Compfiles: Catalog Of Math Problems Formalized In Lean

Imo1994P5

import Mathlib.Tactic

/-!
# International Mathematical Olympiad 1994, Problem 5

Let S be the set of all real numbers greater than -1.
Find all functions f : S→S such that f(x + f(y) + xf(y)) = y + f(x) + yf(x) for all x and y,
and f(x)/x is strictly increasing on each of the intervals -1 < x < 0 and 0 < x.
-/

namespace Imo1994P5

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

theorem imo1994_p5 (f : ℝ → ℝ)
  (hM : ∀ x y: ℝ, -1 < x ∧ x < 0 ∧ -1 < y ∧ y < 0 ∧ x < y → f x < f y)
  (hM2 : ∀ x y: ℝ, 0 < x ∧ 0 < y ∧ x < y → f x < f y)
  (h₀ : ∀ x, -1 < x → f x > -1)
  (h₁ : ∀ x y, -1 < x → -1 < y → f (x + f y + x * f y) = y + f x + y * f x) :
    f ∈ solution_set := sorry


end Imo1994P5

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

This problem does not yet have a complete formalized solution.