intros a b c ha hb hc hab hbc
⊢ ∀ (a b c : ℝ), a > 0 → b > 0 → c > 0 → a ≥ b → b ≥ c → a ^ a * b ^ b * c ^ c ≥ (a * b * c) ^ ((a + b + c) / 3)
a b c : ℝ
ha : a > 0
hb : b > 0
hc : c > 0
hab : a ≥ b
hbc : b ≥ c
⊢ a ^ a * b ^ b * c ^ c ≥ (a * b * c) ^ ((a + b + c) / 3)