Pair Graph Prepared32 — all trace zero checked

Proved

D1Bound5.PairGraphPrepared32.all_trace_zero_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairGraphPrepared32.all_trace_zero_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_PairGraphNoThreeTransfer_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs32_Definitions

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

theorem _root_.D1Bound5.PairGraphPrepared32.all_trace_zero_checked :
    pairAllTraceZeroBool smallPairLarge_32 = true := by sorry



end D1Bound5
end

Source

D1Bound5/SmallPairGraphTriangle32.lean, lines 9-11, SHA-256 690f85bc066eb0817f5e7eac1fdc67eaa4dffaac85c1fea15bfddc8b4808010a. Project: https://github.com/tomislav-math/d1-bound5-lean

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