specialize h a
case cons
α : Type u
β : Type v
p q : α → Bool
h : ∀ (a : α), (p a && q a) = false
a : α
l : List α
IH : countP (fun a => p a || q a) l = countP p l + countP q l
⊢ (countP (fun a => p a || q a) l + if (p a || q a) = true then 1 else 0) =
    (countP p l + if p a = true then 1 else 0) + (countP q l + if q a = true then 1 else 0)
case cons
α : Type u
β : Type v
p q : α → Bool
a : α
l : List α
IH : countP (fun a => p a || q a) l = countP p l + countP q l
h : (p a && q a) = false
⊢ (countP (fun a => p a || q a) l + if (p a || q a) = true then 1 else 0) =
    (countP p l + if p a = true then 1 else 0) + (countP q l + if q a = true then 1 else 0)