Set Warnings "-extraction-opaque-accessed,-extraction".
Set Warnings "-notation-overridden,-parsing".
(* TODO rename this file to util.v -- not only for nats *)
(* TODO do implicits for the rest of the file *)
Set Implicit Arguments.
Unset Strict Implicit.

Lemma eq_symm {A : Type} (x y : A) :
x = y -> y = x.