This file defines sublattices.
Subsemilattices, if people care about them.
A sublattice of a lattice is a set containing the suprema and infima of any of its elements.
Turn a set closed under supremum and infimum into a sublattice.
Copy of a sublattice with a new
carrier equal to the old one. Useful to fix definitional
The top sublattice is isomorphic to the lattice.
This is the sublattice version of
The preimage of a sublattice along a lattice homomorphism.
The image of a sublattice along a monoid homomorphism is a sublattice.