diff options
Diffstat (limited to 'theories/ZArith/Zdigits.v')
| -rw-r--r-- | theories/ZArith/Zdigits.v | 26 |
1 files changed, 13 insertions, 13 deletions
diff --git a/theories/ZArith/Zdigits.v b/theories/ZArith/Zdigits.v index a9348785a..d252b3e92 100644 --- a/theories/ZArith/Zdigits.v +++ b/theories/ZArith/Zdigits.v @@ -90,13 +90,13 @@ Section ENCODING_VALUE. Lemma Zmod2_twice : forall z:Z, z = (2 * Zmod2 z + bit_value (Z.odd z))%Z. Proof. - destruct z; simpl in |- *. + destruct z; simpl. trivial. - destruct p; simpl in |- *; trivial. + destruct p; simpl; trivial. - destruct p; simpl in |- *. - destruct p as [p| p| ]; simpl in |- *. + destruct p; simpl. + destruct p as [p| p| ]; simpl. rewrite <- (Pos.pred_double_succ p); trivial. trivial. @@ -145,17 +145,17 @@ Section Z_BRIC_A_BRAC. (z >= 0)%Z -> Z_to_binary (S n) (bit_value b + 2 * z) = Bcons b n (Z_to_binary n z). Proof. - destruct b; destruct z; simpl in |- *; auto. + destruct b; destruct z; simpl; auto. intro H; elim H; trivial. Qed. Lemma binary_value_pos : forall (n:nat) (bv:Bvector n), (binary_value n bv >= 0)%Z. Proof. - induction bv as [| a n v IHbv]; simpl in |- *. + induction bv as [| a n v IHbv]; simpl. omega. - destruct a; destruct (binary_value n v); simpl in |- *; auto. + destruct a; destruct (binary_value n v); simpl; auto. auto with zarith. Qed. @@ -174,7 +174,7 @@ Section Z_BRIC_A_BRAC. Proof. destruct b; destruct z as [| p| p]; auto. destruct p as [p| p| ]; auto. - destruct p as [p| p| ]; simpl in |- *; auto. + destruct p as [p| p| ]; simpl; auto. intros; rewrite (Pos.succ_pred_double p); trivial. Qed. @@ -201,7 +201,7 @@ Section Z_BRIC_A_BRAC. auto. destruct p; auto. - simpl in |- *; intros; omega. + simpl; intros; omega. intro H; elim H; trivial. Qed. @@ -233,7 +233,7 @@ Section Z_BRIC_A_BRAC. Lemma Zeven_bit_value : forall z:Z, Zeven.Zeven z -> bit_value (Z.odd z) = 0%Z. Proof. - destruct z; unfold bit_value in |- *; auto. + destruct z; unfold bit_value; auto. destruct p; tauto || (intro H; elim H). destruct p; tauto || (intro H; elim H). Qed. @@ -241,7 +241,7 @@ Section Z_BRIC_A_BRAC. Lemma Zodd_bit_value : forall z:Z, Zeven.Zodd z -> bit_value (Z.odd z) = 1%Z. Proof. - destruct z; unfold bit_value in |- *; auto. + destruct z; unfold bit_value; auto. intros; elim H. destruct p; tauto || (intros; elim H). destruct p; tauto || (intros; elim H). @@ -310,7 +310,7 @@ Section COHERENT_VALUE. (z < two_power_nat n)%Z -> binary_value n (Z_to_binary n z) = z. Proof. induction n as [| n IHn]. - unfold two_power_nat, shift_nat in |- *; simpl in |- *; intros; omega. + unfold two_power_nat, shift_nat; simpl; intros; omega. intros; rewrite Z_to_binary_Sn_z. rewrite binary_value_Sn. @@ -328,7 +328,7 @@ Section COHERENT_VALUE. (z < two_power_nat n)%Z -> two_compl_value n (Z_to_two_compl n z) = z. Proof. induction n as [| n IHn]. - unfold two_power_nat, shift_nat in |- *; simpl in |- *; intros. + unfold two_power_nat, shift_nat; simpl; intros. assert (z = (-1)%Z \/ z = 0%Z). omega. intuition; subst z; trivial. |