Definition IsSucc (n:nat) : Prop :=
match n with
| O => False
| S p => True
end.
(** Zero is not the successor of a number *)

(* Specifications: *)
Theorem O_S : forall n:nat, 0 <> S n.
#[global]
Hint Resolve O_S: core.
Theorem n_Sn : forall n:nat, n <> S n.
#[global]
Hint Resolve n_Sn: core.