A product bound under a lower bound on a pairwise product

Proved

WorkbookCorrected.base_15599

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

corrected-formalizationlean-workbooksource-checked

Given two positive numbers $a, b$ so that $ab\geqq \frac{3}{2}$ . Prove that :

3(2b+ a- 3)(2a+ b- 3)\geqq (a- b)^{2}+ \frac{21}{20}

Source: InternLM Lean-Workbook, record lean_workbook_15599 (Apache-2.0). Natural-language proposition preserved; missing source domain assumptions restored. Proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookCorrected.base_15599 (a b : ℝ) (source_domain_a : 0 < a) (source_domain_b : 0 < b) (hab : a * b ≥ 3 / 2) : 3 * (2 * b + a - 3) * (2 * a + b - 3) ≥ (a - b) ^ 2 + 21 / 20  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15599; Apache-2.0

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