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, 2 insertions, 3 deletions

diff --git a/theories/Arith/Peano_dec.v b/theories/Arith/Peano_dec.v
index 340a79689..f8020a50e 100644
--- a/theories/Arith/Peano_dec.v
+++ b/theories/Arith/Peano_dec.v
@@ -38,8 +38,7 @@ intros m n.
 generalize (eq_refl (S n)).
 generalize n at -1.
 induction (S n) as [|n0 IHn0]; try discriminate.
-clear n; intros n H; injection H; clear H; intro H.
-rewrite <- H; intros le_mn1 le_mn2; clear n H.
+clear n; intros n [= <-] le_mn1 le_mn2.
 pose (def_n2 := eq_refl n0); transitivity (eq_ind _ _ le_mn2 _ def_n2).
   2: reflexivity.
 generalize def_n2; revert le_mn1 le_mn2.
@@ -50,7 +49,7 @@ destruct le_mn1; intros le_mn2; destruct le_mn2.
   now destruct (Nat.nle_succ_diag_l _ le_mn0).
 + intros def_n0; generalize le_mn1; rewrite def_n0; intros le_mn0.
   now destruct (Nat.nle_succ_diag_l _ le_mn0).
-+ intros def_n0; injection def_n0; intros ->.
++ intros def_n0. injection def_n0 as ->.
   rewrite (UIP_nat _ _ def_n0 eq_refl); simpl.
   assert (H : le_mn1 = le_mn2).
     now apply IHn0.