Small Pair Closure 27 checked

Proved

D1Bound5.smallPairClosure_27_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairClosure_27_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_SmallPairGraphInputs27_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs27_Definitions_002

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

open PairGraphPrepared27



theorem _root_.D1Bound5.smallPairClosure_27_checked :
    pairClosureBool smallPairA_27 smallPairB_27
      (10^1100) smallPairClosure_27 = true := by sorry

end D1Bound5
end

Source

D1Bound5/SmallPairGraphClosure27.lean, lines 15-19, SHA-256 d077587b50fdf4bae44e9ac3733a891d809f3bd20c8ce63e05c8cfa6313203f6. Project: https://github.com/tomislav-math/d1-bound5-lean

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