A shifted quadratic reciprocal upper bound at fixed sum three

Proved

WorkbookSource.base_10295

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

lean-workbooksource-checked

Let $a,b,c$ are positive real number such that $a+b+c=3$ , prove that $\frac{1}{11+a^{2}}+\frac{1}{11+b^{2}}+\frac{1}{11+c^{2}}\leqslant \frac{1}{4}.$

Source: InternLM Lean-Workbook, record lean_workbook_10295 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10295 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : 1 / (11 + a^2) + 1 / (11 + b^2) + 1 / (11 + c^2) ≤ 1 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10295; Apache-2.0

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