Quad Int — floor Obstruction Bool sound
ProvedD1Bound5.QuadInt.floorObstructionBool_sounddiophantine-tuplesnumber-theory
Soundness of the inexpensive floor-witness checker. It uses the accepted rational-square classification and multiplicativity of norm; no candidate square root is computed.
Preamble
import Mathlib.Algebra.Order.Ring.Abs import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Data.Int.Sqrt import Mathlib.Tactic.Linarith import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_QuadSquareFloorObstruction_Definitions
Formal statement
section
namespace D1Bound5
namespace QuadInt
theorem _root_.D1Bound5.QuadInt.floorObstructionBool_sound {tau nu : ℤ}
(hd : 0 < discriminant tau nu) {z : QuadInt tau nu} {k : ℕ}
(h : floorObstructionBool z k = true) :
¬ ∃ r : QuadInt tau nu, r * r = z := by sorry
end QuadInt
end D1Bound5
end
Source
D1Bound5/QuadSquareFloorObstruction.lean, lines 103-149, SHA-256 189bc6919f96623fb014a3f2f03e165069f8dce0da25caec94ef0406cc2c9b3e. Project: https://github.com/tomislav-math/d1-bound5-lean