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Proof of `Homomorphism polynomials outside the span of a graph class`

groundedproofs/Lax461425Proofs/NonUniformClosureProof.lean · lax-461425

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.

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Description

Non-uniform closure. Fix v0v₀ and evaluate at the (padded) bi-adjacency matrices of the bipartite double covers of the filled CFI graphs Ĝ_0 and Ĝ_{δ_{v₀}}. Both evaluations agree on every homF′,Nhom_{F',N} with F′∈FF' ∈ \mathcal{F} (NU.minorLiftingeqNU.minorLifting_eq, using NU.evalhomNU.eval_hom, NU.homBippadNU.homBip_pad), hence on homSpanhomSpan, but differ on homF,Nhom_{F,N} (NU.minorLiftingltNU.minorLifting_lt).