In other words, it is a total order compatible with the partial order.

Equality is both an equivalence relation and a partial order.

However, ordered by the subsequence relation is a well partial order.

In fact, even some relations that are not partial orders are of special interest.

The notion and terminology is generalized to a partial order.

A group G with a partial order is called an ordered group.

The following proposition says that inclusion is a partial order.

It follows that the relation defined in this way is only a partial order.

In this case no partial order for commitment events can be found.

A reaction rate can have a negative partial order with respect to a substance.