A rational inequality with a sum-product constraint

Proved

WorkbookSource.plus_26160

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

lean-workbooksource-checked

Let $a,b$ be positive real numbers such that $a+b+ab=1$ . Prove that $\frac{1+b^2}{1+a^2}\ge 2b.$

Source: InternLM Lean-Workbook, record lean_workbook_plus_26160 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.plus_26160 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a + b + a * b = 1) : (1 + b ^ 2) / (1 + a ^ 2) ≥ 2 * b   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_26160; Apache-2.0

View graph