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authorJasper Hugunin2020-10-08 17:29:18 -0700
committerJasper Hugunin2020-10-08 17:29:18 -0700
commitdd66aba3df643b5edde09e99033954b1efe5c7a1 (patch)
tree42617d81bdf8b25e1031f6f5ef83638a0c897968 /theories/Numbers
parent460a9bb281a69da2be1113adc146e168586de0bd (diff)
Modify Numbers/Integer/Abstract/ZLcm.v to compile with -mangle-names
Diffstat (limited to 'theories/Numbers')
-rw-r--r--theories/Numbers/Integer/Abstract/ZLcm.v12
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZLcm.v b/theories/Numbers/Integer/Abstract/ZLcm.v
index 6aa828ebfc..c45ea12868 100644
--- a/theories/Numbers/Integer/Abstract/ZLcm.v
+++ b/theories/Numbers/Integer/Abstract/ZLcm.v
@@ -33,14 +33,14 @@ Module Type ZLcmProp
Lemma quot_div_nonneg : forall a b, 0<=a -> 0<b -> a÷b == a/b.
Proof.
- intros. apply div_unique_pos with (a rem b).
+ intros a b **. apply div_unique_pos with (a rem b).
now apply rem_bound_pos.
apply quot_rem. order.
Qed.
Lemma rem_mod_nonneg : forall a b, 0<=a -> 0<b -> a rem b == a mod b.
Proof.
- intros. apply mod_unique_pos with (a÷b).
+ intros a b **. apply mod_unique_pos with (a÷b).
now apply rem_bound_pos.
apply quot_rem. order.
Qed.
@@ -290,7 +290,7 @@ Qed.
Lemma lcm_divide_iff : forall n m p,
(lcm n m | p) <-> (n | p) /\ (m | p).
Proof.
- intros. split. split.
+ intros n m p. split. split.
transitivity (lcm n m); trivial using divide_lcm_l.
transitivity (lcm n m); trivial using divide_lcm_r.
intros (H,H'). now apply lcm_least.
@@ -387,7 +387,7 @@ Qed.
Lemma lcm_abs_l : forall n m, lcm (abs n) m == lcm n m.
Proof.
- intros. destruct (abs_eq_or_opp n) as [H|H]; rewrite H.
+ intros n m. destruct (abs_eq_or_opp n) as [H|H]; rewrite H.
easy. apply lcm_opp_l.
Qed.
@@ -438,7 +438,7 @@ Qed.
Lemma lcm_mul_mono_l_nonneg :
forall n m p, 0<=p -> lcm (p*n) (p*m) == p * lcm n m.
Proof.
- intros. rewrite <- (abs_eq p) at 3; trivial. apply lcm_mul_mono_l.
+ intros n m p ?. rewrite <- (abs_eq p) at 3; trivial. apply lcm_mul_mono_l.
Qed.
Lemma lcm_mul_mono_r :
@@ -450,7 +450,7 @@ Qed.
Lemma lcm_mul_mono_r_nonneg :
forall n m p, 0<=p -> lcm (n*p) (m*p) == lcm n m * p.
Proof.
- intros. rewrite <- (abs_eq p) at 3; trivial. apply lcm_mul_mono_r.
+ intros n m p ?. rewrite <- (abs_eq p) at 3; trivial. apply lcm_mul_mono_r.
Qed.
Lemma gcd_1_lcm_mul : forall n m, n~=0 -> m~=0 ->