Pell CFPrefix Check pairs

Proved

D1Bound5.pellCFPrefixCheck_pairs

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

diophantine-tuplesnumber-theory

Auxiliary result pellCFPrefixCheck_pairs 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.Rat.Lemmas
import Mathlib.NumberTheory.DiophantineApproximation.Basic
import Mathlib.NumberTheory.Real.Irrational
import Mathlib.RingTheory.Coprime.Lemmas
import Mathlib.RingTheory.Int.Basic
import Mathlib.Tactic
import Definitions.Def_D1Bound5_PellCFPrefixCheck_Definitions
import Definitions.Def_D1Bound5_PellConvergentCompleteness_Definitions

Formal statement

section
namespace D1Bound5













































theorem _root_.D1Bound5.pellCFPrefixCheck_pairs {d a0 : ℤ} {N : ℕ}
    (h : pellCFPrefixCheck d a0 N = true) :
    ∀ i ≤ N, pellConvergentPair (Real.sqrt (d : ℝ)) i =
      ((pellCFAt d a0 (pellCFInit a0) i).p,
       (pellCFAt d a0 (pellCFInit a0) i).q) := by sorry





end D1Bound5
end

Source

D1Bound5/PellCFPrefixCheck.lean, lines 213-272, SHA-256 a5468d17d5b8fd8febaae9f486b606a6148827a88a3b76dca5782d036662adba. Project: https://github.com/tomislav-math/d1-bound5-lean

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