A sum of squared and linear ratios is at least seven quarters

Proved

WorkbookSource.base_29761

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers . Show that $\frac{a^2}{b^2}+\frac{b}{c+a}+\frac{c}{b}\geq \frac{7}{4}$

Source: InternLM Lean-Workbook, record lean_workbook_29761 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_29761 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / b^2 + b / (c + a) + c / b) ≥ 7 / 4  :=  by sorry

Source