Compfiles: Catalog Of Math Problems Formalized In Lean

Usa1980P5


import Mathlib.Tactic

/-!
# USA Mathematical Olympiad 1980, Problem 5

Let x,y,z be real numbers in the closed interval [0,1]. Show that

 x/(y + z + 1) + y/(z + x + 1) + z/(x + y + 1) ≤ 1 + (1 - x)(1 - y)(1 - z).
-/

namespace Usa1980P5

theorem usa1980_p5 (x y z : ℝ)
    (hx : x ∈ Set.Icc 0 1)
    (hy : y ∈ Set.Icc 0 1)
    (hz : z ∈ Set.Icc 0 1) :
    x / (y + z + 1) + y / (z + x + 1) + z / (x + y + 1) ≤
    1 + (1 - x) * (1 - y) * (1 - z) := sorry

This problem does not yet have a complete formalized solution.

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