First release of Vector library.

To avoid names&notations clashs with list, Vector shouldn't be
"Import"ed but one can "Import Vector.VectorNotations." to have
notations.

SetoidVector at least remains to do.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13702 85f007b7-540e-0410-9357-904b9bb8a0f7

5 files changed, 30 insertions, 23 deletions

diff --git a/theories/Arith/Bool_nat.v b/theories/Arith/Bool_nat.v
index 08a090325..f384e1488 100644
--- a/theories/Arith/Bool_nat.v
+++ b/theories/Arith/Bool_nat.v
@@ -34,4 +34,4 @@ Definition nat_noteq_bool x y :=
   bool_of_sumbool (sumbool_not _ _ (eq_nat_dec x y)).
 
 Definition zerop_bool x := bool_of_sumbool (zerop x).
-Definition notzerop_bool x := bool_of_sumbool (notzerop x).
\ No newline at end of file
+Definition notzerop_bool x := bool_of_sumbool (notzerop x).
diff --git a/theories/Arith/Compare.v b/theories/Arith/Compare.v
index c6bf35bb0..c9e6d3cf3 100644
--- a/theories/Arith/Compare.v
+++ b/theories/Arith/Compare.v
@@ -50,4 +50,4 @@ Qed.
 
 Require Export Wf_nat.
 
-Require Export Min Max.
\ No newline at end of file
+Require Export Min Max.
diff --git a/theories/Arith/Min.v b/theories/Arith/Min.v
index 2b2cf860d..bcfbe0efe 100644
--- a/theories/Arith/Min.v
+++ b/theories/Arith/Min.v
@@ -39,4 +39,4 @@ Definition min_glb := Nat.min_glb.
 (* Compatibility *)
 Notation min_case2 := min_case (only parsing).
 Notation min_SS := Nat.succ_min_distr (only parsing).
-(* end hide *)
\ No newline at end of file
+(* end hide *)
diff --git a/theories/Arith/Peano_dec.v b/theories/Arith/Peano_dec.v
index 9e3823d7a..6eb667c11 100644
--- a/theories/Arith/Peano_dec.v
+++ b/theories/Arith/Peano_dec.v
@@ -7,7 +7,8 @@
 (************************************************************************)
 
 Require Import Decidable.
-
+Require Eqdep_dec.
+Require Import Le Lt.
 Open Local Scope nat_scope.
 
 Implicit Types m n x y : nat.
@@ -30,3 +31,22 @@ Hint Resolve O_or_S eq_nat_dec: arith.
 Theorem dec_eq_nat : forall n m, decidable (n = m).
   intros x y; unfold decidable in |- *; elim (eq_nat_dec x y); auto with arith.
 Defined.
+
+Definition UIP_nat:= Eqdep_dec.UIP_dec eq_nat_dec.
+
+Lemma le_unique: forall m n (h1 h2: m <= n), h1 = h2.
+Proof.
+fix 3.
+refine (fun m _ h1 => match h1 as h' in _ <= k return forall hh: m <= k, h' = hh
+  with le_n => _ |le_S i H => _ end).
+refine (fun hh => match hh as h' in _ <= k return forall eq: m = k, 
+  le_n m = match eq in _ = p return m <= p -> m <= m with |eq_refl => fun bli => bli end h' with
+    |le_n => fun eq => _ |le_S j H' => fun eq => _ end eq_refl).
+rewrite (UIP_nat _ _ eq eq_refl). reflexivity.
+subst m. destruct (Lt.lt_irrefl j H').
+refine (fun hh => match hh as h' in _ <= k return match k as k' return m <= k' -> Prop
+  with |0 => fun _ => True |S i' => fun h'' => forall H':m <= i', le_S m i' H' = h'' end h'
+    with |le_n => _ |le_S j H2 => fun H' => _ end H).
+destruct m. exact I. intros; destruct (Lt.lt_irrefl m H').
+f_equal. apply le_unique.
+Qed.
diff --git a/theories/Arith/Plus.v b/theories/Arith/Plus.v
index 48d730319..eb2d4df4c 100644
--- a/theories/Arith/Plus.v
+++ b/theories/Arith/Plus.v
@@ -24,17 +24,10 @@ Open Local Scope nat_scope.
 
 Implicit Types m n p q : nat.
 
-(** * Zero is neutral *)
-
-Lemma plus_0_l : forall n, 0 + n = n.
-Proof.
-  reflexivity.
-Qed.
-
-Lemma plus_0_r : forall n, n + 0 = n.
-Proof.
-  intro; symmetry  in |- *; apply plus_n_O.
-Qed.
+(** * Zero is neutral 
+Deprecated : Already in Init/Peano.v *)
+Definition plus_0_l n := eq_sym (plus_O_n n).
+Definition plus_0_r n := eq_sym (plus_n_O n).
 
 (** * Commutativity *)
 
@@ -47,14 +40,8 @@ Hint Immediate plus_comm: arith v62.
 
 (** * Associativity *)
 
-Lemma plus_Snm_nSm : forall n m, S n + m = n + S m.
-Proof.
-  intros.
-  simpl in |- *.
-  rewrite (plus_comm n m).
-  rewrite (plus_comm n (S m)).
-  trivial with arith.
-Qed.
+Definition plus_Snm_nSm : forall n m, S n + m = n + S m:=
+ plus_n_Sm.
 
 Lemma plus_assoc : forall n m p, n + (m + p) = n + m + p.
 Proof.