diff options
Diffstat (limited to 'theories/Arith/Mult.v')
| -rw-r--r-- | theories/Arith/Mult.v | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/theories/Arith/Mult.v b/theories/Arith/Mult.v index e4084ba47..4b13e145a 100644 --- a/theories/Arith/Mult.v +++ b/theories/Arith/Mult.v @@ -23,35 +23,35 @@ Local Open Scope nat_scope. (** ** Zero property *) -Notation mult_0_l := Nat.mul_0_l (compat "8.4"). (* 0 * n = 0 *) -Notation mult_0_r := Nat.mul_0_r (compat "8.4"). (* n * 0 = 0 *) +Notation mult_0_l := Nat.mul_0_l (only parsing). (* 0 * n = 0 *) +Notation mult_0_r := Nat.mul_0_r (only parsing). (* n * 0 = 0 *) (** ** 1 is neutral *) -Notation mult_1_l := Nat.mul_1_l (compat "8.4"). (* 1 * n = n *) -Notation mult_1_r := Nat.mul_1_r (compat "8.4"). (* n * 1 = n *) +Notation mult_1_l := Nat.mul_1_l (only parsing). (* 1 * n = n *) +Notation mult_1_r := Nat.mul_1_r (only parsing). (* n * 1 = n *) Hint Resolve mult_1_l mult_1_r: arith. (** ** Commutativity *) -Notation mult_comm := Nat.mul_comm (compat "8.4"). (* n * m = m * n *) +Notation mult_comm := Nat.mul_comm (only parsing). (* n * m = m * n *) Hint Resolve mult_comm: arith. (** ** Distributivity *) Notation mult_plus_distr_r := - Nat.mul_add_distr_r (compat "8.4"). (* (n+m)*p = n*p + m*p *) + Nat.mul_add_distr_r (only parsing). (* (n+m)*p = n*p + m*p *) Notation mult_plus_distr_l := - Nat.mul_add_distr_l (compat "8.4"). (* n*(m+p) = n*m + n*p *) + Nat.mul_add_distr_l (only parsing). (* n*(m+p) = n*m + n*p *) Notation mult_minus_distr_r := - Nat.mul_sub_distr_r (compat "8.4"). (* (n-m)*p = n*p - m*p *) + Nat.mul_sub_distr_r (only parsing). (* (n-m)*p = n*p - m*p *) Notation mult_minus_distr_l := - Nat.mul_sub_distr_l (compat "8.4"). (* n*(m-p) = n*m - n*p *) + Nat.mul_sub_distr_l (only parsing). (* n*(m-p) = n*m - n*p *) Hint Resolve mult_plus_distr_r: arith. Hint Resolve mult_minus_distr_r: arith. @@ -59,7 +59,7 @@ Hint Resolve mult_minus_distr_l: arith. (** ** Associativity *) -Notation mult_assoc := Nat.mul_assoc (compat "8.4"). (* n*(m*p)=n*m*p *) +Notation mult_assoc := Nat.mul_assoc (only parsing). (* n*(m*p)=n*m*p *) Lemma mult_assoc_reverse n m p : n * m * p = n * (m * p). Proof. @@ -83,8 +83,8 @@ Qed. (** ** Multiplication and successor *) -Notation mult_succ_l := Nat.mul_succ_l (compat "8.4"). (* S n * m = n * m + m *) -Notation mult_succ_r := Nat.mul_succ_r (compat "8.4"). (* n * S m = n * m + n *) +Notation mult_succ_l := Nat.mul_succ_l (only parsing). (* S n * m = n * m + m *) +Notation mult_succ_r := Nat.mul_succ_r (only parsing). (* n * S m = n * m + n *) (** * Compatibility with orders *) |