A bound for the largest three of seven ordered numbers

Proved

WorkbookSource.problem_52474

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

lean-workbooksource-checked

Let $x_1 \leq x_2 \leq ... \leq x_7$ . Then $x_5+x_6+x_7 \geq \frac{3}{7}(x_1+...+x_7)=142\frac{2}{7}$

Source: InternLM Lean-Workbook, record lean_workbook_52474 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_52474 (x : ℕ → ℝ) (hx: x 1 ≤ x 2 ∧ x 2 ≤ x 3 ∧ x 3 ≤ x 4 ∧ x 4 ≤ x 5 ∧ x 5 ≤ x 6 ∧ x 6 ≤ x 7): x 5 + x 6 + x 7 ≥ 3/7 * (x 1 + x 2 + x 3 + x 4 + x 5 + x 6 + x 7)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_52474; Apache-2.0

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