(* coq-prog-args: ("-color" "on" "-diffs" "on" "-async-proofs" "off") *)
(* Re: -async-proofs off, see https://github.com/coq/coq/issues/9671 *)
(* Shows diffs in an error message for an "Unable to unify" error *)
Inductive btree (T : Type) : Type :=
Leaf | Node (val : T) (t1 t2 : btree T).
Arguments Leaf {T}.
Arguments Node {T}.
Fixpoint rev_tree {T : Type} (t : btree T) : btree T :=
match t with
| Leaf => Leaf
| Node x t1 t2 => Node x (rev_tree t2) (rev_tree t1)
end.
Fixpoint count {T : Type} (p : T -> bool) (t : btree T) : nat :=
match t with
| Leaf => 0
| Node x t1 t2 =>
(if p x then 1 else 0) + (count p t1 + count p t2)
end.

Lemma count_rev_tree {T} (p : T -> bool) t : count p (rev_tree t) = count p t.