Small Pair Closure 8 checked

Proved

D1Bound5.smallPairClosure_8_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairClosure_8_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.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_PairExtensionCore_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs8_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs8_Definitions_002

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

open PairGraphPrepared8



theorem _root_.D1Bound5.smallPairClosure_8_checked :
    pairClosureBool smallPairA_8 smallPairB_8
      (10^1100) smallPairClosure_8 = true := by sorry

end D1Bound5
end

Source

D1Bound5/SmallPairGraphClosure8.lean, lines 13-17, SHA-256 9b2db0faad4ae31d91972cf93dac590b99b2eca9b9aa70b6bb9c8f9adc876200. Project: https://github.com/tomislav-math/d1-bound5-lean

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