Small Pair Closure 31 checked

Proved

D1Bound5.smallPairClosure_31_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairClosure_31_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 Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_PairExtensionCore_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs31_Definitions

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

open PairGraphPrepared31



theorem _root_.D1Bound5.smallPairClosure_31_checked :
    pairClosureBool smallPairA_31 smallPairB_31
      (10^1100) smallPairClosure_31 = true := by sorry

end D1Bound5
end

Source

D1Bound5/SmallPairGraphClosure31.lean, lines 15-19, SHA-256 158ad2bc2984a2c5ba3dac1285f2ee71d25d8138367e6f04ba67264e3cc71dca. Project: https://github.com/tomislav-math/d1-bound5-lean

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