Both halves of the S↔F correspondence in one instance — the convenience an implementor reaches for when supplying project and embed together. A given Basis satisfies both a Project and an Embed requirement.
S
F
project
embed
given Basis
Project
Embed
Glue one layer: rebuild an S node from an F of already-built children.
Peel one layer: expose S's immediate children as F's recursive slots.