Pell Convergent Pair pos

Proved

D1Bound5.pellConvergentPair_pos

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

diophantine-tuplesnumber-theory

Auxiliary result pellConvergentPair_pos 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_PellConvergentCompleteness_Definitions

Formal statement

section
namespace D1Bound5







theorem _root_.D1Bound5.pellConvergentPair_pos {x : ℝ} (hx : Irrational x) (hx1 : 1 < x)
    (n : ℕ) :
    0 < (pellConvergentPair x n).1 ∧ 0 < (pellConvergentPair x n).2 := by sorry















end D1Bound5
end

Source

D1Bound5/PellConvergentCompleteness.lean, lines 28-42, SHA-256 c43074daa228222fbe1ca798070304a8be11d05710c382ec9a9e73d7799c8266. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph