diff options
Diffstat (limited to 'theories/ZArith/Znumtheory.v')
| -rw-r--r-- | theories/ZArith/Znumtheory.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/ZArith/Znumtheory.v b/theories/ZArith/Znumtheory.v index 33f4dc7f4..5d6550f99 100644 --- a/theories/ZArith/Znumtheory.v +++ b/theories/ZArith/Znumtheory.v @@ -305,7 +305,7 @@ Section extended_euclid_algorithm. v1 * a + v2 * b = v3 -> (forall d:Z, Zis_gcd u3 v3 d -> Zis_gcd a b d) -> Euclid. Proof. - intros v3 Hv3; generalize Hv3; pattern v3 in |- *. + intros v3 Hv3; generalize Hv3; pattern v3. apply Zlt_0_rec. clear v3 Hv3; intros. elim (Z_zerop x); intro. @@ -319,8 +319,8 @@ Section extended_euclid_algorithm. apply Z_mod_lt; omega. assert (xpos : x > 0). omega. generalize (Z_div_mod_eq u3 x xpos). - unfold q in |- *. - intro eq; pattern u3 at 2 in |- *; rewrite eq; ring. + unfold q. + intro eq; pattern u3 at 2; rewrite eq; ring. apply (H (u3 - q * x) Hq (proj1 Hq) v1 v2 x (u1 - q * v1) (u2 - q * v2)). tauto. replace ((u1 - q * v1) * a + (u2 - q * v2) * b) with @@ -459,12 +459,12 @@ Proof. apply Gauss with a. rewrite H3. auto with zarith. - red in |- *; auto with zarith. + red; auto with zarith. apply Gauss with c. rewrite Z.mul_comm. rewrite <- H3. auto with zarith. - red in |- *; auto with zarith. + red; auto with zarith. Qed. (** After factorization by a gcd, the original numbers are relatively prime. *) @@ -479,7 +479,7 @@ Proof. elim H1; intros. elim H4; intros. rewrite H2 in H6; subst b; omega. - unfold rel_prime in |- *. + unfold rel_prime. destruct H1. destruct H1 as (a',H1). destruct H3 as (b',H3). |