Pair Light Prepared39 — right Vertices eq

Proved

D1Bound5.PairLightPrepared39.rightVertices_eq

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

diophantine-tuplesnumber-theory

Auxiliary result PairLightPrepared39.rightVertices_eq in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

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_SmallPairGraphInputs39_Definitions_003
import Definitions.Def_D1Bound5_SmallPairGraphInputs39_Definitions_004
import Definitions.Def_D1Bound5_SmallPairLightData39RightVertices_Definitions

Formal statement

section
namespace D1Bound5.PairLightPrepared39
set_option maxRecDepth 100000
set_option maxHeartbeats 0











theorem _root_.D1Bound5.PairLightPrepared39.rightVertices_eq :
    rightVertices = (pairSplitByMask smallPairLarge_39 PairGraphPrepared39.colors).2.map pairLightCoordinates := by sorry







end D1Bound5.PairLightPrepared39
end

Source

D1Bound5/SmallPairLightAssembly39.lean, lines 31-33, SHA-256 ae9b1a9efdeed04c72a03b7178601eaf72f5411bc35132f12586e6972c401a38. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph