Proof of `Sparse residual contractions belong to the actual primal pins` (4th 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 sparse contraction argument works in either sign. The quotient test places it in the indicated barred space; sparse key elimination and the same-sign protected/private complement put it in the actual pin.