lean_workbook_plus_14036

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c\in[\frac{1}{2},1]$ . Prove that $ab+bc+ca+\frac{3}{4} \geq a+b+c$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14036 (a b c : ℝ) (ha : a ∈ Set.Icc (1 / 2) 1) (hb : b ∈ Set.Icc (1 / 2) 1) (hc : c ∈ Set.Icc (1 / 2) 1) : a * b + b * c + c * a + 3 / 4 ≥ a + b + c   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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