diff options
| -rw-r--r-- | theories/Numbers/NatInt/NZParity.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/Numbers/NatInt/NZParity.v b/theories/Numbers/NatInt/NZParity.v index ee6f4014f0..07a33e3f67 100644 --- a/theories/Numbers/NatInt/NZParity.v +++ b/theories/Numbers/NatInt/NZParity.v @@ -47,7 +47,7 @@ Qed. Lemma Even_or_Odd : forall x, Even x \/ Odd x. Proof. - nzinduct x. + intro x; nzinduct x. - left. exists 0. now nzsimpl. - intros x. split; intros [(y,H)|(y,H)]. @@ -86,7 +86,7 @@ Qed. Lemma orb_even_odd : forall n, orb (even n) (odd n) = true. Proof. - intros. + intros n. destruct (Even_or_Odd n) as [H|H]. - rewrite <- even_spec in H. now rewrite H. - rewrite <- odd_spec in H. now rewrite H, orb_true_r. @@ -94,7 +94,7 @@ Qed. Lemma negb_odd : forall n, negb (odd n) = even n. Proof. - intros. + intros n. generalize (Even_or_Odd n) (Even_Odd_False n). rewrite <- even_spec, <- odd_spec. destruct (odd n), (even n) ; simpl; intuition. @@ -188,7 +188,7 @@ Qed. Lemma even_add : forall n m, even (n+m) = Bool.eqb (even n) (even m). Proof. - intros. + intros n m. case_eq (even n); case_eq (even m); rewrite <- ?negb_true_iff, ?negb_even, ?odd_spec, ?even_spec; intros (m',Hm) (n',Hn). @@ -200,7 +200,7 @@ Qed. Lemma odd_add : forall n m, odd (n+m) = xorb (odd n) (odd m). Proof. - intros. rewrite <- !negb_even. rewrite even_add. + intros n m. rewrite <- !negb_even. rewrite even_add. now destruct (even n), (even m). Qed. @@ -208,7 +208,7 @@ Qed. Lemma even_mul : forall n m, even (mul n m) = even n || even m. Proof. - intros. + intros n m. case_eq (even n); simpl; rewrite ?even_spec. - intros (n',Hn). exists (n'*m). now rewrite Hn, mul_assoc. - case_eq (even m); simpl; rewrite ?even_spec. @@ -222,7 +222,7 @@ Qed. Lemma odd_mul : forall n m, odd (mul n m) = odd n && odd m. Proof. - intros. rewrite <- !negb_even. rewrite even_mul. + intros n m. rewrite <- !negb_even. rewrite even_mul. now destruct (even n), (even m). Qed. |