Proof of `Sparse residual contractions belong to the actual primal pins` (3rd statement)
groundedproofs/Lax342547Proofs/PrimalContractions.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
The generic quotient test puts the individual contraction in the actual barred space. Its own endpoint has the given unselected sparse support, and the other endpoint is zero. Strong exclusion and protected/private complementarity therefore put it in the actual pinned primal subspace.