diff options
Diffstat (limited to 'theories/Numbers/NatInt/NZGcd.v')
| -rw-r--r-- | theories/Numbers/NatInt/NZGcd.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Numbers/NatInt/NZGcd.v b/theories/Numbers/NatInt/NZGcd.v index 63cc725aec..c542c3fc2c 100644 --- a/theories/Numbers/NatInt/NZGcd.v +++ b/theories/Numbers/NatInt/NZGcd.v @@ -147,7 +147,7 @@ Qed. Lemma mul_divide_cancel_r : forall n m p, p ~= 0 -> ((n * p | m * p) <-> (n | m)). Proof. - intros. rewrite 2 (mul_comm _ p). now apply mul_divide_cancel_l. + intros n m p ?. rewrite 2 (mul_comm _ p). now apply mul_divide_cancel_l. Qed. Lemma divide_add_r : forall n m p, (n | m) -> (n | p) -> (n | m + p). @@ -215,7 +215,7 @@ Qed. Lemma gcd_divide_iff : forall n m p, (p | gcd n m) <-> (p | n) /\ (p | m). Proof. - intros. split. - split. + intros n m p. split. - split. + transitivity (gcd n m); trivial using gcd_divide_l. + transitivity (gcd n m); trivial using gcd_divide_r. - intros (H,H'). now apply gcd_greatest. @@ -273,18 +273,18 @@ Qed. Lemma gcd_eq_0_l : forall n m, gcd n m == 0 -> n == 0. Proof. - intros. + intros n m H. generalize (gcd_divide_l n m). rewrite H. apply divide_0_l. Qed. Lemma gcd_eq_0_r : forall n m, gcd n m == 0 -> m == 0. Proof. - intros. apply gcd_eq_0_l with n. now rewrite gcd_comm. + intros n m ?. apply gcd_eq_0_l with n. now rewrite gcd_comm. Qed. Lemma gcd_eq_0 : forall n m, gcd n m == 0 <-> n == 0 /\ m == 0. Proof. - intros. split. + intros n m. split. - split. + now apply gcd_eq_0_l with m. + now apply gcd_eq_0_r with n. |