induction/destruct : nicer syntax for generating equations (solves #2741)

 The ugly syntax "destruct x as [ ]_eqn:H" is replaced by:

  destruct x eqn:H
  destruct x as [ ] eqn:H

 Some with induction. Of course, the pattern behind "as" is arbitrary.
 For an anonymous version, H could be replaced by ?. The old syntax
 with "_eqn" still works for the moment, by triggers a warning.

 For making this new syntax work, we had to change the seldom-used
 "induction x y z using foo" into "induction x, y, z using foo".
 Now, only one "using" can be used per command instead of one per
 comma-separated group earlier, but I doubt this will bother anyone.

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15566 85f007b7-540e-0410-9357-904b9bb8a0f7

3 files changed, 7 insertions, 7 deletions

diff --git a/theories/MSets/MSetInterface.v b/theories/MSets/MSetInterface.v
index f2b908af0..6778deffa 100644
--- a/theories/MSets/MSetInterface.v
+++ b/theories/MSets/MSetInterface.v
@@ -480,7 +480,7 @@ Module WRaw2SetsOn (E:DecidableType)(M:WRawSets E) <: WSetsOn E.
  Proof.
   intros (s,Hs) (s',Hs').
   change ({M.Equal s s'}+{~M.Equal s s'}).
-  destruct (M.equal s s') as [ ]_eqn:H; [left|right];
+  destruct (M.equal s s') eqn:H; [left|right];
    rewrite <- M.equal_spec; congruence.
  Defined.
 
diff --git a/theories/MSets/MSetList.v b/theories/MSets/MSetList.v
index bcf68f1d4..d9b1fd9bb 100644
--- a/theories/MSets/MSetList.v
+++ b/theories/MSets/MSetList.v
@@ -662,7 +662,7 @@ Module MakeRaw (X: OrderedType) <: RawSets X.
   Proof.
   induction s; simpl; intros.
   split; intuition; inv.
-  destruct (f a) as [ ]_eqn:F; rewrite !InA_cons, ?IHs; intuition.
+  destruct (f a) eqn:F; rewrite !InA_cons, ?IHs; intuition.
   setoid_replace x with a; auto.
   setoid_replace a with x in F; auto; congruence.
   Qed.
@@ -674,7 +674,7 @@ Module MakeRaw (X: OrderedType) <: RawSets X.
   Proof.
   unfold For_all; induction s; simpl; intros.
   split; intros; auto. inv.
-  destruct (f a) as [ ]_eqn:F.
+  destruct (f a) eqn:F.
   rewrite IHs; auto. firstorder. inv; auto.
   setoid_replace x with a; auto.
   split; intros H'. discriminate.
@@ -688,7 +688,7 @@ Module MakeRaw (X: OrderedType) <: RawSets X.
   Proof.
   unfold Exists; induction s; simpl; intros.
   firstorder. discriminate. inv.
-  destruct (f a) as [ ]_eqn:F.
+  destruct (f a) eqn:F.
   firstorder.
   rewrite IHs; auto.
   firstorder.
diff --git a/theories/MSets/MSetWeakList.v b/theories/MSets/MSetWeakList.v
index 76f09c76e..fd4114cd4 100644
--- a/theories/MSets/MSetWeakList.v
+++ b/theories/MSets/MSetWeakList.v
@@ -396,7 +396,7 @@ Module MakeRaw (X:DecidableType) <: WRawSets X.
   induction s; simpl.
   intuition; inv.
   intros.
-  destruct (f a) as [ ]_eqn:E; rewrite ?InA_cons, IHs; intuition.
+  destruct (f a) eqn:E; rewrite ?InA_cons, IHs; intuition.
   setoid_replace x with a; auto.
   setoid_replace a with x in E; auto. congruence.
   Qed.
@@ -420,7 +420,7 @@ Module MakeRaw (X:DecidableType) <: WRawSets X.
   unfold For_all; induction s; simpl.
   intuition. inv.
   intros; inv.
-  destruct (f a) as [ ]_eqn:F.
+  destruct (f a) eqn:F.
   rewrite IHs; intuition. inv; auto.
   setoid_replace x with a; auto.
   split; intros H'; try discriminate.
@@ -436,7 +436,7 @@ Module MakeRaw (X:DecidableType) <: WRawSets X.
   unfold Exists; induction s; simpl.
   split; [discriminate| intros (x & Hx & _); inv].
   intros.
-  destruct (f a) as [ ]_eqn:F.
+  destruct (f a) eqn:F.
   split; auto.
   exists a; auto.
   rewrite IHs; firstorder.