Corollary: Influence is contained in scheduled ancestry

For the device class of Section sec:onelayer, an intervention localized in a region disjoint from the initial ancestor region cannot change the terminal unconditioned law. Hence

for the declared operational interventions. The inclusion can be strict.

Proof. Lemma lem:devicesupport makes the exterior device fix the ancestor algebra, and Theorem thm:ancestry places the terminal pullback there. Apply Theorem thm:nosignalling. The constant report in Example ex:constant supplies strictness.