Proof of `Retractions with bounded rank on the primal inputs`
groundedproofs/Lax342547Proofs/PrimalRetractions.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 primal space surjects onto the quotient by table plus keys. Choose a linear section of that surjection and subtract its lifted quotient map from the identity. The resulting retraction preserves the primal space. Its primal range lies in the intersection with table plus keys, whose dimension is at most the table-primal dimension plus the key dimension.