One Small Cutoff Rows finite N3Ab Fixed Bound
ProvedD1Bound5.oneSmallCutoffRows_finiteN3AbFixedBounddiophantine-tuplesnumber-theory
The actual printed fixed-triple rows have verified N3 coefficients on the ab anchor pair, evaluated before taking norms.
Preamble
import Lean.Elab.Tactic.Omega import Mathlib.Algebra.BigOperators.Fin import Mathlib.Algebra.Group.Int.Units import Mathlib.Algebra.Polynomial.Monic import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Algebra.Squarefree.Basic import Mathlib.Analysis.Complex.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Analysis.Complex.Polynomial.Basic import Mathlib.Analysis.Normed.Ring.Basic import Mathlib.Data.Fin.Tuple.Sort import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Fintype.EquivFin import Mathlib.Data.Int.GCD import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.Data.List.Range import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.LinearAlgebra.Matrix.Determinant.Basic import Mathlib.LinearAlgebra.Matrix.NonsingularInverse import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.Convert import Mathlib.Tactic.FieldSimp import Mathlib.Tactic.FinCases import Mathlib.Tactic.GCongr import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.NormNum import Mathlib.Tactic.Positivity import Mathlib.Tactic.Ring import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_FiniteN3FixedHeight_Definitions import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_001 import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_002 import Definitions.Def_D1Bound5_OneSmallRows_Definitions
Formal statement
section
namespace D1Bound5
open QuadInt
/- Exact evaluated N3 coefficient certificates on the ab anchors. -/
set_option maxRecDepth 100000
set_option maxHeartbeats 0
theorem _root_.D1Bound5.oneSmallCutoffRows_finiteN3AbFixedBound (r : OneSmallCutoffRow)
(hr : r ∈ oneSmallCutoffRows) :
∃ w : Fin 3 → Fin 2 → Fin 4 → ℚ,
FiniteN3FixedBound r.triple.anchorA r.triple.anchorB r.Mn w := by sorry
end D1Bound5
end
Source
D1Bound5/OneSmallN3AbFixedArithmetic.lean, lines 524-588, SHA-256 c4e17b5c41fbd6a8ab71c64b13d026787c2d0b699f64a6314bd1bca495ab8385. Project: https://github.com/tomislav-math/d1-bound5-lean