First Pair classified 1 7

Proved

D1Bound5.firstPair_classified_1_7

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

diophantine-tuplesnumber-theory

Auxiliary result firstPair_classified_1_7 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_FirstPairData_Definitions
import Definitions.Def_D1Bound5_OneSmallFiniteCheck_Definitions

Formal statement

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 12000000







































































































































theorem _root_.D1Bound5.firstPair_classified_1_7
    (a b : QuadInt 1 7) (hnorm : FirstPairNorms a b) (hroot : ∃ q, q*q = a*b+1) :
    (a = 1 ∧ b = 3) ∨ (a = -1 ∧ b = -3) ∨ firstPairCoordinates a b ∈ firstPairTable 1 7 := by sorry







end D1Bound5
end

Source

D1Bound5/FirstPairData.lean, lines 309-314, SHA-256 7313a343cb5732f1d2357b582d7fff94832a88101669f0b066de7d6ee8e698a5. Project: https://github.com/tomislav-math/d1-bound5-lean

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