Lax Lean Archive

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Proof of `Existence of the top fast space`

groundedproofs/Lax606786Proofs/Cocycle/FastSpace.lean · lax-606786

What this proof establishes

thm✓Lax606786.TopFastSpace

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitLab

Description

The proof of Lemma 28 of Lee (2024): the images đ“›Ïƒâˆ’nω(n)W𝓛^{(n)}_{σ^{-n}ω} W of near-optimal subspaces form a Cauchy sequence in the Grassmannian by the contraction estimate, and the limits obtained for different tolerances agree by uniqueness below the spectral gap.