Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Open Scope ring_scope.
(** Starting from cyril exercise *)
Section PreliminaryLemmas.

Lemma Cnat_add_eq1 : {in Cnat &, forall x y,
(x + y == 1) = ((x == 1) && (y == 0)) || ((x == 0) && (y == 1))}.