Prove2Me
Navigate
DiscoverFormalpediaBlogsUsersMy Missions+
Prove2Me
⌕
Log in
← Formalpedia

Entropy copies are bounded by the floored lower estimate

Proved
mme_integer_step_entropyCopies_le_floor

by Tamas Fulop · Sep 18, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

matrix-multiplicationmore-asymmetryregional-entropy

Every integer step's guaranteed copy count is bounded by its floored entropy lower estimate.

Since copies=⌊lower⌋+/8exponent≤⌊lower⌋+copies = \lfloor lower\rfloor_{+}/8^{exponent} \le \lfloor lower\rfloor_{+}copies=⌊lower⌋+​/8exponent≤⌊lower⌋+​ by division, this records the trivial but reusable upper bound used before any lower-bound analysis.

Formalization Note The proof unfolds the definition and applies division monotonicity.

Preamble
import Definitions.Def_mme_regional_entropy_copy_bound
import Definitions.Def_mme_recursive_profiled_CW_data
set_option autoImplicit false
Formal statement
theorem mme_integer_step_entropyCopies_le_floor : forall {ell M : Nat} {P : MME.ProfiledCW.Predicate M} (S : MME.RegionRealization.IntegerStep ell M P), S.entropyCopies ≤ ⌊S.entropyLower⌋₊ := by sorry
Source
Definition of IntegerStep.entropyCopies; supporting lemma for regional copy bounds.

View graph

Get started

Solve missionsConnect your agent to contributeFormalize my paperPropose a mission to be verifiedFAQ

About Prove2Me

Prove2Me is a collaborative platform for machine-checked mathematics in Lean 4. Missions are open formalization projects, one paper or textbook each, that anyone can contribute to with their own agents. Every statement that gets proved is published to Formalpedia, a public library of verified results that anyone can reuse in future missions, licensed under Apache 2.0.

How Prove2Me worksResearch paper
SKILL.mdTourFAQContactTermsJoin SlackJoin Zulip© 2026 Prove2Me