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authorJasper Hugunin2020-10-08 17:26:48 -0700
committerJasper Hugunin2020-10-08 17:26:48 -0700
commit460a9bb281a69da2be1113adc146e168586de0bd (patch)
tree6299355ec48ca0435a3074fcb7549fd17e315a38
parent8c3231dc17e851a2c1e2777833f6fa5e24ba5e8e (diff)
Modify Numbers/Integer/Abstract/ZGcd.v to compile with -mangle-names
-rw-r--r--theories/Numbers/Integer/Abstract/ZGcd.v12
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZGcd.v b/theories/Numbers/Integer/Abstract/ZGcd.v
index 09d28a18ec..755557ff17 100644
--- a/theories/Numbers/Integer/Abstract/ZGcd.v
+++ b/theories/Numbers/Integer/Abstract/ZGcd.v
@@ -98,7 +98,7 @@ Qed.
Lemma gcd_abs_l : forall n m, gcd (abs n) m == gcd 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 gcd_opp_l.
Qed.
@@ -125,7 +125,7 @@ Qed.
Lemma gcd_add_mult_diag_r : forall n m p, gcd n (m+p*n) == gcd n m.
Proof.
- intros. apply gcd_unique_alt; try apply gcd_nonneg.
+ intros n m p. apply gcd_unique_alt; try apply gcd_nonneg.
intros. rewrite gcd_divide_iff. split; intros (U,V); split; trivial.
apply divide_add_r; trivial. now apply divide_mul_r.
apply divide_add_cancel_r with (p*n); trivial.
@@ -164,12 +164,12 @@ Proof.
(* First, a version restricted to natural numbers *)
assert (aux : forall n, 0<=n -> forall m, 0<=m -> Bezout n m (gcd n m)).
intros n Hn; pattern n.
- apply strong_right_induction with (z:=0); trivial.
+ apply (fun H => strong_right_induction _ H 0); trivial.
unfold Bezout. solve_proper.
clear n Hn. intros n Hn IHn.
apply le_lteq in Hn; destruct Hn as [Hn|Hn].
intros m Hm; pattern m.
- apply strong_right_induction with (z:=0); trivial.
+ apply (fun H => strong_right_induction _ H 0); trivial.
unfold Bezout. solve_proper.
clear m Hm. intros m Hm IHm.
destruct (lt_trichotomy n m) as [LT|[EQ|LT]].
@@ -227,7 +227,7 @@ Qed.
Lemma gcd_mul_mono_l_nonneg :
forall n m p, 0<=p -> gcd (p*n) (p*m) == p * gcd n m.
Proof.
- intros. rewrite <- (abs_eq p) at 3; trivial. apply gcd_mul_mono_l.
+ intros n m p ?. rewrite <- (abs_eq p) at 3; trivial. apply gcd_mul_mono_l.
Qed.
Lemma gcd_mul_mono_r :
@@ -239,7 +239,7 @@ Qed.
Lemma gcd_mul_mono_r_nonneg :
forall n m p, 0<=p -> gcd (n*p) (m*p) == gcd n m * p.
Proof.
- intros. rewrite <- (abs_eq p) at 3; trivial. apply gcd_mul_mono_r.
+ intros n m p ?. rewrite <- (abs_eq p) at 3; trivial. apply gcd_mul_mono_r.
Qed.
Lemma gauss : forall n m p, (n | m * p) -> gcd n m == 1 -> (n | p).