Pair Light Prepared11 — right checked

Proved

D1Bound5.PairLightPrepared11.right_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairLightPrepared11.right_checked 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_SmallPairGraphInputs11_Definitions_002
import Definitions.Def_D1Bound5_SmallPairSieve_0_1_Definitions

Formal statement

section
namespace D1Bound5.PairLightPrepared11
set_option maxRecDepth 100000
set_option maxHeartbeats 0

















theorem _root_.D1Bound5.PairLightPrepared11.right_checked :
    pairIndependentBool smallPairSieve_0_1 (pairSplitByMask smallPairLarge_11 PairGraphPrepared11.colors).2 = true := by sorry

end D1Bound5.PairLightPrepared11
end

Source

D1Bound5/SmallPairLightAssembly11.lean, lines 42-47, SHA-256 e7005de29879d0c1f756e05b4ab6bb8008ac22743be8e6172cf5d11c233a7754. Project: https://github.com/tomislav-math/d1-bound5-lean

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