First Pair Geometry Rows have fixed row

Proved

D1Bound5.firstPairGeometryRows_have_fixed_row

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

diophantine-tuplesnumber-theory

Auxiliary result firstPairGeometryRows_have_fixed_row 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.Data.List.Range
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_FirstPairGeometryData_Definitions_001
import Definitions.Def_D1Bound5_FirstPairGeometryData_Definitions_002
import Definitions.Def_D1Bound5_FirstPairGeometryFixedRows_Definitions
import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_001
import Definitions.Def_D1Bound5_OneSmallCutoffArithmetic_Definitions_002

Formal statement

section
namespace D1Bound5





set_option maxRecDepth 100000
set_option maxHeartbeats 0



















































































theorem _root_.D1Bound5.firstPairGeometryRows_have_fixed_row (g : FirstPairGeometryRow)
    (hg : g ∈ firstPairGeometryRows) :
    ∃ r ∈ oneSmallCutoffRows, FirstPairGeometryMatches g r := by sorry

end D1Bound5
end

Source

D1Bound5/FirstPairGeometryFixedRows.lean, lines 266-311, SHA-256 84225093eb3f30b90e3cc61b11e72d39cd0cb1bab3442a3d330db9c6b02d9f97. Project: https://github.com/tomislav-math/d1-bound5-lean

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