Keyed unification option, compiling the whole standard library

(but deactivated still).

Set Keyed Unification to activate the option, which changes
subterm selection to _always_ use full conversion _after_ finding a
subterm whose head/key matches the key of the term we're looking for.
This applies to rewrite and higher-order unification in
apply/elim/destruct.

Most proof scripts already abide by these semantics. For those that
don't, it's usually only a matter of using:

Declare Equivalent Keys f g.

This make keyed unification consider f and g to match as keys.
This takes care of most cases of abbreviations: typically Def foo :=
bar and rewriting with a bar-headed lhs in a goal mentioning foo works
once they're set equivalent.
For canonical structures, these hints should be automatically declared.

For non-global-reference headed terms, the key is the constructor name
(Sort, Prod...). Evars and metas are no keys.

INCOMPATIBILITIES:
In FMapFullAVL, a Function definition doesn't go through with keyed
unification on.

2 files changed, 5 insertions, 4 deletions

diff --git a/theories/Reals/Binomial.v b/theories/Reals/Binomial.v
index ad076c488..16f2661fe 100644
--- a/theories/Reals/Binomial.v
+++ b/theories/Reals/Binomial.v
@@ -172,13 +172,12 @@ Proof.
   apply sum_eq.
   intros; apply H1.
   unfold N; apply le_lt_trans with n; [ assumption | apply lt_n_Sn ].
-  intros; unfold Bn, Cn.
-  replace (S N - S i)%nat with (N - i)%nat; reflexivity.
+  reflexivity.
   unfold An; fold N; rewrite <- minus_n_n; rewrite H0;
     simpl; ring.
   apply sum_eq.
-  intros; unfold An, Bn; replace (S N - S i)%nat with (N - i)%nat;
-    [ idtac | reflexivity ].
+  intros; unfold An, Bn.
+  change (S N - S i)%nat with (N - i)%nat.
   rewrite <- pascal;
     [ ring
       | apply le_lt_trans with n; [ assumption | unfold N; apply lt_n_Sn ] ].
diff --git a/theories/Reals/Rlimit.v b/theories/Reals/Rlimit.v
index 375cc2752..cf7b91af8 100644
--- a/theories/Reals/Rlimit.v
+++ b/theories/Reals/Rlimit.v
@@ -174,6 +174,8 @@ Definition limit_in (X X':Metric_Space) (f:Base X -> Base X')
 Definition R_met : Metric_Space :=
   Build_Metric_Space R R_dist R_dist_pos R_dist_sym R_dist_refl R_dist_tri.
 
+Declare Equivalent Keys dist R_dist.
+
 (*******************************)
 (** *      Limit 1 arg         *)
 (*******************************)