diff options
Diffstat (limited to 'theories/Numbers/Integer/BigZ/BigZ.v')
| -rw-r--r-- | theories/Numbers/Integer/BigZ/BigZ.v | 18 |
1 files changed, 11 insertions, 7 deletions
diff --git a/theories/Numbers/Integer/BigZ/BigZ.v b/theories/Numbers/Integer/BigZ/BigZ.v index 09abf424..cb920124 100644 --- a/theories/Numbers/Integer/BigZ/BigZ.v +++ b/theories/Numbers/Integer/BigZ/BigZ.v @@ -8,7 +8,7 @@ (* Benjamin Gregoire, Laurent Thery, INRIA, 2007 *) (************************************************************************) -(*i $Id: BigZ.v 11040 2008-06-03 00:04:16Z letouzey $ i*) +(*i $Id: BigZ.v 11282 2008-07-28 11:51:53Z msozeau $ i*) Require Export BigN. Require Import ZMulOrder. @@ -42,25 +42,27 @@ Infix "?=" := BigZ.compare : bigZ_scope. Infix "==" := BigZ.eq (at level 70, no associativity) : bigZ_scope. Infix "<" := BigZ.lt : bigZ_scope. Infix "<=" := BigZ.le : bigZ_scope. +Notation "x > y" := (BigZ.lt y x)(only parsing) : bigZ_scope. +Notation "x >= y" := (BigZ.le y x)(only parsing) : bigZ_scope. Notation "[ i ]" := (BigZ.to_Z i) : bigZ_scope. Open Scope bigZ_scope. (** Some additional results about [BigZ] *) -Theorem spec_to_Z: forall n:bigZ, +Theorem spec_to_Z: forall n:bigZ, BigN.to_Z (BigZ.to_N n) = ((Zsgn [n]) * [n])%Z. Proof. -intros n; case n; simpl; intros p; +intros n; case n; simpl; intros p; generalize (BigN.spec_pos p); case (BigN.to_Z p); auto. intros p1 H1; case H1; auto. intros p1 H1; case H1; auto. Qed. -Theorem spec_to_N n: +Theorem spec_to_N n: ([n] = Zsgn [n] * (BigN.to_Z (BigZ.to_N n)))%Z. Proof. -intros n; case n; simpl; intros p; +intros n; case n; simpl; intros p; generalize (BigN.spec_pos p); case (BigN.to_Z p); auto. intros p1 H1; case H1; auto. intros p1 H1; case H1; auto. @@ -69,7 +71,7 @@ Qed. Theorem spec_to_Z_pos: forall n, (0 <= [n])%Z -> BigN.to_Z (BigZ.to_N n) = [n]. Proof. -intros n; case n; simpl; intros p; +intros n; case n; simpl; intros p; generalize (BigN.spec_pos p); case (BigN.to_Z p); auto. intros p1 _ H1; case H1; auto. intros p1 H1; case H1; auto. @@ -87,7 +89,7 @@ Qed. (** [BigZ] is a ring *) -Lemma BigZring : +Lemma BigZring : ring_theory BigZ.zero BigZ.one BigZ.add BigZ.mul BigZ.sub BigZ.opp BigZ.eq. Proof. constructor. @@ -102,6 +104,8 @@ exact sub_opp. exact add_opp. Qed. +Typeclasses unfold NZadd NZmul NZsub NZeq. + Add Ring BigZr : BigZring. (** Todo: tactic translating from [BigZ] to [Z] + omega *) |