Proof of `Sparse unselected primal vectors in barred spaces lie in the pins` (3rd statement)
groundedproofs/Lax342547Proofs/BarredElimination.lean · lax-342547
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Project a barred decomposition onto each primal endpoint. Private channels project to zero, and unselected sparse supports force both projected key vectors to vanish. Keys have no channels, hence the nominal key vector is zero. Protected/private complementarity then reduces the remaining decomposition to a pin vector.