A four-variable complementary product bound

Proved

WorkbookSource.base_9719

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

lean-workbooksource-checked

Prove that if $x,y,z,t>0 ,x+y+z+t=1$ then $(1-x)(1-y)(1-z)(1-t)\leq\frac{5}{16}+xyzt$

Source: InternLM Lean-Workbook, record lean_workbook_9719 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9719 (x y z t : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) (ht : 0 < t) (h : x + y + z + t = 1) : (1 - x) * (1 - y) * (1 - z) * (1 - t) ≤ 5 / 16 + x * y * z * t  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9719; Apache-2.0

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