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Exposed mode dimension budget

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

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    Natural Language Statement

    Lemma

    The span of any subset of rank-bounded mode spaces has dimension at most the single-space budget times the full sample size.

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

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    Lean source view on GitHub

    1import Lax342547.ListDeficits
    2
    3/-!
    4---
    5title: Exposed mode dimension budget
    6type: lemma
    7---
    8The span of any subset of rank-bounded mode spaces has dimension at most the single-space budget times the full sample size.
    9-/
    10
    11namespace Lax342547.ModeBudgets
    12
    13open scoped BigOperators
    14
    15axiom mode_span_budget {K V ι : Type} [Field K] [Fintype ι] [DecidableEq ι]
    16 [AddCommGroup V] [Module K V] [FiniteDimensional K V]
    17 (S : ι → Submodule K V) (r : ℝ) (hr : 0 ≤ r)
    18 (hS : ∀ i, (Module.finrank K (S i) : ℝ) ≤ r) (I : Finset ι) :
    19 (Module.finrank K (I.sup S : Submodule K V) : ℝ) ≤ r*Fintype.card ι
    20
    21end Lax342547.ModeBudgets
    22
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    From Mathlib

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