Pell Pair Checks sound

Proved

D1Bound5.pellPairChecks_sound

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

diophantine-tuplesnumber-theory

Auxiliary result pellPairChecks_sound 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.Data.List.Defs
import Mathlib.Data.ZMod.Basic
import Mathlib.Tactic
import Definitions.Def_D1Bound5_PellMatchingCheck_Definitions

Formal statement

section
namespace D1Bound5

























theorem _root_.D1Bound5.pellPairChecks_sound (d : ℤ) (ms : List PellSquareMasks)
    (hvalid : ∀ m ∈ ms, m.Valid d) (x : ℤ) (ys : List ℤ)
    (ws : List (ℕ × ℕ)) (hcheck : pellPairChecks ms x ys ws = true)
    (y : ℤ) (hy : y ∈ ys) :
    (¬∃ r : ℤ, r*r = x*y+1) ∧ (¬∃ r : ℤ, d*r*r = x*y-1) := by sorry



















end D1Bound5
end

Source

D1Bound5/PellMatchingCheck.lean, lines 81-104, SHA-256 c1c0284d3cb9fe91ae3599a7d1d28cf05b2201c8cbaef193b20c1b2b5f4ccfa0. Project: https://github.com/tomislav-math/d1-bound5-lean

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