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Quad Int — root Candidate complete

Proved
D1Bound5.QuadInt.rootCandidate_complete

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

diophantine-tuplesnumber-theory

Completeness of the exact candidate, for every positive-discriminant coordinate ring and arbitrary input size. No nonzero-root assumption occurs.

Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Data.Int.Sqrt
import Mathlib.Tactic.Linarith
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_SquareTest_Definitions

Formal statement
section
namespace D1Bound5.QuadInt

variable {tau nu : ℤ}












theorem _root_.D1Bound5.QuadInt.rootCandidate_complete (hd : 0 < discriminant tau nu)
    {z : QuadInt tau nu} (hz : ∃ r, r*r = z) : rootCandidate z*rootCandidate z = z := by sorry













end D1Bound5.QuadInt
end
Source
D1Bound5/SquareTest.lean, lines 66-106, SHA-256 adcc13a33378056841f44d21785e69909232e4def68eb73ca742e5a49ce15ac3. Project: https://github.com/tomislav-math/d1-bound5-lean

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