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Dimensions of projected mode spaces

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

proven

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    Natural Language Statement

    Lemma

    The dimension of an actual mode space in an exposed quotient equals its span dimension increase.

    Concept map
    4 concepts
    100%
    Proven claimThis conceptRelated conceptA → B: B builds on ADescendants are omitted for concepts with more than 10 descendants.
    Evidence

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    1import Lax342547.GreedySpans
    2
    3/-!
    4---
    5title: Dimensions of projected mode spaces
    6type: lemma
    7---
    8The dimension of an actual mode space in an exposed quotient equals its span dimension increase.
    9-/
    10
    11namespace Lax342547.ProjectedSpans
    12
    13open Lax342547.GreedySpans
    14open scoped BigOperators
    15
    16axiom projected_dimension_gain {K V : Type} [Field K] [AddCommGroup V] [Module K V]
    17 [FiniteDimensional K V] (W S : Submodule K V) :
    18 (Module.finrank K (S.map W.mkQ) : ℝ) = gain W S
    19
    20end Lax342547.ProjectedSpans
    21
    Show Proof
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