Pair Light Prepared4 — right checked

Proved

D1Bound5.PairLightPrepared4.right_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairLightPrepared4.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_SmallPairGraphInputs4_Definitions_003
import Definitions.Def_D1Bound5_SmallPairGraphInputs4_Definitions_004
import Definitions.Def_D1Bound5_SmallPairSieve_0_1_Definitions

Formal statement

section
namespace D1Bound5.PairLightPrepared4
set_option maxRecDepth 100000
set_option maxHeartbeats 0

















theorem _root_.D1Bound5.PairLightPrepared4.right_checked :
    pairIndependentBool smallPairSieve_0_1 (pairSplitByMask smallPairLarge_4 PairGraphPrepared4.colors).2 = true := by sorry

end D1Bound5.PairLightPrepared4
end

Source

D1Bound5/SmallPairLightAssembly4.lean, lines 42-47, SHA-256 a33d4d40649da2331bd8a9202b6f96f06e58f1b224932a9a23787556c880875f. Project: https://github.com/tomislav-math/d1-bound5-lean

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