Prove2Me

lean_workbook_plus_32820

Proved

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

So we only have to prove that (a+b+c)2≥a+b+c+ab+bc+ca  ⟺  a2+b2+c2+ab+bc+ca≥a+b+c(a + b + c)^2\geq a + b + c + ab + bc + ca \iff a^2 + b^2 + c^2 + ab + bc + ca\geq a + b + c

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_32820 (a b c : ℝ) : (a + b + c) ^ 2 ≥ a + b + c + a * b + b * c + c * a ↔ a ^ 2 + b ^ 2 + c ^ 2 + a * b + b * c + c * a ≥ a + b + c   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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