Lax Lean Archive

Draft — mutable and not usable as a dependency; its citation marks the draft state.

Proof of `Sparse graph thinning lemma`

groundedproofs/Lax54Proofs/AveragingLemma.lean · lax-54

What this proof establishes

no assumptions

thm✓Lax54.AveragingLemma

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 GitHub

Description

Proof of Lemma 4.2. Average the ordered edge count over all (2m−1)(2m-1)-element subsets, select a subset no denser than the ambient graph, and retain mm vertices whose degrees do not exceed the stated bound.