Various bug fixes in type classes and subtac:

- Cases on multiple objects
- Avoid dangerous coercion with evars in subtac_coercion
- Resolve typeclasses method-by-method to get better error messages.
- Correct merging of instance databases (and add debug printer)
- Fix a script in NOrder where a setoid_replace was not working before.


git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11198 85f007b7-540e-0410-9357-904b9bb8a0f7

2 files changed, 7 insertions, 8 deletions

diff --git a/theories/Classes/Morphisms.v b/theories/Classes/Morphisms.v
index 724021799..3ffa8040d 100644
--- a/theories/Classes/Morphisms.v
+++ b/theories/Classes/Morphisms.v
@@ -75,7 +75,7 @@ Arguments Scope respectful [type_scope type_scope signature_scope signature_scop
 
 Open Local Scope signature_scope.
 
-(** Pointwise lifting is just respect with leibnize equality on the left. *)
+(** Pointwise lifting is just respect with leibniz equality on the left. *)
 
 Definition pointwise_relation {A B : Type} (R : relation B) : relation (A -> B) := 
   fun f g => forall x : A, R (f x) (g x).
@@ -222,8 +222,8 @@ Program Instance trans_sym_contra_impl_morphism
     transitivity x0... symmetry...
   Qed.
 
-Program Instance equivalence_partial_app_morphism
-  [ Equivalence A R ] : Morphism (R ==> iff) (R x) | 1.
+Program Instance per_partial_app_morphism
+  [ PER A R ] : Morphism (R ==> iff) (R x) | 1.
 
   Next Obligation.
   Proof with auto.
diff --git a/theories/Numbers/Natural/Abstract/NOrder.v b/theories/Numbers/Natural/Abstract/NOrder.v
index bcd4b92d6..5212e6381 100644
--- a/theories/Numbers/Natural/Abstract/NOrder.v
+++ b/theories/Numbers/Natural/Abstract/NOrder.v
@@ -309,13 +309,12 @@ Proof NZgt_wf.
 
 Theorem lt_wf_0 : well_founded lt.
 Proof.
-assert (H : relations_eq lt (fun n m : N => 0 <= n /\ n < m)).
+setoid_replace lt with (fun n m : N => 0 <= n /\ n < m) 
+  using relation (@relations_eq N N).
+apply lt_wf.
 intros x y; split.
 intro H; split; [apply le_0_l | assumption]. now intros [_ H].
-rewrite H; apply lt_wf.
-(* does not work:
-setoid_replace lt with (fun n m : N => 0 <= n /\ n < m) using relation relations_eq.*)
-Qed.
+Defined.
 
 (* Theorems that are true for natural numbers but not for integers *)