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 ltn0Sn_pair {A : Type} (n : nat) (g : A)  :
0 < (n.+1, g).1.