A mixed pairwise and triple-product inequality at unit sum

Proved

WorkbookSource.base_18213

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

lean-workbooksource-checked

The stronger inequality holds: If $a,b,c$ are positive real numbers such that $a+b+c=1,$ then $3(ab+bc+ca)(1+48abc)\geq 75abc.$

Source: InternLM Lean-Workbook, record lean_workbook_18213 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_18213 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 1) : 3 * (a * b + b * c + c * a) * (1 + 48 * a * b * c) ≥ 75 * a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18213; Apache-2.0

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