Proof of `A small Fourier decoding set independent of side conditions` (2nd statement)
groundedproofs/Lax253009Proofs/FourierDecoding.lean · lax-253009
What this proof establishes
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
A support meeting the positive threshold and containing a point is nonempty, so its projected coefficient cannot vanish. The projection formula forces the support to lie in U and identifies its coefficient with the original one.