A sum of three fractions with a common denominator

Proved

WorkbookSource.problem_48567

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

lean-workbooksource-checked

Correction: The inequality holds only for positive $a, b, c$ .

Source: InternLM Lean-Workbook, record lean_workbook_48567 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_48567 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a / (b + c + a) + b / (c + a + b) + c / (a + b + c) < 3 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_48567; Apache-2.0

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