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Append fresh directions to the independent key tuple

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

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    Natural Language Statement

    Lemma

    Key directions independent modulo old pins and additional directions independent modulo pins plus keys form a joint tuple independent modulo old pins. Its full rank is available to the leaf image cap.

    Concept map
    5 concepts; 8 descendants hidden
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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A
    Evidence

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    1import Lax342547.LeafImages
    2
    3/-!
    4---
    5title: Append fresh directions to the independent key tuple
    6type: lemma
    7---
    8Key directions independent modulo old pins and additional directions independent modulo pins plus keys form a joint tuple independent modulo old pins. Its full rank is available to the leaf image cap.
    9-/
    10
    11namespace Lax342547.JointDirections
    12
    13open Lax342547.MomentSpace
    14
    15axiom appended_quotient_injective {U V W : Type}
    16 [AddCommGroup U] [Module Binary U] [AddCommGroup V] [Module Binary V]
    17 [AddCommGroup W] [Module Binary W]
    18 (P : Submodule Binary W) (keys : U →ₗ[Binary] W) (fresh : V →ₗ[Binary] W)
    19 (hkeys : Function.Injective (P.mkQ.comp keys))
    20 (hfresh : Function.Injective ((P ⊔ LinearMap.range keys).mkQ.comp fresh)) :
    21 Function.Injective (P.mkQ.comp (keys.coprod fresh))
    22
    23end Lax342547.JointDirections
    24
    Show Proof
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