Small Pair No Triangle 37 checked

Proved

D1Bound5.smallPairNoTriangle_37_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairNoTriangle_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.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_SmallPairGraphCheck_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs37_Definitions_003
import Definitions.Def_D1Bound5_SmallPairSieve_1_2_Definitions

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0



theorem _root_.D1Bound5.smallPairNoTriangle_37_checked :
    pairGraphTriangleFreeBool smallPairSieve_1_2 smallPairLarge_37 = true := by sorry

end D1Bound5
end

Source

D1Bound5/SmallPairGraphTriangle37.lean, lines 13-17, SHA-256 83c52ca82dffbb6e620c5ebbfe9a207409c223b81ecc80fd1de8bd0e8709fa5c. Project: https://github.com/tomislav-math/d1-bound5-lean

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