Local Arguments add !x !y.

(* Specifications: *)
Lemma add_assoc_pos p n m : pos p + (n + m) = pos p + n + m.
Lemma add_assoc n m p : n + (m + p) = n + m + p.
(** ** Opposite is inverse for addition *)
Lemma add_opp_diag_r n : n + - n = 0.
(** ** Multiplication and Opposite *)
Lemma mul_opp_r n m : n * - m = - (n * m).
(** ** Distributivity of multiplication over addition *)
Lemma mul_add_distr_pos (p:positive) n m :
(n + m) * pos p = n * pos p + m * pos p.
Lemma mul_add_distr_r n m p : (n + m) * p = n * p + m * p.
End Private_BootStrap.