Prove2Me

Expanding a quotient product inequality

Proved
WorkbookSource.problem_15655

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

lean-workbooksource-checked

Derive the inequality a2b2+1≤5a2b\frac{a^2}{b^2} + 1 \le \frac{5a}{2b} from (ab−12)(ab−2)≤0\left( \frac{a}{b} - \frac{1}{2} \right) \left( \frac{a}{b} -2 \right) \le 0.

Source: InternLM Lean-Workbook, record lean_workbook_15655 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_15655 (a b : ℝ) : (a / b - 1 / 2) * (a / b - 2) ≤ 0 → a^2 / b^2 + 1 ≤ 5 * a / (2 * b)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15655; Apache-2.0

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