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authorJasper Hugunin2020-08-25 13:47:07 -0700
committerJasper Hugunin2020-08-25 13:53:34 -0700
commitd10c7e19fe760f139f31809975291b955705dc27 (patch)
tree277f6a5315709d61da688073d92eab61c5936e5e
parent3692f244fee5871b00557cb16ce85b40d413c3ec (diff)
Modify Numbers/NatInt/NZGcd.v to compile with -mangle-names
-rw-r--r--theories/Numbers/NatInt/NZGcd.v10
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.