Finite A3 height five regions

Proved

D1Bound5.finiteA3_height_five_regions

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Actual ratio-refined height for the constructed finite family. The statement supplies no coefficient or height certificate: the integer rows and all five rational table margins are proved above.

Preamble

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Tactic
import Mathlib.Tactic.Convert
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteA3Matrix_Definitions
import Definitions.Def_D1Bound5_FiniteA3RatioHeight_Definitions
import Definitions.Def_D1Bound5_FiniteHomogeneousRatio_Definitions

Formal statement

section
noncomputable section

namespace D1Bound5












theorem _root_.D1Bound5.finiteA3_height_five_regions (region : Fin 5) (x y c : ℂ)
    (hy : y ≠ 0) (hxy : ‖x‖ ≤ fiveRegionAnchorRatio region*‖y‖)
    (hYC : 1000 ≤ ‖y‖*‖c‖) (i : Fin 3) :
    (101/100 : ℝ)*(‖finiteA3Left x y c i‖+‖finiteA3Right x y c i‖) <
      fiveRegionA3Height region*‖y‖^6*‖c‖^3 := by sorry

end D1Bound5
end

Source

D1Bound5/FiniteA3RatioHeight.lean, lines 62-86, SHA-256 747d84efb3a599bfd5fb9dfc2190b17d3fd8f676687d8e8b401785ccf8d1c7d7. Project: https://github.com/tomislav-math/d1-bound5-lean

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