A reciprocal constraint implies a weighted lower bound

Proved

WorkbookSource.problem_6918

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

lean-workbooksource-checked

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

a+2b\geq 3

Source: InternLM Lean-Workbook, record lean_workbook_6918 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_6918 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : 1 / (1 + a) + 1 / (1 + b^2) = 1) : a + 2 * b ≥ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_6918; Apache-2.0

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