An inequality between ordered consecutive gaps

Proved

WorkbookSource.problem_13705

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

lean-workbooksource-checked

Let $a\geqslant b\geqslant c$ and $a-b=x, b-c=y$ . Then the inequality is equivalent to $(x+y+(x+y))^2 \geqslant 2(x^2+y^2+(x+y)^2)$

Source: InternLM Lean-Workbook, record lean_workbook_13705 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_13705 {a b c x y : ℝ} (h₁ : a ≥ b ∧ b ≥ c) (h₂ : x = a - b) (h₃ : y = b - c) : (x + y + (x + y))^2 ≥ 2 * (x^2 + y^2 + (x + y)^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_13705; Apache-2.0

View graph