Pell Matching Check no three
ProvedD1Bound5.pellMatchingCheck_no_threediophantine-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