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Signed entry good or neg

Proved
D1Bound5.signed_entry_good_or_neg

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

diophantine-tuplesnumber-theory

One of the two integral signs satisfies both normalized bounds. The proof uses only the two possible signs of an existing root.

Preamble
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_RootMatrixSigns_Definitions

Formal statement
section
namespace D1Bound5




theorem _root_.D1Bound5.signed_entry_good_or_neg {R : Type*} [CommRing R]
    (f : R →+* ℂ) (a b r : R) (u v : ℂ)
    (hu : u^2 = f a) (hv : v^2 = f b)
    (hr : r^2 = a*b+1) (hab : 9 ≤ ‖f a * f b‖) :
    SignedEntryGood f a b u v r ∨ SignedEntryGood f a b u v (-r) := by sorry

end D1Bound5

namespace D1Bound5





end D1Bound5

namespace D1Bound5



end D1Bound5
end
Source
D1Bound5/RootMatrixSigns.lean, lines 12-31, SHA-256 ebdfe7f3d298bcbeeffe34affc4b69cd64eed73b495d78d2fa97d30c70560fcd. Project: https://github.com/tomislav-math/d1-bound5-lean

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