First Pair Table 0 5 orbits

Proved

D1Bound5.firstPairTable_0_5_orbits

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

diophantine-tuplesnumber-theory

Auxiliary result firstPairTable_0_5_orbits 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

Formal statement

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 12000000















































theorem _root_.D1Bound5.firstPairTable_0_5_orbits :
    firstPairs_0_5.toFinset = firstPairRepresentatives_0_5.biUnion (firstPairOrbit 0) := by sorry































































































end D1Bound5
end

Source

D1Bound5/FirstPairData.lean, lines 98-100, SHA-256 7313a343cb5732f1d2357b582d7fff94832a88101669f0b066de7d6ee8e698a5. Project: https://github.com/tomislav-math/d1-bound5-lean

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