lean_workbook_plus_27229

Proved

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

Given $a,b,c,d>0$ such that $a+2(b^4+c^4+d^4)+\frac{1}{abcd}=\frac{135}{8}.$ Prove that $a\leq16.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_27229 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (habc : a * b * c * d = 1) (h : a + 2 * (b ^ 4 + c ^ 4 + d ^ 4) + 1 / (a * b * c * d) = 135 / 8) : a ≤ 16   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph