Prove2Me

lean_workbook_plus_39257

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that (a−b)2+(c−1)2+2c(a−1)(b−1)≥0  ⟺  a2+b2+c2+2abc+1≥2(ab+bc+ca)(a-b)^2 +(c-1)^2+2c(a-1)(b-1) \geq 0 \iff a^2+b^2+c^2+2abc+1 \geq 2(ab+bc+ca)

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_39257 (a b c : ℝ) : (a - b) ^ 2 + (c - 1) ^ 2 + 2 * c * (a - 1) * (b - 1) ≥ 0 ↔ a ^ 2 + b ^ 2 + c ^ 2 + 2 * a * b * c + 1 ≥ 2 * (a * b + b * c + a * c)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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