lean_workbook_plus_33920

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove the Completeness Property: A non-empty set $S$ of real numbers that has an upper bound has a least upper bound

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_33920 (S : Set ℝ) (hS : S.Nonempty) (hS' : ∃ x, ∀ y ∈ S, y ≤ x) : ∃ x, IsLUB S x   :=  by sorry

Source