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An actual common point with diagonal tester one

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

proven

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    Natural Language Statement

    Lemma

    A shared-only point is allowed at every tag and has tester value one whenever the tester has a pair; it removes the common diagonal predictor coefficient.

    Concept map
    11 concepts; 2 descendants hidden
    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 shared_point_allowed proven

    2 shared_point_eta_one proven

    Lean source view on GitHub

    1import Lax342547.CommonAtoms
    2import Lax342547.ConcreteGeometry
    3
    4/-!
    5---
    6title: An actual common point with diagonal tester one
    7type: lemma
    8---
    9A shared-only point is allowed at every tag and has tester value one whenever the tester has a pair; it removes the common diagonal predictor coefficient.
    10-/
    11
    12namespace Lax342547.SharedTesterPoint
    13
    14open Lax342547.MomentSpace Lax342547.Atoms Lax342547.TagGeometry Lax342547.ConcreteGeometry
    15open scoped BigOperators
    16
    17def sharedTesterPoint {k n : ℕ} : Base k n → Binary
    18 | Sum.inl _ => 0
    19 | Sum.inr (q,i) => if q = 0 ∧ i.val < 2 then 1 else 0
    20
    21axiom shared_point_allowed {k n : ℕ} (l : Tag k) :
    22 ∀ i,i ∉ allowedBase k n l → sharedTesterPoint (k := k) (n := n) i = 0
    23
    24axiom shared_point_eta_one {k n b degree r : ℕ} (hr : 2*r ≤ n) (hr0 : 0 < r) (s : Fin b → Binary) :
    25 eta (k := k) (b := b) (degree := degree) hr (pointMoment selectorEval s sharedTesterPoint) = 1
    26
    27end Lax342547.SharedTesterPoint
    28
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    From Mathlib

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