Small Pair Closure 37 checked

Proved

D1Bound5.smallPairClosure_37_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairClosure_37_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_SmallPairGraphInputs37_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs37_Definitions_002

Formal statement

section
set_option autoImplicit false

namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

open PairGraphPrepared37



theorem _root_.D1Bound5.smallPairClosure_37_checked :
    pairClosureBool smallPairA_37 smallPairB_37
      (10^1100) smallPairClosure_37 = true := by sorry

end D1Bound5
end

Source

D1Bound5/SmallPairGraphClosure37.lean, lines 132-136, SHA-256 22f56e380519bc3957a3254f19fade940b347c7f1e2a204e28d8901e2f0cc0c0. Project: https://github.com/tomislav-math/d1-bound5-lean

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