Compfiles: Catalog Of Math Problems Formalized In Lean

Imo1972P4

import Mathlib.Tactic

/-!
# International Mathematical Olympiad 1972, Problem 4

Find all positive real solutions to:

(x_1^2 - x_3x_5)(x_2^2 - x_3x_5) ≤ 0
(x_2^2 - x_4x_1)(x_3^2 - x_4x_1) ≤ 0
(x_3^2 - x_5x_2)(x_4^2 - x_5x_2) ≤ 0
(x_4^2 - x_1x_3)(x_5^2 - x_1x_3) ≤ 0
(x_5^2 - x_2x_4)(x_1^2 - x_2x_4) ≤ 0
-/

namespace Imo1972P4

/- determine -/ abbrev solution_set : Set (ℝ × ℝ × ℝ × ℝ × ℝ) := sorry

theorem imo1972_p4 (a b c d e : ℝ)
  (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d ∧ 0 < e):
    (a^2 - c * e) * (b^2 - c * e) ≤ 0 ∧
    (b^2 - d * a) * (c^2 - d * a) ≤ 0 ∧
    (c^2 - e * b) * (d^2 - e * b) ≤ 0 ∧
    (d^2 - a * c) * (e^2 - a * c) ≤ 0 ∧
    (e^2 - b * d) * (a^2 - b * d) ≤ 0 ↔
      (a, b, c, d, e) ∈ solution_set := sorry


end Imo1972P4

File author(s): InternLM-MATH LEAN Formalizer v0.1

This problem does not yet have a complete formalized solution.