Prove2Me

An asymmetric quadratic lower bound at sum three

Proved
WorkbookSource.plus_15135

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

lean-workbooksource-checked

Let a,b,ca, b, c be nonnegative real numbers such that a+b+c=3.a + b + c = 3. Prove that

a2+12b2+c2+ab+ca≥3a^2+\frac{1}{2}b^2+c^2+ab+ca\geq 3

Source: InternLM Lean-Workbook, record lean_workbook_plus_15135 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.plus_15135 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a + b + c = 3) : a^2 + (1 / 2) * b^2 + c^2 + a * b + c * a ≥ 3   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_15135; Apache-2.0

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