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

1 files changed, 21 insertions, 1 deletions

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.