CompSpecType, a clone of CompSpec but in Type instead of Prop

 In interfaces fields like compare_spec, a CompSpec is prefered to get
 nice extraction, but then no "destruct (compare_spec .. ..)" is
 possible in a Type context. Now you can say there
 "destruct (CompSpec2Type (compare_spec ... ...))"
 This translate to the Type variant, and make the analysis on it
 (which is equivalent to analysing the comparison directly).

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12753 85f007b7-540e-0410-9357-904b9bb8a0f7

3 files changed, 20 insertions, 21 deletions

diff --git a/theories/Structures/GenericMinMax.v b/theories/Structures/GenericMinMax.v
index a62d96aa0..68f201897 100644
--- a/theories/Structures/GenericMinMax.v
+++ b/theories/Structures/GenericMinMax.v
@@ -51,26 +51,26 @@ Module GenericMinMax (Import O:OrderedTypeFull') <: HasMinMax O.
 
  Lemma max_l : forall x y, y<=x -> max x y == x.
  Proof.
- intros. unfold max, gmax. destruct (compare_spec x y); auto with relations.
- elim (ge_not_lt x y); auto.
+ intros. unfold max, gmax. case compare_spec; auto with relations.
+ intros; elim (ge_not_lt x y); auto.
  Qed.
 
  Lemma max_r : forall x y, x<=y -> max x y == y.
  Proof.
- intros. unfold max, gmax. destruct (compare_spec x y); auto with relations.
- elim (ge_not_lt y x); auto.
+ intros. unfold max, gmax. case compare_spec; auto with relations.
+ intros; elim (ge_not_lt y x); auto.
  Qed.
 
  Lemma min_l : forall x y, x<=y -> min x y == x.
  Proof.
- intros. unfold min, gmin. destruct (compare_spec x y); auto with relations.
- elim (ge_not_lt y x); auto.
+ intros. unfold min, gmin. case compare_spec; auto with relations.
+ intros; elim (ge_not_lt y x); auto.
  Qed.
 
  Lemma min_r : forall x y, y<=x -> min x y == y.
  Proof.
- intros. unfold min, gmin. destruct (compare_spec x y); auto with relations.
- elim (ge_not_lt x y); auto.
+ intros. unfold min, gmin. case compare_spec; auto with relations.
+ intros; elim (ge_not_lt x y); auto.
  Qed.
 
 End GenericMinMax.
@@ -483,12 +483,12 @@ Lemma max_case_strong : forall n m (P:t -> Type),
   (m<=n -> P n) -> (n<=m -> P m) -> P (max n m).
 Proof.
 intros n m P Compat Hl Hr.
-assert (H:=compare_spec n m). destruct (compare n m).
-assert (n<=m) by (inversion H; rewrite le_lteq; auto).
+destruct (CompSpec2Type (compare_spec n m)) as [EQ|LT|GT].
+assert (n<=m) by (rewrite le_lteq; auto).
 apply (Compat m), Hr; auto. symmetry; apply max_r; auto.
-assert (n<=m) by (inversion H; rewrite le_lteq; auto).
+assert (n<=m) by (rewrite le_lteq; auto).
 apply (Compat m), Hr; auto. symmetry; apply max_r; auto.
-assert (m<=n) by (inversion H; rewrite le_lteq; auto).
+assert (m<=n) by (rewrite le_lteq; auto).
 apply (Compat n), Hl; auto. symmetry; apply max_l; auto.
 Defined.
 
@@ -512,12 +512,12 @@ Lemma min_case_strong : forall n m (P:O.t -> Type),
  (n<=m -> P n) -> (m<=n -> P m) -> P (min n m).
 Proof.
 intros n m P Compat Hl Hr.
-assert (H:=compare_spec n m). destruct (compare n m).
-assert (n<=m) by (inversion H; rewrite le_lteq; auto).
+destruct (CompSpec2Type (compare_spec n m)) as [EQ|LT|GT].
+assert (n<=m) by (rewrite le_lteq; auto).
 apply (Compat n), Hl; auto. symmetry; apply min_l; auto.
-assert (n<=m) by (inversion H; rewrite le_lteq; auto).
+assert (n<=m) by (rewrite le_lteq; auto).
 apply (Compat n), Hl; auto. symmetry; apply min_l; auto.
-assert (m<=n) by (inversion H; rewrite le_lteq; auto).
+assert (m<=n) by (rewrite le_lteq; auto).
 apply (Compat m), Hr; auto. symmetry; apply min_r; auto.
 Defined.
 
diff --git a/theories/Structures/OrdersAlt.v b/theories/Structures/OrdersAlt.v
index 261e75e1c..d86b02a15 100644
--- a/theories/Structures/OrdersAlt.v
+++ b/theories/Structures/OrdersAlt.v
@@ -101,9 +101,8 @@ Module Backport_OT (O:OrderedType) <: OrderedTypeOrig.
 
  Definition compare : forall x y, Compare lt eq x y.
  Proof.
-  intros. assert (H:=O.compare_spec x y).
-  destruct (O.compare x y); [apply EQ|apply LT|apply GT];
-   inversion H; auto.
+  intros x y; destruct (CompSpec2Type (O.compare_spec x y));
+   [apply EQ|apply LT|apply GT]; auto.
  Defined.
 
 End Backport_OT.
diff --git a/theories/Structures/OrdersFacts.v b/theories/Structures/OrdersFacts.v
index a318ecb85..a28b79776 100644
--- a/theories/Structures/OrdersFacts.v
+++ b/theories/Structures/OrdersFacts.v
@@ -134,8 +134,8 @@ Module OrderedTypeFacts (Import O: OrderedType').
 
   Lemma lt_dec : forall x y : t, {lt x y} + {~ lt x y}.
   Proof.
-   intros; assert (H:=compare_spec x y); destruct (compare x y);
-    [ right | left | right ]; inversion_clear H; order.
+   intros x y; destruct (CompSpec2Type (compare_spec x y));
+    [ right | left | right ]; order.
   Defined.
 
   Definition eqb x y : bool := if eq_dec x y then true else false.