Prove2Me

Pair Light Prepared43 — right checked

Proved
D1Bound5.PairLightPrepared43.right_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairLightPrepared43.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_SmallPairGraphInputs43_Definitions_003
import Definitions.Def_D1Bound5_SmallPairGraphInputs43_Definitions_004
import Definitions.Def_D1Bound5_SmallPairSieve_1_3_Definitions
Formal statement
section
namespace D1Bound5.PairLightPrepared43
set_option maxRecDepth 100000
set_option maxHeartbeats 0

















theorem _root_.D1Bound5.PairLightPrepared43.right_checked :
    pairIndependentBool smallPairSieve_1_3 (pairSplitByMask smallPairLarge_43 PairGraphPrepared43.colors).2 = true := by sorry

end D1Bound5.PairLightPrepared43
end
Source
D1Bound5/SmallPairLightAssembly43.lean, lines 42-47, SHA-256 a1f93b85259f267bea1466e442343da00fa48b8f5128ef4939b965627b146f42. Project: https://github.com/tomislav-math/d1-bound5-lean

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