Pell CFAt mem trace

Proved

D1Bound5.pellCFAt_mem_trace

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result pellCFAt_mem_trace 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

Formal statement

section
namespace D1Bound5



























theorem _root_.D1Bound5.pellCFAt_mem_trace (d a0 : ℤ) (s : PellCFState) {n N : ℕ} (hn : n ≤ N) :
    pellCFAt d a0 s n ∈ pellCFTrace d a0 s N := by sorry























end D1Bound5
end

Source

D1Bound5/PellCFPrefixCheck.lean, lines 66-76, SHA-256 a5468d17d5b8fd8febaae9f486b606a6148827a88a3b76dca5782d036662adba. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph