A lower bound for a weighted unit sum

Proved

WorkbookSource.problem_5176

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c>0$ , $a,b,c\in (0,\frac{1}{2}],a+b+c=1,$ ,prove that:

$2a+3b+4c\geq \frac{5}{2}.$

Source: InternLM Lean-Workbook, record lean_workbook_5176 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_5176 (a b c : ℝ) (ha : 0 < a ∧ a ≤ 1 / 2) (hb : 0 < b ∧ b ≤ 1 / 2) (hc : 0 < c ∧ c ≤ 1 / 2) (hab : a + b + c = 1) : 2 * a + 3 * b + 4 * c ≥ 5 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5176; Apache-2.0

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