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As a first example, consider the
constraint,
which forces at least variables of the collection to be
assigned value . We have that is extensible
with respect to , since adding a variable to an already satisfied instance of
preserves the fact that the new constraint is satisfied.
As an illustration consider the source constraint
and the target constraint
.
Since the first argument is set to the same value, both in the source and the target constraint,
and since the third is also set to the same value both in the source and the target constraint,
we have that
implies
.
As a second example, consider the
constraint,
which forces to equal the item of .
We have that is suffix-extensible with respect to ,
since adding new elements at the end of for an already satisfied instance of
preserves the fact that the new constraint is satisfied.
As an illustration consider the source constraint
and the target constraint
.
Since the first argument is set to the same value, both in the source and the target constraint,
and since the third argument is also set to the same value both in the source and the target constraint,
we have that
implies
.
As a third example, consider the
constraint,
which forces to equal 1 if all variables of
are set to 1, and 0 otherwise.
We have that is extensible with respect to when
is equal to 0. This stems from the fact that, given a satisfied instance of
where , adding any new variable to preserves the fact that the new
constraint is satisfied.
As an illustration consider the source constraint
and the target constraint
.
Since the first argument is set to 0, both in the source and the target constraint,
we have that
implies
.
As a fourth example, consider the
constraint,
which forces to be lexicographically strictly greater than .
We have that is suffix-extensible with respect to
and . This means that, given a satisfied instance of
, adding items at the end of its first argument
and adding other items at the end of its second argument preserves the fact that the new
constraint is satisfied.
As an illustration consider the source constraint
and the target constraint
.
We have that
implies
.
As a fifth example, consider the
constraint,
which given a collection of vectors each of which defined by a collection of variables of the same length,
forces the vector to be lexicographically strictly less than the vector
. We have that
is suffix-extensible with respect to .
This means that, given a satisfied instance of ,
adding items at the end of all collections simultaneously preserves the fact that the new
constraint is satisfied.
As an illustration consider the source constraint
and the target constraint
.
Since each vector of the source constraint is a prefix of the vector located at the same position in the target constraint
the source constraint implies the target constraint.