rw [←dvd_def] at hdvd
case inr.intro
hwo : (∀ (a b c : ℕplus), (a ∣ b → b ∣ c → a ∣ c) ∧ (a ∣ b → b ∣ a → a = b)) ∧ ∀ (a b : ℕplus), a ∣ b ∨ b ∣ a
c : ℕplus
hc : ↑2 = ↑(3 * c)
hdvd : ∃ c, 2 = 3 * c
⊢ False
case inr.intro
hwo : (∀ (a b c : ℕplus), (a ∣ b → b ∣ c → a ∣ c) ∧ (a ∣ b → b ∣ a → a = b)) ∧ ∀ (a b : ℕplus), a ∣ b ∨ b ∣ a
c : ℕplus
hc : ↑2 = ↑(3 * c)
hdvd : 3 ∣ 2
⊢ False