First Pair Geometry Rows valid

Proved

D1Bound5.firstPairGeometryRows_valid

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

diophantine-tuplesnumber-theory

Auxiliary result firstPairGeometryRows_valid 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.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_FirstPairGeometryData_Definitions_001
import Definitions.Def_D1Bound5_FirstPairGeometryData_Definitions_002

Formal statement

section
namespace D1Bound5
open QuadInt



namespace FirstPairGeometryRow






























end FirstPairGeometryRow

set_option maxHeartbeats 0
set_option maxRecDepth 100000







































































































































































theorem _root_.D1Bound5.firstPairGeometryRows_valid (r : FirstPairGeometryRow)
    (hr : r ∈ firstPairGeometryRows) : r.Valid := by sorry























end D1Bound5
end

Source

D1Bound5/FirstPairGeometryData.lean, lines 347-391, SHA-256 ca79ea3d5261caa9f78a67579ed8bf7ee86ad2bdfe411217ba297b1a793cea9a. Project: https://github.com/tomislav-math/d1-bound5-lean

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