Coordinate Square Sieve Valid cons

Proved

D1Bound5.coordinateSquareSieveValid_cons

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

diophantine-tuplesnumber-theory

Auxiliary result coordinateSquareSieveValid_cons 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.Data.Int.Sqrt
import Mathlib.Data.ZMod.Basic
import Mathlib.Tactic.Linarith
import Definitions.Def_D1Bound5_FastSquareTest_Definitions

Formal statement

section
namespace D1Bound5







end D1Bound5

namespace D1Bound5



theorem _root_.D1Bound5.coordinateSquareSieveValid_cons {tau nu : ℤ} {k mask : ℕ}
    {tail : List (ℕ × ℕ)}
    (hm : CoordinateSquareMaskValid tau nu k mask)
    (ht : CoordinateSquareSieveValid tau nu tail) :
    CoordinateSquareSieveValid tau nu ((k,mask)::tail) := by sorry

end D1Bound5
end

Source

D1Bound5/CoordinateSquareMaskCheck.lean, lines 61-70, SHA-256 d2d8bc2ee22d2527d31449ebcfb799b981fd548c07c5db168946e1208c6d24cc. Project: https://github.com/tomislav-math/d1-bound5-lean

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