lean_workbook_plus_13634

Proved

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

Let $x, y, z$ be nonnegative reals such that $x + y + z\geq 5$ . Prove that at least two of the following three inequalities \n\n $2x + 3y + 6z\geq 14 , 2y + 3z + 6x\geq 14,2z + 3x + 6y\geq 14$ \n\n are true.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_13634 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) (h : x + y + z ≥ 5) : ∃ i j : Fin 3, i ≠ j ∧ (2 * x + 3 * y + 6 * z ≥ 14 ∨ 2 * y + 3 * z + 6 * x ≥ 14 ∨ 2 * z + 3 * x + 6 * y ≥ 14)   :=  by sorry

Source

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

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