Seed Root Disk 1 3 eq

Proved

D1Bound5.seedRootDisk_1_3_eq

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

diophantine-tuplesnumber-theory

Auxiliary result seedRootDisk_1_3_eq 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.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_DiskEnumeration_Definitions
import Definitions.Def_D1Bound5_TwoSmallSeedDisks_Definitions

Formal statement

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 8000000








theorem _root_.D1Bound5.seedRootDisk_1_3_eq : disk 1 3 132 = seedRootDisk_1_3.toFinset := by sorry













end D1Bound5
end

Source

D1Bound5/TwoSmallSeedDisks.lean, lines 628-630, SHA-256 510bd0817de84470204906e29a31775f06a975fc27f5a457bad4d81a12b411eb. Project: https://github.com/tomislav-math/d1-bound5-lean

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