lean_workbook_plus_20001

Proved

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

Let $a,b,c$ be positive real numbers such that $a^3+b^3+c^3=abc+2$ . Prove that $(1) abc\leq 1;$ $(2)a+bc\leq 2 ;$ $(3)a+b+c \leq 3 .$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_20001 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a * b * c = 1) (h : a ^ 3 + b ^ 3 + c ^ 3 = a * b * c + 2) : a * b * c ≤ 1 ∧ a + b * c ≤ 2 ∧ a + b + c ≤ 3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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