#[global]
Hint Resolve minus_plus_simpl_l_reverse_stt: arith. (* Minus.minus_plus_simpl_l_reverse *)
#[local]
Definition plus_minus_stt := fun n m p Heq => eq_sym (Nat.add_sub_eq_l n m p (eq_sym Heq)).
Opaque plus_minus_stt.
Add Search Blacklist "Coq.Arith.Arith_base.plus_minus_stt".
#[global]
Hint Immediate plus_minus_stt: arith. (* Minus.plus_minus *)
#[local]
Definition minus_plus_stt := (fun n m => eq_ind _ (fun x => x - n = m) (Nat.add_sub m n) _ (Nat.add_comm _ _)).
Opaque minus_plus_stt.
Add Search Blacklist "Coq.Arith.Arith_base.minus_plus_stt".
#[global]
Hint Resolve minus_plus_stt: arith. (* Minus.minus_plus *)
#[local]
Definition le_plus_minus_stt := fun n m Hle => eq_sym (eq_trans (Nat.add_comm _ _) (Nat.sub_add n m Hle)).
Opaque le_plus_minus_stt.
Add Search Blacklist "Coq.Arith.Arith_base.le_plus_minus_stt".
#[global]
Hint Resolve le_plus_minus_stt: arith. (* Minus.le_plus_minus *)
#[local]
Definition le_plus_minus_r_stt := fun n m Hle => eq_trans (Nat.add_comm _ _) (Nat.sub_add n m Hle).
Opaque le_plus_minus_r_stt.
Add Search Blacklist "Coq.Arith.Arith_base.le_plus_minus_r_stt".
#[global]
Hint Resolve le_plus_minus_r_stt: arith. (* Minus.le_plus_minus_r *)
#[global]
Hint Resolve Nat.sub_lt: arith. (* Minus.lt_minus *)
#[local]
Definition lt_O_minus_lt_stt : forall n m, 0 < n - m -> m < n
:= fun n m => proj2 (Nat.lt_add_lt_sub_r 0 n m).
Opaque lt_O_minus_lt_stt.
Add Search Blacklist "Coq.Arith.Arith_base.lt_O_minus_lt_stt".
#[global]
Hint Immediate lt_O_minus_lt_stt: arith. (* Minus.lt_O_minus_lt *)
(* ** [mul] *)
#[global]
Hint Resolve Nat.mul_1_l Nat.mul_1_r: arith. (* Mult.mult_1_l Mult.mult_1_r *)
#[global]
Hint Resolve Nat.mul_comm: arith. (* Mult.mult_comm *)
#[global]
Hint Resolve Nat.mul_add_distr_r: arith. (* Mult.mult_plus_distr_r *)
#[global]
Hint Resolve Nat.mul_sub_distr_r: arith. (* Mult.mult_minus_distr_r *)
#[global]
Hint Resolve Nat.mul_sub_distr_l: arith. (* Mult.mult_minus_distr_l *)
#[local]
Definition mult_assoc_reverse_stt := fun n m p => eq_sym (Nat.mul_assoc n m p).
Opaque mult_assoc_reverse_stt.
Add Search Blacklist "Coq.Arith.Arith_base.mult_assoc_reverse_stt".
#[global]
Hint Resolve mult_assoc_reverse_stt Nat.mul_assoc: arith. (* Mult.mult_assoc_reverse Mult.mult_assoc *)
#[local]

Lemma mult_O_le_stt n m : m = 0 \/ n <= m * n.
Add Search Blacklist "Coq.Arith.Arith_base.mult_O_le_stt".