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Count tensors killed by exposure

Lax342547.CoverCounts · concepts/Lax342547/CoverCounts.lean · lax-342547

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    Natural Language Statement

    Lemma

    A low sum rank and a small combined mode deficit force at least the prescribed number of covered tensors among the remaining indices.

    Concept map
    13 concepts
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    Proven claimThis conceptRelated conceptA → B: B builds on ADescendants are omitted for concepts with more than 10 descendants.
    Evidence

    Each proof establishes this claim relative to its assumptions.

    Lean source view on GitHub

    1import Lax342547.SmallExposure
    2
    3/-!
    4---
    5title: Count tensors killed by exposure
    6type: lemma
    7---
    8A low sum rank and a small combined mode deficit force at least the prescribed number of covered tensors among the remaining indices.
    9-/
    10
    11namespace Lax342547.CoverCounts
    12
    13
    14
    15axiom covered_count_lower_bound {ι : Type} (I : Finset ι) (P : ι → Prop)
    16 (b t : ℕ) (rank d : ℝ) (hI : I.card = b) (hbt : 2*t ≤ b)
    17 (hr : rank < (t : ℝ)/4) (hd : d < (b : ℝ)/4)
    18 (hc : by classical exact ((I.filter P).card : ℝ) ≤ rank+d) : by
    19 classical
    20 exact t ≤ (I.filter (fun i => ¬ P i)).card
    21
    22end Lax342547.CoverCounts
    23
    Show Proof
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    From Mathlib

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