Pair Light Pilot34 — left Vertices eq

Proved

D1Bound5.PairLightPilot34.leftVertices_eq

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

The independent literal coordinate list is the exact original left class, including its ordering and full coverage. This linear check is separate from the expensive all-pairs computation in the arithmetic-only module.

Preamble

import Init
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.GCD
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Data.List.Basic
import Mathlib.Data.ZMod.Basic
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_PairBipartiteCheck_Definitions
import Definitions.Def_D1Bound5_PairLightArithmeticBridge_Definitions
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs34_Definitions_003
import Definitions.Def_D1Bound5_SmallPairGraphInputs34_Definitions_004
import Definitions.Def_D1Bound5_SmallPairLightData34_Definitions_001

Formal statement

section
namespace D1Bound5.PairLightPilot34
set_option maxRecDepth 100000
set_option maxHeartbeats 0




theorem _root_.D1Bound5.PairLightPilot34.leftVertices_eq :
    leftVertices =
      (pairSplitByMask smallPairLarge_34 PairGraphPrepared34.colors).1.map
        pairLightCoordinates := by sorry







end D1Bound5.PairLightPilot34
end

Source

D1Bound5/SmallPairLightAssembly34.lean, lines 14-21, SHA-256 6a0195e9356ce602881ba23270aeac451918eed77e30e3bdb8e3b35be0fb5140. Project: https://github.com/tomislav-math/d1-bound5-lean

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