$ postulate $x \le y\ \land\ y \le z \Leftrightarrow x\le z$

Here we use infix notation: $x\le y\ \equiv\ \le(x,y)$.

### Discussion

#### Reference

Wikipedia: Order theory, Poset