Pair Negative Integer Obstruction Bool sound

Proved

D1Bound5.pairNegativeIntegerObstructionBool_sound

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

diophantine-tuplesnumber-theory

A successful negative-integer obstruction excludes every square root. In particular, rejection cannot discard a genuine zero root.

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_PairNegativeIntegerObstruction_Definitions

Formal statement

section
namespace D1Bound5










theorem _root_.D1Bound5.pairNegativeIntegerObstructionBool_sound {tau nu : ℤ}
    (z : QuadInt tau nu) (h : pairNegativeIntegerObstructionBool z = true) :
    ¬ ∃ r : QuadInt tau nu, r * r = z := by sorry

end D1Bound5
end

Source

D1Bound5/PairNegativeIntegerObstruction.lean, lines 52-71, SHA-256 099be79d73801fcfb76bdc30024dc74b43ab6bdb2e935fcd75d8e115af902e02. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph