Prove2Me

lean_workbook_plus_74358

Disproved

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

Prove that \n\n a3b3(b+c−a)(c+a−b)+b3c3(c+a−b)(a+b−c)+c3a3(a+b−c)(b+c−a)≥2 R3s\sqrt {{\frac {{a}^{3}{b}^{3}}{ \left( b+c-a \right) \left( c+a-b \right) }}}+\sqrt {{\frac {{b}^{3}{c}^{3}}{ \left( c+a-b \right) \left( a+b-c \right) }}}+\sqrt {{\frac {{c}^{3}{a}^{3}}{ \left( a+b-c \right) \left( b+c-a \right) }}}\geq 2\,R\sqrt {3}s

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_74358 :
  ∀ a b c R s : ℝ, a > 0 ∧ b > 0 ∧ c > 0 ∧ R > 0 ∧ s > 0 →
  Real.sqrt ((a^3 * b^3) / (b + c - a) / (c + a - b)) +
  Real.sqrt ((b^3 * c^3) / (c + a - b) / (a + b - c)) +
  Real.sqrt ((a^3 * c^3) / (a + b - c) / (b + c - a)) ≥
  2 * R * Real.sqrt 3 * s   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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