Finite eta reciprocal lt

Proved

D1Bound5.finite_eta_reciprocal_lt

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

diophantine-tuplesnumber-theory

Auxiliary result finite_eta_reciprocal_lt 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.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum

Formal statement

section
namespace D1Bound5



theorem _root_.D1Bound5.finite_eta_reciprocal_lt (T e : ℝ) (hT : 1000 ≤ T) (he : e ≤ 9) :
    1/(1-1/T)^e < (101/100 : ℝ) := by sorry

end D1Bound5
end

Source

D1Bound5/FiniteEtaBound.lean, lines 26-30, SHA-256 bbe0c480ef14e08f89c2bfd31afb3f5e0e4f98178a555879f1db7d5985f98cf6. Project: https://github.com/tomislav-math/d1-bound5-lean

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