A cubic expression bound under a weighted sum constraint

Proved

WorkbookSource.base_20770

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

prove that : $x+xy+xyz\leq 3$ where $x,y,z$ are positive real numbers and $3x+2y+z=6$

Source: InternLM Lean-Workbook, record lean_workbook_20770 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_20770 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (h : 3 * x + 2 * y + z = 6) : x + x * y + x * y * z ≤ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_20770; Apache-2.0

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