Prove2Me

Pair Graph Prepared48 — indexed coverage checked

Proved
D1Bound5.PairGraphPrepared48.indexed_coverage_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairGraphPrepared48.indexed_coverage_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_Coordinates_Definitions
import Definitions.Def_D1Bound5_PairClosureWitness_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs48_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData48_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData48_Definitions_003
Formal statement
section
namespace D1Bound5.PairGraphPrepared48
set_option autoImplicit false
set_option maxRecDepth 100000
set_option maxHeartbeats 0

theorem _root_.D1Bound5.PairGraphPrepared48.indexed_coverage_checked :
    decide (anchorRoot * anchorRoot = smallPairA_48 * smallPairB_48 + 1 ∧
      witnesses.map PairRootWitness.vertex = smallPairClosure_48) = true := by sorry

end D1Bound5.PairGraphPrepared48
end
Source
D1Bound5/SmallPairGraphClosure48Coverage.lean, lines 9-29, SHA-256 cf547bf730123feb39f681d5a24fa79be0441f9efa99e2fe1672ec6e23f4d1e6. Project: https://github.com/tomislav-math/d1-bound5-lean

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