Prove2Me

Nonnegativity of a triangle-side quotient

Proved
WorkbookSource.problem_37391

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

lean-workbooksource-checked

Let a,b,c≥0a,b,c\ge0 satisfy the strict triangle inequalities. Then

a+c−b2(a+b+c)(c+a)≥0.\frac{a+c-b}{2(a+b+c)(c+a)}\ge0.

Source: InternLM Lean-Workbook, record lean_workbook_37391 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_37391 {a b c : ℝ} (hx: a >= 0 ∧ b >= 0 ∧ c >= 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) : (a + c - b) / (2 * (a + b + c) * (c + a)) ≥ 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_37391; Apache-2.0

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