(** Addition *)

Notation plus := Nat.add (only parsing).Infix "+" := Nat.add : nat_scope.Definition f_equal2_plus := f_equal2 plus.Definition f_equal2_nat := f_equal2 (A1:=nat) (A2:=nat).

(* Specifications: *)
Lemma plus_n_O : forall n:nat, n = n + 0.
Lemma plus_O_n : forall n:nat, 0 + n = n.
Lemma plus_n_Sm : forall n m:nat, S (n + m) = n + S m.
Lemma plus_Sn_m : forall n m:nat, S n + m = S (n + m).