refine trans (s:=LE.le) countP_or_le_add ?_
case cons
α : Type u
β : Type v
inst✝ : DecidableEq β
lb : List β
hnodup : Nodup lb
f : α → β
a : α
la : List α
IH : countP (fun b => decide (∃ a, a ∈ la ∧ f a = b)) lb ≤ length la
⊢ countP (fun b => decide (f a = b) || decide (∃ a, a ∈ la ∧ f a = b)) lb ≤ length (a :: la)
case cons
α : Type u
β : Type v
inst✝ : DecidableEq β
lb : List β
hnodup : Nodup lb
f : α → β
a : α
la : List α
IH : countP (fun b => decide (∃ a, a ∈ la ∧ f a = b)) lb ≤ length la
⊢ countP (fun b => decide (f a = b)) lb + countP (fun b => decide (∃ a, a ∈ la ∧ f a = b)) lb ≤ length (a :: la)