Prove2Me

A sharp bound for three squared differences

Proved
WorkbookSource.plus_30537

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

lean-workbooksource-checked

Let a, b, c a,\ b,\ c be real numbers. Prove that (b−a)2+(c−b)2+(c−a−2)2≥43 (b-a)^{2}+(c-b)^{2}+(c-a-2)^{2}\ge\frac{4}{3}

Source: InternLM Lean-Workbook, record lean_workbook_plus_30537 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.plus_30537 : ∀ a b c : ℝ, (b - a) ^ 2 + (c - b) ^ 2 + (c - a - 2) ^ 2 ≥ 4 / 3   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_30537; Apache-2.0

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