A bound for three variables with a cubic constraint

Proved

WorkbookSource.problem_12605

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

inequalitieslean-workbooksource-checked

If real $a,b,c$ satisfy $a^3+b^3+c^3-1=3(a-1)(b-1)(c-1)$ , then $a+b+c\le2$ .

Source: InternLM Lean-Workbook, record lean_workbook_12605 (Apache-2.0). The complete source proposition is preserved.

Preamble

import Mathlib

Formal statement

theorem WorkbookSource.problem_12605 (a b c : ℝ) (ha : a^3 + b^3 + c^3 - 1 = 3 * (a - 1) * (b - 1) * (c - 1)) : a + b + c ≤ 2  :=  by sorry

Source