A square-sum bound above a unit average

Proved

WorkbookSource.problem_55974

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

lean-workbooksource-checked

Let $a,b,c>0$ such that $a+b+c\geq3$ . Prove the inequality: i) $a^2 +b^2+c^2\geq a+b+c$ .

Source: InternLM Lean-Workbook, record lean_workbook_55974 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_55974 (a b c : ℝ) (h1 : a + b + c ≥ 3) (h2 : a > 0 ∧ b > 0 ∧ c > 0): a^2 + b^2 + c^2 ≥ a + b + c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_55974; Apache-2.0

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