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With the logical 'and' as the tensor product of 2, a 2-category is then nothing but a pre-order.
To compare the knowledge of environments we use the following pre-order.
Then the relation 6 is a pre-order and the relation is an equivalence relation.
The relation is an equivalence because is a pre-order.
The pre-order restriction is more limiting that the safe-unsafe criteria of our generalised deforestation, but the on-line cyclic restriction is something extra.
A pre-order is a reflexive and transitive binary relation.
The trick is to consider a pre-order traversal of the tree, in which subtrees can be simply encoded as intervals.
We are stating here a much stronger property that specifies that queries are monotone with respect to a pre-order that is defined on values (forests, in this case).
Reductions form a pre-order on representations.
The advice we have given to water authorities means that they may pre-order pipes and other materials during the moratorium period.
The pre-order package allowed cell phone users to access a special site featuring image and music downloads.
Exactly one year from the announcement, the beta was made available for pre-order customers without prior warning.
The game's original soundtrack came bundled with the original game as a pre-order bonus.
Customers are able to pre-order at each dealership on a first-come, first-served basis.
Interactive partnered with several retail outlets on a pre-order incentive.