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Galois Connection
Galois connection is defined by two monotonic functions and between partial orders on and on , such that
for all and (intuitively, the condition means that is approximated by ).
Lemma: The condition holds iff the conjunction of these two conditions:
holds for all and .
Lemma: Let and satisfy the condition of Galois connection. Then the following three conditions are equivalent:
- for all
- is a surjective function
- is an injective function