[GOAL]
ι : Type u_1
α : ι → Type u_2
inst✝² : (i : ι) → Zero (α i)
inst✝¹ : Countable ι
inst✝ : ∀ (i : ι), Countable (α i)
⊢ Countable (Π₀ (i : ι), α i)
[PROOFSTEP]
classical
let _ := Encodable.ofCountable ι
let _ := fun i ↦ Encodable.ofCountable (α i)
infer_instance
[GOAL]
ι : Type u_1
α : ι → Type u_2
inst✝² : (i : ι) → Zero (α i)
inst✝¹ : Countable ι
inst✝ : ∀ (i : ι), Countable (α i)
⊢ Countable (Π₀ (i : ι), α i)
[PROOFSTEP]
let _ := Encodable.ofCountable ι
[GOAL]
ι : Type u_1
α : ι → Type u_2
inst✝² : (i : ι) → Zero (α i)
inst✝¹ : Countable ι
inst✝ : ∀ (i : ι), Countable (α i)
x✝ : Encodable ι := Encodable.ofCountable ι
⊢ Countable (Π₀ (i : ι), α i)
[PROOFSTEP]
let _ := fun i ↦ Encodable.ofCountable (α i)
[GOAL]
ι : Type u_1
α : ι → Type u_2
inst✝² : (i : ι) → Zero (α i)
inst✝¹ : Countable ι
inst✝ : ∀ (i : ι), Countable (α i)
x✝¹ : Encodable ι := Encodable.ofCountable ι
x✝ : (i : ι) → Encodable (α i) := fun i => Encodable.ofCountable (α i)
⊢ Countable (Π₀ (i : ι), α i)
[PROOFSTEP]
infer_instance
