import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem algebra_amgm_sumasqdivbgeqsuma
  (a b c d : ℝ)
  (h₀ : 0 < a ∧ 0 < b ∧ 0 < c ∧ 0 < d) :
  a^2 / b + b^2 / c + c^2 / d + d^2 / a ≥ a + b + c + d := by sorry