4 files changed, 19 insertions, 27 deletions
diff --git a/doc/sphinx/addendum/canonical-structures.rst b/doc/sphinx/addendum/canonical-structures.rst
index a9d894cab5..dd21ea09bd 100644
--- a/doc/sphinx/addendum/canonical-structures.rst
+++ b/doc/sphinx/addendum/canonical-structures.rst
@@ -92,7 +92,7 @@ and use the ``==`` notation on terms of this type.
 Derived Canonical Structures
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-We know how to use ``== `` on base types, like ``nat``, ``bool``, ``Z``. Here we show
+We know how to use ``==`` on base types, like ``nat``, ``bool``, ``Z``. Here we show
 how to deal with type constructors, i.e. how to make the following
 example work:
 
diff --git a/doc/sphinx/addendum/implicit-coercions.rst b/doc/sphinx/addendum/implicit-coercions.rst
index d15aacad44..d5523e8561 100644
--- a/doc/sphinx/addendum/implicit-coercions.rst
+++ b/doc/sphinx/addendum/implicit-coercions.rst
@@ -154,8 +154,10 @@ Declaring Coercions
   .. warn:: Ambiguous path.
 
      When the coercion :token:`qualid` is added to the inheritance graph,
-     invalid coercion paths are ignored; they are signaled by a warning
-     displaying these paths of the form :g:`[f₁;..;fₙ] : C >-> D`.
+     invalid coercion paths are ignored. The :cmd:`Coercion` command tries to check
+     that they are convertible with existing ones on the same classes.
+     The paths for which this check fails are displayed by a warning in the form
+     :g:`[f₁;..;fₙ] : C >-> D`.
 
   .. cmdv:: Local Coercion @qualid : @class >-> @class
 
@@ -322,21 +324,8 @@ are also forgotten.
 Coercions and Modules
 ---------------------
 
-.. flag:: Automatic Coercions Import
-
-   Since |Coq| version 8.3, the coercions present in a module are activated
-   only when the module is explicitly imported. Formerly, the coercions
-   were activated as soon as the module was required, whether it was
-   imported or not.
-
-   This option makes it possible to recover the behavior of the versions of
-   |Coq| prior to 8.3.
-
-.. warn:: Coercion used but not in scope: @qualid. If you want to use this coercion, please Import the module that contains it.
-
-   This warning is emitted when typechecking relies on a coercion
-   contained in a module that has not been explicitely imported. It helps
-   migrating code and stop relying on the option above.
+The coercions present in a module are activated only when the module is
+explicitly imported.
 
 Examples
 --------
diff --git a/doc/sphinx/addendum/ring.rst b/doc/sphinx/addendum/ring.rst
index 20e4c6a3d6..3b350d5dc0 100644
--- a/doc/sphinx/addendum/ring.rst
+++ b/doc/sphinx/addendum/ring.rst
@@ -323,7 +323,7 @@ The syntax for adding a new ring is
    decidable :n:`@term`
       declares the ring as computational. The expression
       :n:`@term` is the correctness proof of an equality test ``?=!``
-      (which  hould be evaluable). Its type should be of the form
+      (which should be evaluable). Its type should be of the form
       ``forall x y, x ?=! y = true → x == y``.
 
    morphism :n:`@term`
diff --git a/doc/sphinx/addendum/type-classes.rst b/doc/sphinx/addendum/type-classes.rst
index e6a5b3972c..b069cf27f4 100644
--- a/doc/sphinx/addendum/type-classes.rst
+++ b/doc/sphinx/addendum/type-classes.rst
@@ -561,6 +561,8 @@ Settings
 
 .. flag:: Refine Instance Mode
 
+   .. deprecated:: 8.10
+
    This flag allows to switch the behavior of instance declarations made through
    the Instance command.
 
@@ -573,18 +575,19 @@ Settings
 Typeclasses eauto `:=`
 ~~~~~~~~~~~~~~~~~~~~~~
 
-.. cmd:: Typeclasses eauto := {? debug} {? {dfs | bfs}} depth
+.. cmd:: Typeclasses eauto := {? debug} {? (dfs) | (bfs) } @num
    :name: Typeclasses eauto
 
    This command allows more global customization of the typeclass
    resolution tactic. The semantics of the options are:
 
-   + ``debug`` In debug mode, the trace of successfully applied tactics is
-     printed.  This value can also be set with :flag:`Typeclasses Debug`.
+   + ``debug`` This sets the debug mode. In debug mode, the trace of
+     successfully applied tactics is printed. The debug mode can also
+     be set with :flag:`Typeclasses Debug`.
 
-   + ``dfs, bfs`` This sets the search strategy to depth-first search (the
-     default) or breadth-first search.  This value can also be set with
-     :flag:`Typeclasses Iterative Deepening`.
+   + ``(dfs)``, ``(bfs)`` This sets the search strategy to depth-first
+     search (the default) or breadth-first search. The search strategy
+     can also be set with :flag:`Typeclasses Iterative Deepening`.
 
-   + ``depth`` This sets the depth limit of the search.  This value can also be set with
-     :opt:`Typeclasses Depth`.
+   + :token:`num` This sets the depth limit of the search. The depth
+     limit can also be set with :opt:`Typeclasses Depth`.