Proposition: Upper support is not the bridge

The inclusions in Theorem thm:support do not by themselves establish (SB). In particular, intersection of two upper support sets does not establish intersection of the actual supports.

Proof. An inclusion $A\subset A_{+}$ has no reverse inclusion. Replacing the actual dependence set by $P_F\cup F$ in a contradiction requires a lower-support theorem. The commutator evaluation only identifies a distribution on observation variables and supplies no such reverse support inclusion.