5 files changed, 19 insertions, 13 deletions
diff --git a/doc/sphinx/README.rst b/doc/sphinx/README.rst
index 1643baf0e8..2264b170fc 100644
--- a/doc/sphinx/README.rst
+++ b/doc/sphinx/README.rst
@@ -303,7 +303,7 @@ In addition to the objects and directives above, the ``coqrst`` Sphinx plugin de
        it names the introduced hypothesis :token:`ident`.
 
     Note that this example also uses ``:token:``.  That's because ``ident`` is
-    defined in the the Coq manual as a grammar production, and ``:token:``
+    defined in the Coq manual as a grammar production, and ``:token:``
     creates a link to that.  When referring to a placeholder that happens to be
     a grammar production, ``:token:`…``` is typically preferable to ``:n:`@…```.
 
diff --git a/doc/sphinx/practical-tools/coq-commands.rst b/doc/sphinx/practical-tools/coq-commands.rst
index 0f51b3eba3..88da58c27d 100644
--- a/doc/sphinx/practical-tools/coq-commands.rst
+++ b/doc/sphinx/practical-tools/coq-commands.rst
@@ -107,7 +107,7 @@ and ``coqtop``, unless stated otherwise:
   to the OCaml loadpath. See also: :ref:`names-of-libraries` and the
   command Declare ML Module Section :ref:`compiled-files`.
 :-Q *directory* dirpath: Add physical path *directory* to the list of
-  directories where |Coq| looks for a file and bind it to the the logical
+  directories where |Coq| looks for a file and bind it to the logical
   directory *dirpath*. The subdirectory structure of *directory* is
   recursively available from |Coq| using absolute names (extending the
   dirpath prefix) (see Section :ref:`qualified-names`).Note that only those
diff --git a/doc/sphinx/proof-engine/ltac.rst b/doc/sphinx/proof-engine/ltac.rst
index 6fbb2fac6d..0310dbead5 100644
--- a/doc/sphinx/proof-engine/ltac.rst
+++ b/doc/sphinx/proof-engine/ltac.rst
@@ -391,7 +391,7 @@ tactic to work (i.e. which does not fail) among a panel of tactics:
    focused goal independently and stops if it succeeds; otherwise it
    tries to apply :n:`v__2` and so on. It fails when there is no
    applicable tactic. In other words,
-   :n:`first [@expr__1 | ... | @expr__n]` behaves, in each goal, as the the first
+   :n:`first [@expr__1 | ... | @expr__n]` behaves, in each goal, as the first
    :n:`v__i` to have *at least* one success.
 
    .. exn:: No applicable tactic.
diff --git a/doc/sphinx/proof-engine/proof-handling.rst b/doc/sphinx/proof-engine/proof-handling.rst
index a9d0c16376..e9aacba3a5 100644
--- a/doc/sphinx/proof-engine/proof-handling.rst
+++ b/doc/sphinx/proof-engine/proof-handling.rst
@@ -358,8 +358,10 @@ same bullet ``b``. See the example below.
 
 Different bullets can be used to nest levels. The scope of bullet does
 not go beyond enclosing ``{`` and ``}``, so bullets can be reused as further
-nesting levels provided they are delimited by these. Available bullets
-are ``-``, ``+``, ``*``, ``--``, ``++``, ``**``, ``---``, ``+++``, ``***``, ... (without a terminating period).
+nesting levels provided they are delimited by these. Bullets are made of
+repeated ``-``, ``+`` or ``*`` symbols:
+
+.. prodn:: bullet ::= {+ - } %| {+ + } %| {+ * }
 
 Note again that when a focused goal is proved a message is displayed
 together with a suggestion about the right bullet or ``}`` to unfocus it
@@ -392,19 +394,23 @@ The following example script illustrates all these features:
     - assert True.
     { trivial. }
     assumption.
+    Qed.
 
+.. exn:: Wrong bullet @bullet__1: Current bullet @bullet__2 is not finished.
 
-.. exn:: Wrong bullet @bullet1: Current bullet @bullet2 is not finished.
-
-   Before using bullet :n:`@bullet1` again, you should first finish proving the current focused goal. Note that :n:`@bullet1` and :n:`@bullet2` may be the same.
+   Before using bullet :n:`@bullet__1` again, you should first finish proving
+   the current focused goal.
+   Note that :n:`@bullet__1` and :n:`@bullet__2` may be the same.
 
-.. exn:: Wrong bullet @bullet1: Bullet @bullet2 is mandatory here.
+.. exn:: Wrong bullet @bullet__1: Bullet @bullet__2 is mandatory here.
 
-   You must put :n:`@bullet2` to focus next goal. No other bullet is allowed here.
+   You must put :n:`@bullet__2` to focus on the next goal. No other bullet is
+   allowed here.
 
 .. exn:: No such goal. Focus next goal with bullet @bullet.
 
-   You tried to apply a tactic but no goals were under focus. Using :n:`@bullet` is  mandatory here.
+   You tried to apply a tactic but no goals were under focus.
+   Using :n:`@bullet` is  mandatory here.
 
 .. exn:: No such goal. Try unfocusing with %{.
 
@@ -433,7 +439,7 @@ Requesting information
 
    .. cmdv:: Show @num
 
-      Displays only the :token:`num` th subgoal.
+      Displays only the :token:`num`\-th subgoal.
 
       .. exn:: No such goal.
 
diff --git a/doc/tools/coqrst/coqdomain.py b/doc/tools/coqrst/coqdomain.py
index e6b71a8293..a0dc16aac7 100644
--- a/doc/tools/coqrst/coqdomain.py
+++ b/doc/tools/coqrst/coqdomain.py
@@ -449,7 +449,7 @@ def NotationRole(role, rawtext, text, lineno, inliner, options={}, content=[]):
        it names the introduced hypothesis :token:`ident`.
 
     Note that this example also uses ``:token:``.  That's because ``ident`` is
-    defined in the the Coq manual as a grammar production, and ``:token:``
+    defined in the Coq manual as a grammar production, and ``:token:``
     creates a link to that.  When referring to a placeholder that happens to be
     a grammar production, ``:token:`…``` is typically preferable to ``:n:`@…```.
     """