lean_workbook_plus_77080

Proved

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

Assume $a,b,c$ are positive numbers, such that $a(1-b) = b(1-c) = c(1-a) = \dfrac14$ . Prove that $a=b=c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_77080 (a b c : ℝ) (ha : a > 0 ∧ b > 0 ∧ c > 0)(hab : a * (1 - b) = 1 / 4) (hbc : b * (1 - c) = 1 / 4) (hca : c * (1 - a) = 1 / 4): a = b ∧ b = c ∧ c = a   :=  by sorry

Source

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

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