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Nonempty raw frame spaces

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

proven

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    Natural Language Statement

    Theorem

    The doubled coordinate space has dimension 2(d+h)2(d+h). The plus frame is the coordinate inclusion into its first half; the minus frame has the prescribed Gram block in the first half and an identity in the second. This verifies the raw frame nonemptiness construction in §2.4.

    Concept map
    3 concepts
    100%
    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

    This concept declares 2 statements. Each proof establishes one of them relative to its assumptions.

    1 frame_nonempty proven

    2 frame_nonempty_of_card_le proven

    Lean source view on GitHub

    1import Lax342547.RawFrames
    2
    3/-!
    4---
    5title: Nonempty raw frame spaces
    6type: theorem
    7---
    8The doubled coordinate space has dimension 2(d+h)2(d+h). The plus frame is
    9the coordinate inclusion into its first half; the minus frame has the
    10prescribed Gram block in the first half and an identity in the second.
    11This verifies the raw frame nonemptiness construction in §2.4.
    12-/
    13
    14namespace Lax342547.FrameExistence
    15
    16open Lax342547.MomentSpace Lax342547.RawFrames
    17
    18axiom frame_nonempty {B H : Type} [Fintype B] [Fintype H] (E : Matrix B B Binary) :
    19 Nonempty (Frame B H ((B ⊕ H) ⊕ (B ⊕ H)) E)
    20
    21axiom frame_nonempty_of_card_le {B H : Type} [Fintype B] [Fintype H] {N : Type} [Fintype N]
    22 (E : Matrix B B Binary) (hN : 2 * (Fintype.card B + Fintype.card H) ≤ Fintype.card N) :
    23 Nonempty (Frame B H N E)
    24
    25end Lax342547.FrameExistence
    26
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