(* coq-prog-args: ("-color" "on" "-diffs" "on" "-async-proofs" "off") *) (* Re: -async-proofs off, see https://github.com/coq/coq/issues/9671 *)RequireImport ListDef. (* Shows diffs in an error message for an "Unable to unify" error *) Require ListDef.
Inductive rev_tree{T : Type} (t : btree:btree :java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
java.lang.StringIndexOutOfBoundsException: Range [6, 3) out of bounds for length 42
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.
Axiom add_comm : forall x y, x + y = y + x.
Lemma count_rev_tree {T} (p : T -> bool) t : count p (rev_tree t) = count p t. Proof. induction t as [ | a t1 IH1 t2 IH2].
easy. simpl. rewrite IH1. rewrite IH2.
Fail reflexivity. rewrite (add_comm (count p t2)).
easy. Qed.
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