a modern C++ library for the manipulation of Boolean functions

4.2.5 Entailed, disentailed and equivalent variables
Operations that search and eliminate entailed, disentailed and equivalent variables are
pretty straightforward, provided that the internal representation is already normalized:
that’s why these operations start with a call to the normalization algorithm. The
operations do nothing more than returning and/or clearing the corresponding part of the
internal representation, with the only exception coming from the fact that entailed and
disentailed variables are all equivalent to each other.
4.2.6 Projections and variable renaming
Operations that rename variables can be easily implemented by renaming all components of
the internal representation separately. Although renaming with respect to an equivalence
relation may denormalize the internal representation, shift renaming of course does not.
For projections, the main problem is that we cannot project all components separately,
as it is proven that this may alter the semantics for the case where we project away
variables that appear in more than one component. Note that this case may also occur in
a normalized representation whenever we project away a leader for L that also labels a
node in n. Our solution is to start by normalizing the representation, then replacing each
occurence of all of these leaders l in n with the minimum variable that is equivalent to l
in L and is not going to be projected away. Afterwards we can project on each component
separately.
4.2 Algorithms with composite representations 42