Prove2Me

A symmetric bound including zero boundary values

Proved
WorkbookSource.plus_32281

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

lean-workbooksource-checked

Let a,b,c≥0a,b,c\ge 0 and a+b+c=1.a+b+c=1. Prove that

a2+b2+c2+4abc≤1a^2+b^2+c^2+4abc\le 1

Source: InternLM Lean-Workbook, record lean_workbook_plus_32281 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved. This statement includes nonnegative boundary values; the related positive-variable records plus_16237 and source57253 require all three variables to be positive.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.plus_32281 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (hab : a + b + c = 1) : a^2 + b^2 + c^2 + 4 * a * b * c ≤ 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_32281; Apache-2.0

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