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Pell Matching Check no three

Proved
D1Bound5.pellMatchingCheck_no_three

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

diophantine-tuplesnumber-theory

The graph certificate proves a matching, a stronger property than the triangle exclusion needed by the article. No huge integer square roots are trusted or executed by this checker.

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.pellMatchingCheck_no_three (d : ℤ) (hd : 0 < d)
    (ms : List PellSquareMasks) (hvalid : ∀ m ∈ ms, m.Valid d)
    (xs : List ℤ) (wss : List (List (ℕ × ℕ)))
    (hcheck : pellMatchingCheck ms xs wss = true)
    (hlarge : ∀ x ∈ xs, 2 ≤ x)
    (a b c : ℤ) (ha : PellSignedMember xs a) (hb : PellSignedMember xs b)
    (hc : PellSignedMember xs c) (hab : a ≠ b) (hac : a ≠ c) (hbc : b ≠ c)
    (hsab : PellIntegerSquare d (a*b+1))
    (hsac : PellIntegerSquare d (a*c+1)) : False := by sorry







end D1Bound5
end
Source
D1Bound5/PellMatchingCheck.lean, lines 170-191, SHA-256 c1c0284d3cb9fe91ae3599a7d1d28cf05b2201c8cbaef193b20c1b2b5f4ccfa0. Project: https://github.com/tomislav-math/d1-bound5-lean

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