rewrite [this, Nat.zero_add]
case cons.inr
α : Type u
β : Type v
p : α → Bool
hp : ∀ (a b : α), p a = true → p b = true → a = b
a : α
l : List α
IH : Nodup l → countP p l ≤ 1
hl : Nodup (a :: l)
hlt : countP p l < 1
this : countP p l = 0
⊢ (countP p l + if p a = true then 1 else 0) ≤ 1
case cons.inr
α : Type u
β : Type v
p : α → Bool
hp : ∀ (a b : α), p a = true → p b = true → a = b
a : α
l : List α
IH : Nodup l → countP p l ≤ 1
hl : Nodup (a :: l)
hlt : countP p l < 1
this : countP p l = 0
⊢ (if p a = true then 1 else 0) ≤ 1