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Strict partial order
Definition
$X$ |
$ <\ \in\ \text{StrictPartOrd}(X) $ |
$ R \in \mathrm{Rel}(X) $ |
$ x,y,z\in X $ |
$ x \nless x $ |
$ x<y\land y<z \implies x<z $ |
Here we use infix notation: $x<y\ \equiv\ <(x,y)$.
Discussion
A strict partial order is automatically anti-symmetric.
Reference
Wikipedia: Order theory, Poset