A sum-product lower bound at pairwise sum three

Proved

WorkbookSource.base_38347

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

lean-workbooksource-checked

Let $a,b,c>0,ab+bc+ca=3$ . prove that: $3(a+b+c)+abc\geq 10$

Source: InternLM Lean-Workbook, record lean_workbook_38347 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38347 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a * b + b * c + c * a = 3) : 3 * (a + b + c) + a * b * c ≥ 10  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_38347; Apache-2.0

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