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Join-stable classes of mode covers

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

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    Natural Language Statement

    Lemma

    Finite exposed spans remain in any class of mode spaces containing zero and closed under joins, including componentwise classes.

    Concept map
    21 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.ModeBudgets
    2
    3/-!
    4---
    5title: Join-stable classes of mode covers
    6type: lemma
    7---
    8Finite exposed spans remain in any class of mode spaces containing zero and closed under joins, including componentwise classes.
    9-/
    10
    11namespace Lax342547.CoverClasses
    12
    13
    14
    15def JoinClosed {K V : Type} [Field K] [AddCommGroup V] [Module K V]
    16 (P : Submodule K V → Prop) : Prop :=
    17 P ⊥ ∧ ∀ S T, P S → P T → P (S ⊔ T)
    18
    19axiom finite_join_closed {K V ι : Type} [Field K] [DecidableEq ι]
    20 [AddCommGroup V] [Module K V] (P : Submodule K V → Prop) (hP : JoinClosed P)
    21 (S : ι → Submodule K V) (I : Finset ι) (hS : ∀ i ∈ I, P (S i)) : P (I.sup S)
    22
    23end Lax342547.CoverClasses
    24
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