rewrite [hone, Nat.add_comm]
case cons.inl
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)
hone : countP p l = 1
b : α
hb : b ∈ l ∧ p b = true
⊢ (countP p l + if p a = true then 1 else 0) ≤ 1
case cons.inl
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)
hone : countP p l = 1
b : α
hb : b ∈ l ∧ p b = true
⊢ (if p a = true then 1 else 0) + 1 ≤ 1