Proof of `Extracting fresh label coefficients through pin quotients` (2nd statement)
groundedproofs/Lax342547Proofs/QuotientExtractors.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
On the finite label-coefficient space, a sum lying in the pin has zero coefficient at the fresh label. Factor its coordinate projection through the pin quotient and evaluate it on coefficient vectors supported at one label.