0 to order (= request to buy) a product before it has become available:
1 an act of ordering (= requesting to buy) a product before it has become available:
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).
