Giving a more natural semantics to injection by default.

There were three versions of injection:

1. "injection term" without "as" clause:
   was leaving hypotheses on the goal in reverse order
2. "injection term as ipat", first version:
   was introduction hypotheses using ipat in reverse order without
   checking that the number of ipat was the size of the injection
   (activated with "Unset Injection L2R Pattern Order")
3. "injection term as ipat", second version:
   was introduction hypotheses using ipat in left-to-right order
   checking that the number of ipat was the size of the injection
   and clearing the injecting term by default if an hypothesis
   (activated with "Set Injection L2R Pattern Order", default one from 8.5)

There is now:

4. "injection term" without "as" clause, new version:
   introducing the components of the injection in the context in
   left-to-right order using default intro-patterns "?"
   and clearing the injecting term by default if an hypothesis
   (activated with "Set Structural Injection")

The new versions 3. and 4. are the "expected" ones in the sense that
they have the following good properties:
- introduction in the context is in the natural left-to-right order
- "injection" behaves the same with and without "as", always
  introducing the hypotheses in the goal what corresponds to the
  natural expectation as the changes I made in the proof scripts for
  adaptation confirm
- clear the "injection" hypothesis when an hypothesis which is the
  natural expectation as the changes I made in the proof scripts for
  adaptation confirm

The compatibility can be preserved by "Unset Structural Injection" or
by calling "simple injection".

The flag is currently off.

1 files changed, 3 insertions, 6 deletions

diff --git a/theories/Wellfounded/Lexicographic_Product.v b/theories/Wellfounded/Lexicographic_Product.v
index 4b8447f49..b2ada2f91 100644
--- a/theories/Wellfounded/Lexicographic_Product.v
+++ b/theories/Wellfounded/Lexicographic_Product.v
@@ -44,14 +44,11 @@ Section WfLexicographic_Product.
     apply H2.
     auto with sets.
 
-    injection H1.
-    destruct 2.
-    injection H3.
-    destruct 2; auto with sets.
+    injection H1 as <- _.
+    injection H3 as <- _; auto with sets.
 
     rewrite <- H1.
-    injection H3; intros _ Hx1.
-    subst x1.
+    injection H3 as -> H3.
     apply IHAcc0.
     elim inj_pair2 with A B x y' x0; assumption.
   Defined.