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diff --git a/doc/refman/AddRefMan-pre.tex b/doc/refman/AddRefMan-pre.tex
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index 856a823de0..0000000000
--- a/doc/refman/AddRefMan-pre.tex
+++ /dev/null
@@ -1,63 +0,0 @@
-%\coverpage{Addendum to the Reference Manual}{\ }
-%\addcontentsline{toc}{part}{Additional documentation}
-%BEGIN LATEX
-\setheaders{Presentation of the Addendum}
-%END LATEX
-\chapter*{Presentation of the Addendum}
-%HEVEA\cutname{addendum.html}
-
-Here you will find several pieces of additional documentation for the
-\Coq\ Reference Manual. Each of this chapters is concentrated on a
-particular topic, that should interest only a fraction of the \Coq\
-users: that's the reason why they are apart from the Reference
-Manual.
-
-\begin{description}
-
-\item[Extended pattern-matching] This chapter details the use of
-  generalized pattern-matching. It is contributed by Cristina Cornes
-  and Hugo Herbelin.
-
-\item[Implicit coercions] This chapter details the use of the coercion
-  mechanism.  It is contributed by Amokrane Saïbi.
-
-%\item[Proof of imperative programs] This chapter explains how to
-%  prove properties of annotated programs with imperative features.
-%  It is contributed by Jean-Christophe Filliâtre
-
-\item[Program extraction] This chapter explains how to extract in practice ML
-  files from $\FW$ terms.   It is contributed by Jean-Christophe
-  Filliâtre and Pierre Letouzey.
-
-\item[Program] This chapter explains the use of the \texttt{Program}
-  vernacular which allows the development of certified
-  programs in \Coq. It is contributed by Matthieu Sozeau and replaces
-  the previous \texttt{Program} tactic by Catherine Parent.
-
-%\item[Natural] This chapter is due to Yann Coscoy. It is the user
-%  manual of the tools he wrote for printing proofs in natural
-%  language. At this time, French and English languages are supported.
-
-\item[omega] \texttt{omega}, written by Pierre Crégut, solves a whole
-  class of arithmetic problems.
-
-\item[The {\tt ring} tactic] This is a tactic to do AC rewriting. This
-  chapter explains how to use it and how it works.
-  The chapter is contributed by Patrick Loiseleur.
-
-\item[The {\tt Setoid\_replace} tactic] This is a
-  tactic to do rewriting on types equipped with specific (only partially
-  substitutive) equality. The chapter is contributed by Clément Renard.
-
-\item[Calling external provers] This chapter describes several tactics
-  which call external provers.
-
-\end{description}
-
-\atableofcontents
-
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "Reference-Manual"
-%%% End: 
diff --git a/doc/refman/Misc.tex b/doc/refman/Misc.tex
deleted file mode 100644
index ab00fbfe37..0000000000
--- a/doc/refman/Misc.tex
+++ /dev/null
@@ -1,63 +0,0 @@
-\achapter{\protect{Miscellaneous extensions}}
-%HEVEA\cutname{miscellaneous.html}
-
-\asection{Program derivation}
-
-Coq comes with an extension called {\tt Derive}, which supports
-program derivation. Typically in the style of Bird and Meertens or
-derivations of program refinements. To use the {\tt Derive} extension
-it must first be required with {\tt Require Coq.Derive.Derive}. When
-the extension is loaded, it provides the following command.
-
-\subsection[\tt Derive \ident$_1$ SuchThat \term{} As \ident$_2$]
-       {\tt Derive \ident$_1$ SuchThat \term{} As \ident$_2$\comindex{Derive}}
-
-The name $\ident_1$ can appear in \term. This command opens a new
-proof presenting the user with a goal for \term{} in which the name
-$\ident_1$ is bound to a existential variables {\tt ?x} (formally,
-there are other goals standing for the existential variables but they
-are shelved, as described in Section~\ref{shelve}).
-
-When the proof ends two constants are defined:
-\begin{itemize}
-\item The first one is name $\ident_1$ and is defined as the proof of
-  the shelved goal (which is also the value of {\tt ?x}). It is
-always transparent.
-\item The second one is name $\ident_2$. It has type {\tt \term}, and
-  its body is the proof of the initially visible goal. It is opaque if
-  the proof ends with {\tt Qed}, and transparent if the proof ends
-  with {\tt Defined}.
-\end{itemize}
-
-\Example
-\begin{coq_example*}
-Require Coq.derive.Derive.
-Require Import Coq.Numbers.Natural.Peano.NPeano.
-
-Section P.
-
-Variables (n m k:nat).
-
-\end{coq_example*}
-\begin{coq_example}
-Derive p SuchThat ((k*n)+(k*m) = p) As h.
-Proof.
-rewrite <- Nat.mul_add_distr_l.
-subst p.
-reflexivity.
-\end{coq_example}
-\begin{coq_example*}
-Qed.
-
-End P.
-
-\end{coq_example*}
-\begin{coq_example}
-Print p.
-Check h.
-\end{coq_example}
-
-Any property can be used as \term, not only an equation. In
-particular, it could be an order relation specifying some form of
-program refinement or a non-executable property from which deriving a
-program is convenient.
diff --git a/doc/refman/RefMan-gal.tex b/doc/refman/RefMan-gal.tex
deleted file mode 100644
index 41ea0a5dcd..0000000000
--- a/doc/refman/RefMan-gal.tex
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@@ -1,1737 +0,0 @@
-\chapter{The \gallina{} specification language
-\label{Gallina}\index{Gallina}}
-%HEVEA\cutname{gallina.html}
-\label{BNF-syntax} % Used referred to as a chapter label
-
-This chapter describes \gallina, the specification language of {\Coq}.
-It allows developing mathematical theories and proofs of specifications
-of programs.  The theories are built from axioms, hypotheses,
-parameters, lemmas, theorems and definitions of constants, functions,
-predicates and sets. The syntax of logical objects involved in
-theories is described in Section~\ref{term}. The language of
-commands, called {\em The Vernacular} is described in section
-\ref{Vernacular}.
-
-In {\Coq}, logical objects are typed to ensure their logical
-correctness. The rules implemented by the typing algorithm are described in
-Chapter \ref{Cic}.
-
-\subsection*{About the grammars in the manual
-\index{BNF metasyntax}}
-
-Grammars are presented in Backus-Naur form (BNF). Terminal symbols are
-set in {\tt typewriter font}.  In addition, there are special
-notations for regular expressions.
-
-An expression enclosed in square brackets \zeroone{\ldots} means at
-most one occurrence of this expression (this corresponds to an
-optional component).
-
-The notation ``\nelist{\entry}{sep}'' stands for a non empty
-sequence of expressions parsed by {\entry} and
-separated by the literal ``{\tt sep}''\footnote{This is similar to the
-expression ``{\entry} $\{$ {\tt sep} {\entry} $\}$'' in
-standard BNF, or ``{\entry}~{$($} {\tt sep} {\entry} {$)$*}'' in
-the syntax of regular expressions.}.
-
-Similarly, the notation ``\nelist{\entry}{}'' stands for a non
-empty sequence of expressions parsed by the ``{\entry}'' entry,
-without any separator between.
-
-Finally, the notation ``\sequence{\entry}{\tt sep}'' stands for a
-possibly empty sequence of expressions parsed by the ``{\entry}'' entry,
-separated by the literal ``{\tt sep}''.
-
-\section{Lexical conventions
-\label{lexical}\index{Lexical conventions}}
-
-\paragraph{Blanks}
-Space, newline and horizontal tabulation are considered as blanks.
-Blanks are ignored but they separate tokens.
-
-\paragraph{Comments}
-
-Comments in {\Coq} are enclosed between {\tt (*} and {\tt
-  *)}\index{Comments}, and can be nested. They can contain any
-character. However, string literals must be correctly closed. Comments
-are treated as blanks.
-
-\paragraph{Identifiers and access identifiers}
-
-Identifiers, written {\ident}, are sequences of letters, digits,
-\verb!_! and \verb!'!, that do not start with a digit or \verb!'!.
-That is, they are recognized by the following lexical class:
-
-\index{ident@\ident}
-\begin{center}
-\begin{tabular}{rcl} 
-{\firstletter} & ::= & {\tt a..z} $\mid$ {\tt A..Z} $\mid$ {\tt \_}
-$\mid$ {\tt unicode-letter}  
-\\
-{\subsequentletter} & ::= & {\tt a..z} $\mid$ {\tt A..Z} $\mid$ {\tt 0..9}
-$\mid$ {\tt \_} % $\mid$ {\tt \$}
-$\mid$ {\tt '} 
-$\mid$ {\tt unicode-letter}  
-$\mid$ {\tt unicode-id-part} \\
-{\ident} & ::= & {\firstletter} \sequencewithoutblank{\subsequentletter}{}
-\end{tabular}
-\end{center}
-All characters are meaningful. In particular, identifiers are
-case-sensitive.  The entry {\tt unicode-letter} non-exhaustively
-includes Latin, Greek, Gothic, Cyrillic, Arabic, Hebrew, Georgian,
-Hangul, Hiragana and Katakana characters, CJK ideographs, mathematical
-letter-like symbols, hyphens, non-breaking space, {\ldots} The entry
-{\tt unicode-id-part} non-exhaustively includes symbols for prime
-letters and subscripts.
-
-Access identifiers, written {\accessident}, are identifiers prefixed
-by \verb!.! (dot) without blank. They are used in the syntax of qualified
-identifiers.
-
-\paragraph{Natural numbers and integers}
-Numerals are sequences of digits. Integers are numerals optionally preceded by a minus sign.
-
-\index{num@{\num}}
-\index{integer@{\integer}}
-\begin{center}
-\begin{tabular}{r@{\quad::=\quad}l}
-{\digit} & {\tt 0..9} \\
-{\num} & \nelistwithoutblank{\digit}{} \\
-{\integer} & \zeroone{\tt -}{\num} \\
-\end{tabular}
-\end{center}
-
-\paragraph[Strings]{Strings\label{strings}
-\index{string@{\qstring}}}
-Strings are delimited by \verb!"! (double quote), and enclose a
-sequence of any characters different from \verb!"! or the sequence
-\verb!""! to denote the double quote character. In grammars, the
-entry for quoted strings is {\qstring}.
-
-\paragraph{Keywords}
-The following identifiers are reserved keywords, and cannot be
-employed otherwise:
-\begin{center}
-\begin{tabular}{llllll}
-\verb!_!          &
-\verb!as!         &
-\verb!at!         &
-\verb!cofix!      &
-\verb!else!       &
-\verb!end!        \\
-%
-\verb!exists!     &
-\verb!exists2!    &
-\verb!fix!        &
-\verb!for!        &
-\verb!forall!     &
-\verb!fun!        \\
-%
-\verb!if!         &
-\verb!IF!         &
-\verb!in!         &
-\verb!let!        &
-\verb!match!      &
-\verb!mod!        \\
-%
-\verb!Prop!       &
-\verb!return!     &
-\verb!Set!        &
-\verb!then!       &
-\verb!Type!       &
-\verb!using!      \\
-%
-\verb!where!      &
-\verb!with!       &
-\end{tabular}
-\end{center}
-
-
-\paragraph{Special tokens}
-The following sequences of characters are special tokens:
-\begin{center}
-\begin{tabular}{lllllll}
-\verb/!/   &
-\verb!%!  &
-\verb!&!   &
-\verb!&&!  &
-\verb!(!   &
-\verb!()!  &
-\verb!)!   \\
-%
-\verb!*!   &
-\verb!+!   &
-\verb!++!  &
-\verb!,!   &
-\verb!-!   &
-\verb!->!  &
-\verb!.!   \\
-%
-\verb!.(!  &
-\verb!..!  &
-\verb!/!   &
-\verb!/\!  &
-\verb!:!   &
-\verb!::!  &
-\verb!:<!  \\
-%
-\verb!:=!  &
-\verb!:>!  &
-\verb!;!   &
-\verb!<!   &
-\verb!<-!  &
-\verb!<->! &
-\verb!<:!  \\
-%
-\verb!<=!  &
-\verb!<>!  &
-\verb!=!   &
-\verb!=>!  &
-\verb!=_D! &
-\verb!>!   &
-\verb!>->! \\
-%
-\verb!>=!  &
-\verb!?!   &
-\verb!?=!  &
-\verb!@!   &
-\verb![!   &
-\verb!\/!  &
-\verb!]!   \\
-%
-\verb!^!   &
-\verb!{!   &
-\verb!|!   &
-\verb!|-!  &
-\verb!||!  &
-\verb!}!   &
-\verb!~!   \\
-\end{tabular}
-\end{center}
-
-Lexical ambiguities are resolved according to the ``longest match''
-rule: when a sequence of non alphanumerical characters can be decomposed
-into several different ways, then the first token is the longest
-possible one (among all tokens defined at this moment), and so on.
-
-\section{Terms \label{term}\index{Terms}}
-
-\subsection{Syntax of terms}
-
-Figures \ref{term-syntax} and \ref{term-syntax-aux} describe the basic syntax of
-the terms of the {\em Calculus of Inductive Constructions} (also
-called \CIC). The formal presentation of {\CIC} is given in Chapter
-\ref{Cic}. Extensions of this syntax are given in chapter
-\ref{Gallina-extension}. How to customize the syntax is described in Chapter
-\ref{Addoc-syntax}.
-
-\begin{figure}[htbp]
-\begin{centerframe}
-\begin{tabular}{lcl@{\quad~}r}  % warning: page width exceeded with \qquad 
-{\term} & ::= &
-         {\tt forall} {\binders} {\tt ,} {\term}  &(\ref{products})\\
- & $|$ & {\tt fun} {\binders} {\tt =>} {\term} &(\ref{abstractions})\\
- & $|$ & {\tt fix} {\fixpointbodies} &(\ref{fixpoints})\\
- & $|$ & {\tt cofix} {\cofixpointbodies} &(\ref{fixpoints})\\
- & $|$ & {\tt let} {\ident} \zeroone{\binders} {\typecstr} {\tt :=} {\term}
-         {\tt in} {\term} &(\ref{let-in})\\
- & $|$ & {\tt let fix} {\fixpointbody} {\tt in} {\term} &(\ref{fixpoints})\\
- & $|$ & {\tt let cofix} {\cofixpointbody}
-         {\tt in} {\term} &(\ref{fixpoints})\\
- & $|$ & {\tt let} {\tt (} \sequence{\name}{,} {\tt )} \zeroone{\ifitem}
-         {\tt :=} {\term}
-         {\tt in} {\term}  &(\ref{caseanalysis}, \ref{Mult-match})\\
- & $|$ & {\tt let '} {\pattern} \zeroone{{\tt in} {\term}} {\tt :=} {\term}
-        \zeroone{\returntype} {\tt in} {\term} & (\ref{caseanalysis}, \ref{Mult-match})\\
- & $|$ & {\tt if} {\term} \zeroone{\ifitem} {\tt then} {\term}
-         {\tt else} {\term} &(\ref{caseanalysis}, \ref{Mult-match})\\
- & $|$ & {\term} {\tt :} {\term} &(\ref{typecast})\\
- & $|$ & {\term} {\tt <:} {\term} &(\ref{typecast})\\
- & $|$ & {\term} {\tt :>} &(\ref{ProgramSyntax})\\
- & $|$ & {\term} {\tt ->} {\term} &(\ref{products})\\
- & $|$ & {\term} \nelist{\termarg}{}&(\ref{applications})\\
- & $|$ & {\tt @} {\qualid} \sequence{\term}{}
-            &(\ref{Implicits-explicitation})\\
- & $|$ & {\term} {\tt \%} {\ident} &(\ref{scopechange})\\
- & $|$ & {\tt match} \nelist{\caseitem}{\tt ,}
-                 \zeroone{\returntype} {\tt with} &\\
-    &&   ~~~\zeroone{\zeroone{\tt |} \nelist{\eqn}{|}} {\tt end}
-    &(\ref{caseanalysis})\\
- & $|$ & {\qualid} &(\ref{qualid})\\
- & $|$ & {\sort} &(\ref{Gallina-sorts})\\
- & $|$ & {\num} &(\ref{numerals})\\
- & $|$ & {\_} &(\ref{hole})\\
- & $|$ & {\tt (} {\term} {\tt )} & \\
- & & &\\
-{\termarg} & ::= & {\term} &\\
- & $|$ & {\tt (} {\ident} {\tt :=} {\term} {\tt )}
-         &(\ref{Implicits-explicitation})\\
-%% & $|$ & {\tt (} {\num} {\tt :=} {\term} {\tt )}
-%%         &(\ref{Implicits-explicitation})\\
-&&&\\
-{\binders} & ::= & \nelist{\binder}{}  \\
-&&&\\
-{\binder} & ::= &   {\name} & (\ref{Binders}) \\
- & $|$ & {\tt (} \nelist{\name}{} {\tt :} {\term} {\tt )} &\\  
- & $|$ & {\tt (} {\name} {\typecstr} {\tt :=} {\term} {\tt )} &\\
- & $|$ & {\tt '} {\pattern} &\\
-& & &\\
-{\name} & ::= & {\ident} &\\
- & $|$ & {\tt \_} &\\
-&&&\\
-{\qualid} & ::= & {\ident} & \\
- & $|$ & {\qualid} {\accessident} &\\
- & & &\\
-{\sort} & ::= & {\tt Prop} ~$|$~ {\tt Set} ~$|$~ {\tt Type} &
-\end{tabular}
-\end{centerframe}
-\caption{Syntax of terms}
-\label{term-syntax}
-\index{term@{\term}}
-\index{sort@{\sort}}
-\end{figure}
-
-
-
-\begin{figure}[htb]
-\begin{centerframe}
-\begin{tabular}{lcl}
-{\fixpointbodies} & ::= &
-         {\fixpointbody} \\
- & $|$ & {\fixpointbody} {\tt with} \nelist{\fixpointbody}{{\tt with}}
-         {\tt for} {\ident} \\
-{\cofixpointbodies} & ::= &
-         {\cofixpointbody} \\
- & $|$ & {\cofixpointbody} {\tt with} \nelist{\cofixpointbody}{{\tt with}}
-         {\tt for} {\ident} \\
-&&\\
-{\fixpointbody} & ::= &
-    {\ident} {\binders} \zeroone{\annotation} {\typecstr}
-    {\tt :=} {\term} \\
-{\cofixpointbody} & ::= & {\ident} \zeroone{\binders} {\typecstr} {\tt :=} {\term} \\
-  & &\\
-{\annotation} & ::= & {\tt \{ struct} {\ident} {\tt \}} \\ 
-&&\\
-{\caseitem} & ::= & {\term} \zeroone{{\tt as} \name}
-     \zeroone{{\tt in} \qualid \sequence{\pattern}{}} \\
-&&\\
-{\ifitem} & ::= & \zeroone{{\tt as} {\name}} {\returntype} \\
-&&\\
-{\returntype} & ::= & {\tt return} {\term} \\
-&&\\
-{\eqn} & ::= & \nelist{\multpattern}{\tt |} {\tt =>} {\term}\\
-&&\\
-{\multpattern} & ::= & \nelist{\pattern}{\tt ,}\\
-&&\\
-{\pattern} & ::= & {\qualid} \nelist{\pattern}{}  \\
- & $|$ & {\tt @} {\qualid} \nelist{\pattern}{} \\
-
- & $|$ & {\pattern} {\tt as} {\ident}             \\
- & $|$ & {\pattern} {\tt \%} {\ident}         \\
- & $|$ & {\qualid}                              \\
- & $|$ & {\tt \_}                                  \\
- & $|$ & {\num}                                 \\
- & $|$ & {\tt (} \nelist{\orpattern}{,} {\tt )}     \\
-\\
-{\orpattern} & ::= & \nelist{\pattern}{\tt |}\\
-\end{tabular}
-\end{centerframe}
-\caption{Syntax of terms (continued)}
-\label{term-syntax-aux}
-\end{figure}
-
-
-%%%%%%%
-
-\subsection{Types}
-
-{\Coq} terms are typed. {\Coq} types are recognized by the same
-syntactic class as {\term}. We denote by {\type} the semantic subclass
-of types inside the syntactic class {\term}.
-\index{type@{\type}}
-
-
-\subsection{Qualified identifiers and simple identifiers
-\label{qualid}
-\label{ident}}
-
-{\em Qualified identifiers} ({\qualid}) denote {\em global constants}
-(definitions, lemmas, theorems, remarks or facts), {\em global
-variables} (parameters or axioms), {\em inductive
-types} or {\em constructors of inductive types}.
-{\em Simple identifiers} (or shortly {\ident}) are a
-syntactic subset of qualified identifiers.  Identifiers may also
-denote local {\em variables}, what qualified identifiers do not.
-
-\subsection{Numerals
-\label{numerals}}
-
-Numerals have no definite semantics in the calculus. They are mere
-notations that can be bound to objects through the notation mechanism
-(see Chapter~\ref{Addoc-syntax} for details). Initially, numerals are
-bound to Peano's representation of natural numbers
-(see~\ref{libnats}).
-
-Note: negative integers are not at the same level as {\num}, for this
-would make precedence unnatural.
-
-\subsection{Sorts 
-\index{Sorts}
-\index{Type@{\Type}}
-\index{Set@{\Set}}
-\index{Prop@{\Prop}}
-\index{Sorts}
-\label{Gallina-sorts}}
-
-There are three sorts \Set, \Prop\ and \Type.
-\begin{itemize}
-\item \Prop\ is the universe of {\em logical propositions}.
-The logical propositions themselves are typing the proofs.
-We denote propositions by {\form}. This constitutes a semantic
-subclass of the syntactic class {\term}.
-\index{form@{\form}}
-\item \Set\ is is the universe of {\em program
-types} or {\em specifications}.
-The specifications themselves are typing the programs.
-We denote specifications by {\specif}. This constitutes a semantic
-subclass of the syntactic class {\term}.
-\index{specif@{\specif}}
-\item {\Type} is the type of {\Set} and {\Prop}
-\end{itemize}
-\noindent More on sorts can be found in Section~\ref{Sorts}.
-
-\subsection{Binders
-\label{Binders}
-\index{binders}}
-
-Various constructions such as {\tt fun}, {\tt forall}, {\tt fix} and
-{\tt cofix} {\em bind} variables. A binding is represented by an
-identifier. If the binding variable is not used in the expression, the
-identifier can be replaced by the symbol {\tt \_}.  When the type of a
-bound variable cannot be synthesized by the system, it can be
-specified with the notation {\tt (}\,{\ident}\,{\tt :}\,{\type}\,{\tt
-)}. There is also a notation for a sequence of binding variables
-sharing the same type: {\tt (}\,{\ident$_1$}\ldots{\ident$_n$}\,{\tt
-:}\,{\type}\,{\tt )}. A binder can also be any pattern prefixed by a quote,
-e.g. {\tt '(x,y)}.
-
-Some constructions allow the binding of a variable to value. This is
-called a ``let-binder''. The entry {\binder} of the grammar accepts
-either an assumption binder as defined above or a let-binder. 
-The notation in the
-latter case is {\tt (}\,{\ident}\,{\tt :=}\,{\term}\,{\tt )}. In a
-let-binder, only one variable can be introduced at the same
-time. It is also possible to give the type of the variable as follows:
-{\tt (}\,{\ident}\,{\tt :}\,{\term}\,{\tt :=}\,{\term}\,{\tt )}.
-
-Lists of {\binder} are allowed. In the case of {\tt fun} and {\tt
-  forall}, it is intended that at least one binder of the list is an
-assumption otherwise {\tt fun} and {\tt forall} gets identical. Moreover,
-parentheses can be omitted in the case of a single sequence of
-bindings sharing the same type (e.g.: {\tt fun~(x~y~z~:~A)~=>~t} can
-be shortened in {\tt fun~x~y~z~:~A~=>~t}).
-
-\subsection{Abstractions
-\label{abstractions}
-\index{abstractions}}
-\index{fun@{{\tt fun \ldots => \ldots}}}
-
-The expression ``{\tt fun} {\ident} {\tt :} {\type} {\tt =>}~{\term}''
-defines the {\em abstraction} of the variable {\ident}, of type
-{\type}, over the term {\term}. It denotes a function of the variable
-{\ident} that evaluates to the expression {\term} (e.g. {\tt fun x:$A$
-=> x} denotes the identity function on type $A$).
-% The variable {\ident} is called the {\em parameter} of the function 
-% (we sometimes say the {\em formal parameter}).
-The keyword {\tt fun} can be followed by several binders as given in
-Section~\ref{Binders}. Functions over several variables are
-equivalent to an iteration of one-variable functions.  For instance the
-expression ``{\tt fun}~{\ident$_{1}$}~{\ldots}~{\ident$_{n}$}~{\tt
-:}~\type~{\tt =>}~{\term}'' denotes the same function as ``{\tt
-fun}~{\ident$_{1}$}~{\tt :}~\type~{\tt =>}~{\ldots}~{\tt
-fun}~{\ident$_{n}$}~{\tt :}~\type~{\tt =>}~{\term}''. If a let-binder
-occurs in the list of binders, it is expanded to a let-in definition
-(see Section~\ref{let-in}).
-
-\subsection{Products
-\label{products}
-\index{products}}
-\index{forall@{{\tt forall \ldots, \ldots}}}
-
-The expression ``{\tt forall}~{\ident}~{\tt :}~{\type}{\tt
-,}~{\term}'' denotes the {\em product} of the variable {\ident} of
-type {\type}, over the term {\term}. As for abstractions, {\tt forall}
-is followed by a binder list, and products over several variables are
-equivalent to an iteration of one-variable products. 
-Note that {\term} is intended to be a type.
-
-If the variable {\ident} occurs in {\term}, the product is called {\em
-dependent product}.  The intention behind a dependent product {\tt
-forall}~$x$~{\tt :}~{$A$}{\tt ,}~{$B$} is twofold. It denotes either
-the universal quantification of the variable $x$ of type $A$ in the
-proposition $B$ or the functional dependent product from $A$ to $B$ (a
-construction usually written $\Pi_{x:A}.B$ in set theory).
-
-Non dependent product types have a special notation: ``$A$ {\tt ->}
-$B$'' stands for ``{\tt forall \_:}$A${\tt ,}~$B$''. The {\em non dependent
-product} is used both to denote the propositional implication and
-function types.
-
-\subsection{Applications
-\label{applications}
-\index{applications}}
-
-The expression \term$_0$ \term$_1$ denotes the application of
-\term$_0$ to \term$_1$.
-
-The expression {\tt }\term$_0$ \term$_1$ ...  \term$_n${\tt}
-denotes the application of the term \term$_0$ to the arguments
-\term$_1$ ... then \term$_n$.  It is equivalent to {\tt (} {\ldots}
-{\tt (} {\term$_0$} {\term$_1$} {\tt )} {\ldots} {\tt )} {\term$_n$} {\tt }:
-associativity is to the left.
-
-The notation {\tt (}\,{\ident}\,{\tt :=}\,{\term}\,{\tt )} for
-arguments is used for making explicit the value of implicit arguments
-(see Section~\ref{Implicits-explicitation}).
-
-\subsection{Type cast
-\label{typecast}
-\index{Cast}}
-\index{cast@{{\tt(\ldots: \ldots)}}}
-
-The expression ``{\term}~{\tt :}~{\type}'' is a type cast
-expression. It enforces the type of {\term} to be {\type}.
-
-``{\term}~{\tt <:}~{\type}'' locally sets up the virtual machine for checking
-that {\term} has type {\type}.
-
-\subsection{Inferable subterms
-\label{hole}
-\index{\_}}
-
-Expressions often contain redundant pieces of information. Subterms that
-can be automatically inferred by {\Coq} can be replaced by the
-symbol ``\_'' and {\Coq} will guess the missing piece of information.
-
-\subsection{Let-in definitions
-\label{let-in}
-\index{Let-in definitions}
-\index{let-in}}
-\index{let@{{\tt let \ldots := \ldots in \ldots}}}
-
-
-{\tt let}~{\ident}~{\tt :=}~{\term$_1$}~{\tt in}~{\term$_2$} denotes
-the local binding of \term$_1$ to the variable $\ident$ in
-\term$_2$. 
-There is a syntactic sugar for let-in definition of functions: {\tt
-let} {\ident} {\binder$_1$} {\ldots} {\binder$_n$} {\tt :=} {\term$_1$}
-{\tt in} {\term$_2$} stands for {\tt let} {\ident} {\tt := fun}
-{\binder$_1$} {\ldots} {\binder$_n$} {\tt =>} {\term$_1$} {\tt in}
-{\term$_2$}.
-
-\subsection{Definition by case analysis
-\label{caseanalysis}
-\index{match@{\tt match\ldots with\ldots end}}}
-
-Objects of inductive types can be destructurated by a case-analysis
-construction called {\em pattern-matching} expression.  A
-pattern-matching expression is used to analyze the structure of an
-inductive objects and to apply specific treatments accordingly.
-
-This paragraph describes the basic form of pattern-matching. See
-Section~\ref{Mult-match} and Chapter~\ref{Mult-match-full} for the
-description of the general form. The basic form of pattern-matching is
-characterized by a single {\caseitem} expression, a {\multpattern}
-restricted to a single {\pattern} and {\pattern} restricted to the
-form {\qualid} \nelist{\ident}{}.
-
-The expression {\tt match} {\term$_0$} {\returntype} {\tt with}
-{\pattern$_1$} {\tt =>} {\term$_1$} {\tt $|$} {\ldots} {\tt $|$}
-{\pattern$_n$} {\tt =>} {\term$_n$} {\tt end}, denotes a {\em
-pattern-matching} over the term {\term$_0$} (expected to be of an
-inductive type $I$).  The terms {\term$_1$}\ldots{\term$_n$} are the
-{\em branches} of the pattern-matching expression. Each of
-{\pattern$_i$} has a form \qualid~\nelist{\ident}{} where {\qualid}
-must denote a constructor. There should be exactly one branch for
-every constructor of $I$.
-
-The {\returntype} expresses the type returned by the whole {\tt match}
-expression. There are several cases.  In the {\em non dependent} case,
-all branches have the same type, and the {\returntype} is the common
-type of branches. In this case, {\returntype} can usually be omitted
-as it can be inferred from the type of the branches\footnote{Except if
-the inductive type is empty in which case there is no equation that can be 
-used to infer the return type.}.
-
-In the {\em dependent} case, there are three subcases. In the first
-subcase, the type in each branch may depend on the exact value being
-matched in the branch. In this case, the whole pattern-matching itself
-depends on the term being matched. This dependency of the term being
-matched in the return type is expressed with an ``{\tt as {\ident}}''
-clause where {\ident} is dependent in the return type.
-For instance, in the following example:
-\begin{coq_example*}
-Inductive bool : Type := true : bool | false : bool.
-Inductive eq (A:Type) (x:A) : A -> Prop := eq_refl : eq A x x.
-Inductive or (A:Prop) (B:Prop) : Prop :=
-| or_introl : A -> or A B
-| or_intror : B -> or A B.
-Definition bool_case (b:bool) : or (eq bool b true) (eq bool b false)
-:= match b as x return or (eq bool x true) (eq bool x false) with
-   | true  => or_introl (eq bool true true) (eq bool true false)
-                (eq_refl bool true)
-   | false => or_intror (eq bool false true) (eq bool false false)
-                (eq_refl bool false)
-   end.
-\end{coq_example*}
-the branches have respective types {\tt or (eq bool true true) (eq
-bool true false)} and {\tt or (eq bool false true) (eq bool false
-false)} while the whole pattern-matching expression has type {\tt or
-(eq bool b true) (eq bool b false)}, the identifier {\tt x} being used
-to represent the dependency.  Remark that when the term being matched
-is a variable, the {\tt as} clause can be omitted and the term being
-matched can serve itself as binding name in the return type. For
-instance, the following alternative definition is accepted and has the
-same meaning as the previous one.
-\begin{coq_eval}
-Reset bool_case.
-\end{coq_eval}
-\begin{coq_example*}
-Definition bool_case (b:bool) : or (eq bool b true) (eq bool b false)
-:= match b return or (eq bool b true) (eq bool b false) with
-   | true  => or_introl (eq bool true true) (eq bool true false)
-                (eq_refl bool true)
-   | false => or_intror (eq bool false true) (eq bool false false)
-                (eq_refl bool false)
-   end.
-\end{coq_example*}
-
-The second subcase is only relevant for annotated inductive types such
-as the equality predicate (see Section~\ref{Equality}), the order
-predicate on natural numbers % (see Section~\ref{le}) % undefined reference
-or the type of
-lists of a given length (see Section~\ref{listn}). In this configuration,
-the type of each branch can depend on the type dependencies specific
-to the branch and the whole pattern-matching expression has a type
-determined by the specific dependencies in the type of the term being
-matched. This dependency of the return type in the annotations of the
-inductive type is expressed using a 
-  ``in~I~\_~$\ldots$~\_~\pattern$_1$~$\ldots$~\pattern$_n$'' clause, where
-\begin{itemize}
-\item $I$ is the inductive type of the term being matched;
-
-\item the {\_}'s are matching the parameters of the inductive type:
-the return type is not dependent on them.
-
-\item the \pattern$_i$'s are matching the annotations of the inductive
-  type: the return type is dependent on them
-
-\item in the basic case which we describe below, each \pattern$_i$ is a
-  name \ident$_i$; see \ref{match-in-patterns} for the general case
-
-\end{itemize}
-
-For instance, in the following example:
-\begin{coq_example*}
-Definition eq_sym (A:Type) (x y:A) (H:eq A x y) : eq A y x :=
-  match H in eq _ _ z return eq A z x with
-  | eq_refl _ _ => eq_refl A x
-  end.
-\end{coq_example*}
-the type of the branch has type {\tt eq~A~x~x} because the third
-argument of {\tt eq} is {\tt x} in the type of the pattern {\tt
-refl\_equal}. On the contrary, the type of the whole pattern-matching
-expression has type {\tt eq~A~y~x} because the third argument of {\tt
-eq} is {\tt y} in the type of {\tt H}. This dependency of the case
-analysis in the third argument of {\tt eq} is expressed by the
-identifier {\tt z} in the return type.
-
-Finally, the third subcase is a combination of the first and second
-subcase. In particular, it only applies to pattern-matching on terms
-in a type with annotations. For this third subcase, both
-the clauses {\tt as} and {\tt in} are available.
- 
-There are specific notations for case analysis on types with one or
-two constructors: ``{\tt if {\ldots} then {\ldots} else {\ldots}}''
-and ``{\tt let (}\nelist{\ldots}{,}{\tt ) := } {\ldots} {\tt in}
-{\ldots}'' (see Sections~\ref{if-then-else} and~\ref{Letin}).
-
-%\SeeAlso Section~\ref{Mult-match} for convenient extensions of pattern-matching.
-
-\subsection{Recursive functions
-\label{fixpoints}
-\index{fix@{fix \ident$_i$\{\dots\}}}}
-
-The expression ``{\tt fix} \ident$_1$ \binder$_1$ {\tt :} {\type$_1$}
-\texttt{:=} \term$_1$ {\tt with} {\ldots} {\tt with} \ident$_n$
-\binder$_n$~{\tt :} {\type$_n$} \texttt{:=} \term$_n$ {\tt for}
-{\ident$_i$}'' denotes the $i$\nth component of a block of functions
-defined by mutual well-founded recursion. It is the local counterpart
-of the {\tt Fixpoint} command. See Section~\ref{Fixpoint} for more
-details. When $n=1$, the ``{\tt for}~{\ident$_i$}'' clause is omitted.
-
-The expression ``{\tt cofix} \ident$_1$~\binder$_1$ {\tt :}
-{\type$_1$} {\tt with} {\ldots} {\tt with} \ident$_n$ \binder$_n$ {\tt
-:} {\type$_n$}~{\tt for} {\ident$_i$}'' denotes the $i$\nth component of
-a block of terms defined by a mutual guarded co-recursion. It is the
-local counterpart of the {\tt CoFixpoint} command. See
-Section~\ref{CoFixpoint} for more details. When $n=1$, the ``{\tt
-for}~{\ident$_i$}'' clause is omitted.
-
-The association of a single fixpoint and a local
-definition have a special syntax: ``{\tt let fix}~$f$~{\ldots}~{\tt
-  :=}~{\ldots}~{\tt in}~{\ldots}'' stands for ``{\tt let}~$f$~{\tt :=
-  fix}~$f$~\ldots~{\tt :=}~{\ldots}~{\tt in}~{\ldots}''. The same
-  applies for co-fixpoints.
-
-
-\section{The Vernacular
-\label{Vernacular}}
-
-\begin{figure}[tbp]
-\begin{centerframe}
-\begin{tabular}{lcl}
-{\sentence} & ::= & {\assumption} \\
-            & $|$ & {\definition} \\
-            & $|$ & {\inductive} \\
-            & $|$ & {\fixpoint} \\
-            & $|$ & {\assertion} {\proof} \\
-&&\\
-%% Assumptions
-{\assumption} & ::= & {\assumptionkeyword} {\assums} {\tt .} \\
-&&\\
-{\assumptionkeyword} & $\!\!$ ::= & {\tt Axiom} $|$ {\tt Conjecture} \\
-  & $|$  & {\tt Parameter} $|$  {\tt Parameters} \\
-  & $|$  & {\tt Variable}  $|$ {\tt Variables}  \\
-  & $|$  & {\tt Hypothesis}  $|$ {\tt Hypotheses}\\
-&&\\
-{\assums} & ::= & \nelist{\ident}{} {\tt :} {\term} \\
-          & $|$ & \nelist{{\tt (} \nelist{\ident}{} {\tt :} {\term} {\tt )}}{} \\
-&&\\
-%% Definitions
-{\definition} & ::= & 
-         \zeroone{\tt Local} {\tt Definition} {\ident} \zeroone{\binders} {\typecstr} {\tt :=} {\term} {\tt .} \\
- & $|$ & {\tt Let} {\ident} \zeroone{\binders} {\typecstr} {\tt :=} {\term} {\tt .} \\
-&&\\
-%% Inductives
-{\inductive} & ::= & 
-           {\tt Inductive} \nelist{\inductivebody}{with} {\tt .} \\
- & $|$ & {\tt CoInductive} \nelist{\inductivebody}{with} {\tt .} \\
-           & & \\
-{\inductivebody} & ::= &
-  {\ident} \zeroone{\binders} {\typecstr} {\tt :=} \\
-   && ~~\zeroone{\zeroone{\tt |} \nelist{$\!${\ident}$\!$ \zeroone{\binders} {\typecstr}}{|}} \\
-           & & \\  %% TODO: where ...
-%% Fixpoints
-{\fixpoint} & ::= & {\tt Fixpoint} \nelist{\fixpointbody}{with} {\tt .} \\
-       & $|$ &  {\tt CoFixpoint} \nelist{\cofixpointbody}{with} {\tt .} \\
-&&\\
-%% Lemmas & proofs
-{\assertion} & ::= &
-  {\statkwd} {\ident} \zeroone{\binders} {\tt :} {\term} {\tt .} \\
-&&\\
-  {\statkwd} & ::= & {\tt Theorem} $|$ {\tt Lemma} \\
-   & $|$ & {\tt Remark} $|$ {\tt Fact}\\
-   & $|$ & {\tt Corollary} $|$ {\tt Proposition} \\
-   & $|$ & {\tt Definition} $|$ {\tt Example} \\\\
-&&\\
-{\proof} & ::= & {\tt Proof} {\tt .} {\dots} {\tt Qed} {\tt .}\\
-   & $|$ & {\tt Proof} {\tt .} {\dots} {\tt Defined} {\tt .}\\
-   & $|$ & {\tt Proof} {\tt .} {\dots} {\tt Admitted} {\tt .}\\
-\end{tabular}
-\end{centerframe}
-\caption{Syntax of sentences}
-\label{sentences-syntax}
-\end{figure}
-
-Figure \ref{sentences-syntax} describes {\em The Vernacular} which is the
-language of commands of \gallina.  A sentence of the vernacular
-language, like in many natural languages, begins with a capital letter
-and ends with a dot.
-
-The different kinds of command are described hereafter. They all suppose
-that the terms occurring in the sentences are well-typed.
-
-%%
-%% Axioms and Parameters
-%%
-\subsection{Assumptions
-\index{Declarations}
-\label{Declarations}}
-
-Assumptions extend the environment\index{Environment} with axioms,
-parameters, hypotheses or variables. An assumption binds an {\ident}
-to a {\type}. It is accepted by {\Coq} if and only if this {\type} is
-a correct type in the environment preexisting the declaration and if
-{\ident} was not previously defined in the same module. This {\type}
-is considered to be the type (or specification, or statement) assumed
-by {\ident} and we say that {\ident} has type {\type}.
-
-\subsubsection{{\tt Axiom {\ident} :{\term} .}
-\comindex{Axiom}
-\label{Axiom}}
-
-This command links {\term} to the name {\ident} as its specification
-in the global context. The fact asserted by {\term} is thus assumed as
-a postulate.
-
-\begin{ErrMsgs}
-\item \errindex{{\ident} already exists}
-\end{ErrMsgs}
-
-\begin{Variants} 
-\item \comindex{Parameter}\comindex{Parameters}
-  {\tt Parameter {\ident} :{\term}.} \\
-  Is equivalent to {\tt Axiom {\ident} : {\term}}
-
-\item {\tt Parameter {\ident$_1$} {\ldots} {\ident$_n$} {\tt :}{\term}.}\\
-  Adds $n$ parameters with specification {\term}
-
-\item
- {\tt Parameter\,%
-(\,{\ident$_{1,1}$} {\ldots} {\ident$_{1,k_1}$}\,{\tt :}\,{\term$_1$} {\tt )}\;%
-\ldots\;{\tt (}\,{\ident$_{n,1}$}{\ldots}{\ident$_{n,k_n}$}\,{\tt :}\,%
-{\term$_n$} {\tt )}.}\\ 
-  Adds $n$ blocks of parameters with different specifications.
-
-\item {\tt Local Axiom {\ident} : {\term}.}\\
-\comindex{Local Axiom}
-  Such axioms are never made accessible through their unqualified name by
-  {\tt Import} and its variants (see \ref{Import}). You have to explicitly
-  give their fully qualified name to refer to them.
-
-\item \comindex{Conjecture}
-  {\tt Conjecture {\ident} :{\term}.}\\
-  Is equivalent to {\tt Axiom {\ident} : {\term}}.
-\end{Variants}
-
-\noindent {\bf Remark: } It is possible to replace {\tt Parameter} by
-{\tt Parameters}.
-
-
-\subsubsection{{\tt Variable {\ident} :{\term}}.
-\comindex{Variable}
-\comindex{Variables}
-\label{Variable}}
-
-This command links {\term} to the name {\ident} in the context of the
-current section (see Section~\ref{Section} for a description of the section
-mechanism). When the current section is closed, name {\ident} will be
-unknown and every object using this variable will be explicitly
-parametrized (the variable is {\em discharged}). Using the {\tt
-Variable} command out of any section is equivalent to using {\tt
-Local Parameter}.
-
-\begin{ErrMsgs}
-\item \errindex{{\ident} already exists}
-\end{ErrMsgs}
-
-\begin{Variants}
-\item {\tt Variable {\ident$_1$} {\ldots} {\ident$_n$} {\tt :}{\term}.}\\
-  Links {\term} to names {\ident$_1$} {\ldots} {\ident$_n$}.
-\item
- {\tt Variable\,%
-(\,{\ident$_{1,1}$} {\ldots} {\ident$_{1,k_1}$}\,{\tt :}\,{\term$_1$} {\tt )}\;%
-\ldots\;{\tt (}\,{\ident$_{n,1}$} {\ldots}{\ident$_{n,k_n}$}\,{\tt :}\,%
-{\term$_n$} {\tt )}.}\\ 
-  Adds $n$ blocks of variables with different specifications.
-\item \comindex{Hypothesis}
-      \comindex{Hypotheses}
- {\tt Hypothesis {\ident} {\tt :}{\term}.} \\
-  \texttt{Hypothesis} is a synonymous of \texttt{Variable}
-\end{Variants}
-
-\noindent {\bf Remark: } It is possible to replace {\tt Variable} by
-{\tt Variables} and {\tt Hypothesis} by {\tt Hypotheses}.
-
-It is advised to use the keywords \verb:Axiom: and \verb:Hypothesis:
-for logical postulates (i.e. when the assertion {\term} is of sort
-\verb:Prop:), and to use the keywords \verb:Parameter: and
-\verb:Variable: in other cases (corresponding to the declaration of an
-abstract mathematical entity).
-
-%%
-%% Definitions
-%%
-\subsection{Definitions
-\index{Definitions}
-\label{Basic-definitions}}
-
-Definitions extend the environment\index{Environment} with
-associations of names to terms. A definition can be seen as a way to
-give a meaning to a name or as a way to abbreviate a term.  In any
-case, the name can later be replaced at any time by its definition.
-
-The operation of unfolding a name into its definition is called
-$\delta$-conversion\index{delta-reduction@$\delta$-reduction} (see
-Section~\ref{delta}).  A definition is accepted by the system if and
-only if the defined term is well-typed in the current context of the
-definition and if the name is not already used. The name defined by
-the definition is called a {\em constant}\index{Constant} and the term
-it refers to is its {\em body}.  A definition has a type which is the
-type of its body.
-
-A formal presentation of constants and environments is given in
-Section~\ref{Typed-terms}.
-
-\subsubsection{\tt Definition {\ident} := {\term}.
-\label{Definition}
-\comindex{Definition}}
-
-This command binds {\term} to the name {\ident} in the
-environment, provided that {\term} is well-typed.
-
-\begin{ErrMsgs}
-\item \errindex{{\ident} already exists}
-\end{ErrMsgs}
-
-\begin{Variants}
-\item {\tt Definition} {\ident} {\tt :} {\term$_1$} {\tt :=} {\term$_2$}{\tt .}\\
-  It checks that the type of {\term$_2$} is definitionally equal to
-  {\term$_1$}, and registers {\ident} as being of type {\term$_1$},
-  and bound to value {\term$_2$}.
-\item {\tt Definition} {\ident} {\binder$_1$} {\ldots} {\binder$_n$}
-       {\tt :} \term$_1$ {\tt :=} {\term$_2$}{\tt .}\\
-  This is equivalent to \\
-   {\tt Definition} {\ident} {\tt : forall}%
-       {\binder$_1$} {\ldots} {\binder$_n$}{\tt ,}\,\term$_1$\,{\tt :=}\,%
-       {\tt fun}\,{\binder$_1$} {\ldots} {\binder$_n$}\,{\tt =>}\,{\term$_2$}\,%
-       {\tt .}
-
-\item {\tt Local Definition {\ident} := {\term}.}\\
-\comindex{Local Definition}
-  Such definitions are never made accessible through their unqualified name by
-  {\tt Import} and its variants (see \ref{Import}). You have to explicitly
-  give their fully qualified name to refer to them.
-\item {\tt Example {\ident} := {\term}.}\\
-{\tt Example} {\ident} {\tt :} {\term$_1$} {\tt :=} {\term$_2$}{\tt .}\\
-{\tt Example} {\ident} {\binder$_1$} {\ldots} {\binder$_n$}
-       {\tt :} {\term$_1$} {\tt :=} {\term$_2$}{\tt .}\\
-\comindex{Example}
-These are synonyms of the {\tt Definition} forms.
-\end{Variants}
-
-\begin{ErrMsgs}
-\item \errindex{The term {\term} has type {\type} while it is expected to have type {\type}}
-\end{ErrMsgs}
-
-\SeeAlso Sections \ref{Opaque}, \ref{Transparent}, \ref{unfold}.
-
-\subsubsection{\tt Let {\ident} := {\term}.
-\comindex{Let}}
-
-This command binds the value {\term} to the name {\ident} in the
-environment of the current section. The name {\ident} disappears
-when the current section is eventually closed, and, all
-persistent objects (such as theorems) defined within the
-section and depending on {\ident} are prefixed by the let-in definition
-{\tt let {\ident} := {\term} in}. Using the {\tt
-Let} command out of any section is equivalent to using {\tt
-Local Definition}.
-
-\begin{ErrMsgs}
-\item \errindex{{\ident} already exists}
-\end{ErrMsgs}
-
-\begin{Variants}
-\item {\tt Let {\ident} : {\term$_1$} := {\term$_2$}.}
-\item {\tt Let Fixpoint {\ident} \nelist{\fixpointbody}{with} {\tt .}.}
-\item {\tt Let CoFixpoint {\ident} \nelist{\cofixpointbody}{with} {\tt .}.}
-\end{Variants}
-
-\SeeAlso Sections \ref{Section} (section mechanism), \ref{Opaque},
-\ref{Transparent} (opaque/transparent constants), \ref{unfold} (tactic
-    {\tt unfold}).
-
-%%
-%% Inductive Types
-%%
-\subsection{Inductive definitions
-\index{Inductive definitions}
-\label{gal-Inductive-Definitions}
-\comindex{Inductive}
-\label{Inductive}
-\comindex{Variant}
-\label{Variant}}
-
-We gradually explain simple inductive types, simple
-annotated inductive types, simple parametric inductive types, 
-mutually inductive types. We explain also co-inductive types.
-
-\subsubsection{Simple inductive types}
-
-The definition of a simple inductive type has the following form:
-
-\medskip
-\begin{tabular}{l}
-{\tt Inductive} {\ident} {\tt :} {\sort} {\tt :=} \\
-\begin{tabular}{clcl}
-         & {\ident$_1$} & {\tt :} & {\type$_1$} \\
- {\tt |} & {\ldots} && \\
- {\tt |} & {\ident$_n$} & {\tt :} & {\type$_n$} \\
-\end{tabular}
-\end{tabular}
-\medskip
-
-The name {\ident} is the name of the inductively defined type and
-{\sort} is the universes where it lives.
-The names {\ident$_1$}, {\ldots}, {\ident$_n$}
-are the names of its constructors and {\type$_1$}, {\ldots},
-{\type$_n$} their respective types. The types of the constructors have
-to satisfy a {\em positivity condition} (see Section~\ref{Positivity})
-for {\ident}.  This condition ensures the soundness of the inductive
-definition.  If this is the case, the names {\ident},
-{\ident$_1$}, {\ldots}, {\ident$_n$} are added to the environment with
-their respective types.  Accordingly to the universe where
-the inductive type lives ({\it e.g.} its type {\sort}), {\Coq} provides a
-number of destructors for {\ident}.  Destructors are named
-{\ident}{\tt\_ind}, {\ident}{\tt \_rec} or {\ident}{\tt \_rect} which
-respectively correspond to elimination principles on {\tt Prop}, {\tt
-Set} and {\tt Type}.  The type of the destructors expresses structural
-induction/recursion principles over objects of {\ident}. We give below
-two examples of the use of the {\tt Inductive} definitions.
-
-The set of natural numbers is defined as:
-\begin{coq_example}
-Inductive nat : Set :=
-  | O : nat
-  | S : nat -> nat.
-\end{coq_example}
-
-The type {\tt nat} is defined as the least \verb:Set: containing {\tt
-  O} and closed by the {\tt S} constructor. The names {\tt nat},
-{\tt O} and {\tt S} are added to the environment.
-
-Now let us have a look at the elimination principles. They are three
-of them:
-{\tt nat\_ind}, {\tt nat\_rec} and {\tt nat\_rect}.  The type of {\tt
-  nat\_ind} is:
-\begin{coq_example}
-Check nat_ind.
-\end{coq_example}
-
-This is the well known structural induction principle over natural
-numbers, i.e. the second-order form of Peano's induction principle.
-It allows proving some universal property of natural numbers ({\tt
-forall n:nat, P n}) by induction on {\tt n}.
-
-The types of {\tt nat\_rec} and {\tt nat\_rect} are similar, except
-that they pertain to {\tt (P:nat->Set)} and {\tt (P:nat->Type)}
-respectively . They correspond to primitive induction principles
-(allowing dependent types) respectively over sorts \verb:Set: and
-\verb:Type:. The constant {\ident}{\tt \_ind} is always provided,
-whereas {\ident}{\tt \_rec} and {\ident}{\tt \_rect} can be impossible
-to derive (for example, when {\ident} is a proposition).
-
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-\begin{Variants}
-\item 
-\begin{coq_example*}
-Inductive nat : Set := O | S (_:nat).
-\end{coq_example*}
-In the case where inductive types have no annotations (next section
-gives an example of such annotations), 
-%the positivity condition implies that 
-a constructor can be defined by only giving the type of
-its arguments.
-\end{Variants}
-
-\subsubsection{Simple annotated inductive types}
-
-In an annotated inductive types, the universe where the inductive
-type is defined is no longer a simple sort, but what is called an
-arity, which is a type whose conclusion is a sort.
-
-As an example of annotated inductive types, let us define the
-$even$ predicate:
-
-\begin{coq_example}
-Inductive even : nat -> Prop :=
-  | even_0 : even O
-  | even_SS : forall n:nat, even n -> even (S (S n)).
-\end{coq_example}
-
-The type {\tt nat->Prop} means that {\tt even} is a unary predicate
-(inductively defined) over natural numbers.  The type of its two
-constructors are the defining clauses of the predicate {\tt even}. The
-type of {\tt even\_ind} is:
-
-\begin{coq_example}
-Check even_ind.
-\end{coq_example}
-
-From a mathematical point of view it asserts that the natural numbers
-satisfying the predicate {\tt even} are exactly in the smallest set of
-naturals satisfying the clauses {\tt even\_0} or {\tt even\_SS}. This
-is why, when we want to prove any predicate {\tt P} over elements of
-{\tt even}, it is enough to prove it for {\tt O} and to prove that if
-any natural number {\tt n} satisfies {\tt P} its double successor {\tt
-  (S (S n))} satisfies also {\tt P}. This is indeed analogous to the
-structural induction principle we got for {\tt nat}.
-
-\begin{ErrMsgs}
-\item \errindex{Non strictly positive occurrence of {\ident} in {\type}}
-\item \errindex{The conclusion of {\type} is not valid; it must be
-built from {\ident}}
-\end{ErrMsgs}
-
-\subsubsection{Parametrized inductive types}
-In the previous example, each constructor introduces a
-different instance of the predicate {\tt even}. In some cases, 
-all the constructors introduces the same generic instance of the
-inductive definition, in which case, instead of an annotation, we use
-a context of parameters which are binders shared by all the
-constructors of the definition.
-
-% Inductive types may be parameterized. Parameters differ from inductive
-% type annotations in the fact that recursive invokations of inductive
-% types must always be done with the same values of parameters as its
-% specification.
-
-The general scheme is:
-\begin{center}
-{\tt Inductive} {\ident} {\binder$_1$}\ldots{\binder$_k$} : {\term} :=
-    {\ident$_1$}: {\term$_1$} | {\ldots} | {\ident$_n$}: \term$_n$
-{\tt .}
-\end{center}
-Parameters differ from inductive type annotations in the fact that the
-conclusion of each type of constructor {\term$_i$} invoke the inductive
-type with the same values of parameters as its specification.
-
-
-
-A typical example is the definition of polymorphic lists:
-\begin{coq_example*}
-Inductive list (A:Set) : Set :=
-  | nil : list A
-  | cons : A -> list A -> list A.
-\end{coq_example*}
-
-Note that in the type of {\tt nil} and {\tt cons}, we write {\tt
-  (list A)} and not just {\tt list}.\\ The constructors {\tt nil} and
-{\tt cons} will have respectively types:
-
-\begin{coq_example}
-Check nil.
-Check cons.
-\end{coq_example}
-
-Types of destructors are also quantified with {\tt (A:Set)}.
-
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-\begin{Variants}
-\item
-\begin{coq_example*}
-Inductive list (A:Set) : Set := nil | cons (_:A) (_:list A).
-\end{coq_example*}
-This is an alternative definition of lists where we specify the
-arguments of the constructors rather than their full type.
-\item
-\begin{coq_example*}
-Variant sum (A B:Set) : Set := left : A -> sum A B | right : B -> sum A B.
-\end{coq_example*}
-The {\tt Variant} keyword is identical to the {\tt Inductive} keyword,
-except that it disallows recursive definition of types (in particular
-lists cannot be defined with the {\tt Variant} keyword). No induction
-scheme is generated for this variant, unless the option
-{\tt Nonrecursive Elimination Schemes} is set
-(see~\ref{set-nonrecursive-elimination-schemes}).
-\end{Variants}
-
-\begin{ErrMsgs}
-\item \errindex{The {\num}th argument of {\ident} must be {\ident'} in
-{\type}}
-\end{ErrMsgs}
-
-\paragraph{New from \Coq{} V8.1} The condition on parameters for
-inductive definitions has been relaxed since \Coq{} V8.1. It is now
-possible in the type of a constructor, to invoke recursively the
-inductive definition on an argument which is not the parameter itself.
-
-One can define~:
-\begin{coq_example}
-Inductive list2 (A:Set) : Set :=
-  | nil2 : list2 A
-  | cons2 : A -> list2 (A*A) -> list2 A.
-\end{coq_example}
-\begin{coq_eval}
-Reset list2.
-\end{coq_eval}
-that can also be written by specifying only the type of the arguments:
-\begin{coq_example*}
-Inductive list2 (A:Set) : Set := nil2 | cons2 (_:A) (_:list2 (A*A)).
-\end{coq_example*}
-But the following definition will give an error:
-\begin{coq_example}
-Fail Inductive listw (A:Set) : Set :=
-  | nilw : listw (A*A)
-  | consw : A -> listw (A*A) -> listw (A*A).
-\end{coq_example}
-Because the conclusion of the type of constructors should be {\tt
-  listw A} in both cases. 
-
-A parametrized inductive definition can be defined using
-annotations instead of parameters but it will sometimes give a
-different (bigger) sort for the inductive definition and will produce
-a less convenient rule for case elimination.
-
-\SeeAlso Sections~\ref{Cic-inductive-definitions} and~\ref{Tac-induction}.
-
-
-\subsubsection{Mutually defined inductive types
-\comindex{Inductive}
-\label{Mutual-Inductive}}
-
-The definition of a block of mutually inductive types has the form:
-
-\medskip
-{\tt 
-\begin{tabular}{l}
-Inductive {\ident$_1$} : {\type$_1$} :=  \\
-\begin{tabular}{clcl}
-   & {\ident$_1^1$}     &:& {\type$_1^1$} \\
- | & {\ldots} && \\
- | & {\ident$_{n_1}^1$} &:& {\type$_{n_1}^1$}
-\end{tabular}  \\
-with\\
-~{\ldots} \\
-with {\ident$_m$} : {\type$_m$} := \\
-\begin{tabular}{clcl}
-   & {\ident$_1^m$}     &:& {\type$_1^m$} \\
- | & {\ldots} \\
- | & {\ident$_{n_m}^m$} &:& {\type$_{n_m}^m$}.
-\end{tabular}
-\end{tabular}
-}
-\medskip
-
-\noindent It has the same semantics as the above {\tt Inductive}
-definition for each \ident$_1$, {\ldots}, \ident$_m$. All names
-\ident$_1$, {\ldots}, \ident$_m$ and \ident$_1^1$, \dots,
-\ident$_{n_m}^m$ are simultaneously added to the environment. Then
-well-typing of constructors can be checked. Each one of the
-\ident$_1$, {\ldots}, \ident$_m$ can be used on its own.
-
-It is also possible to parametrize these inductive definitions.
-However, parameters correspond to a local
-context in which the whole set of inductive declarations is done.  For
-this reason, the parameters must be strictly the same for each
-inductive types The extended syntax is:
-
-\medskip
-\begin{tabular}{l}
-{\tt Inductive} {\ident$_1$} {\params} {\tt :} {\type$_1$} {\tt :=}  \\
-\begin{tabular}{clcl}
-         & {\ident$_1^1$}    &{\tt :}& {\type$_1^1$} \\
- {\tt |} & {\ldots} && \\
- {\tt |} & {\ident$_{n_1}^1$} &{\tt :}& {\type$_{n_1}^1$}
-\end{tabular}  \\
-{\tt with}\\
-~{\ldots} \\
-{\tt with} {\ident$_m$} {\params} {\tt :} {\type$_m$} {\tt :=} \\
-\begin{tabular}{clcl}
-         & {\ident$_1^m$}    &{\tt :}& {\type$_1^m$} \\
- {\tt |} & {\ldots} \\
- {\tt |} & {\ident$_{n_m}^m$} &{\tt :}& {\type$_{n_m}^m$}.
-\end{tabular}
-\end{tabular}
-\medskip
-
-\Example
-The typical example of a mutual inductive data type is the one for
-trees and forests. We assume given two types $A$ and $B$ as variables.
-It can be declared the following way.
-
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-\begin{coq_example*}
-Variables A B : Set.
-Inductive tree : Set :=
-    node : A -> forest -> tree
-with forest : Set :=
-  | leaf : B -> forest
-  | cons : tree -> forest -> forest.
-\end{coq_example*}
-
-This declaration generates automatically six induction
-principles. They are respectively 
-called {\tt tree\_rec}, {\tt tree\_ind}, {\tt
-  tree\_rect}, {\tt forest\_rec}, {\tt forest\_ind}, {\tt
-  forest\_rect}.  These ones are not the most general ones but are
-just the induction principles corresponding to each inductive part
-seen as a single inductive definition.
-
-To illustrate this point on our example, we give the types of {\tt
-  tree\_rec} and {\tt forest\_rec}.
-
-\begin{coq_example}
-Check tree_rec.
-Check forest_rec.
-\end{coq_example}
-
-Assume we want to parametrize our mutual inductive definitions with
-the two type variables $A$ and $B$, the declaration should be done the
-following way:
-
-\begin{coq_eval}
-Reset tree.
-\end{coq_eval}
-\begin{coq_example*}
-Inductive tree (A B:Set) : Set :=
-    node : A -> forest A B -> tree A B
-with forest (A B:Set) : Set :=
-  | leaf : B -> forest A B
-  | cons : tree A B -> forest A B -> forest A B.
-\end{coq_example*}
-
-Assume we define an inductive definition inside a section.  When the
-section is closed, the variables declared in the section and occurring
-free in the declaration are added as parameters to the inductive
-definition. 
-
-\SeeAlso Section~\ref{Section}.
-
-\subsubsection{Co-inductive types
-\label{CoInductiveTypes}
-\comindex{CoInductive}}
-
-The objects of an inductive type are well-founded with respect to the
-constructors of the type. In other words, such objects contain only a
-{\it finite} number of constructors. Co-inductive types arise from
-relaxing this condition, and admitting types whose objects contain an
-infinity of constructors. Infinite objects are introduced by a
-non-ending (but effective) process of construction, defined in terms
-of the constructors of the type.
-
-An example of a co-inductive type is the type of infinite sequences of
-natural numbers, usually called streams. It can be introduced in \Coq\
-using the \texttt{CoInductive} command:
-\begin{coq_example}
-CoInductive Stream : Set :=
-    Seq : nat -> Stream -> Stream.
-\end{coq_example}
-
-The syntax of this command is the same as the command \texttt{Inductive}
-(see Section~\ref{gal-Inductive-Definitions}). Notice that no
-principle of induction is derived from the definition of a
-co-inductive type, since such principles only make sense for inductive
-ones. For co-inductive ones, the only elimination principle is case
-analysis. For example, the usual destructors on streams
-\texttt{hd:Stream->nat} and \texttt{tl:Str->Str} can be defined as
-follows:
-\begin{coq_example}
-Definition hd (x:Stream) := let (a,s) := x in a.
-Definition tl (x:Stream) := let (a,s) := x in s.
-\end{coq_example}
-
-Definition of co-inductive predicates and blocks of mutually
-co-inductive definitions are also allowed. An example of a
-co-inductive predicate is the extensional equality on streams:
-
-\begin{coq_example}
-CoInductive EqSt : Stream -> Stream -> Prop :=
-    eqst :
-      forall s1 s2:Stream,
-        hd s1 = hd s2 -> EqSt (tl s1) (tl s2) -> EqSt s1 s2.
-\end{coq_example}
-
-In order to prove the extensionally equality of two streams $s_1$ and
-$s_2$ we have to construct an infinite proof of equality, that is,
-an infinite object of type $(\texttt{EqSt}\;s_1\;s_2)$. We will see
-how to introduce infinite objects in Section~\ref{CoFixpoint}.
-
-%%
-%% (Co-)Fixpoints
-%%
-\subsection{Definition of recursive functions}
-
-\subsubsection{Definition of functions by recursion over inductive objects}
-
-This section describes the primitive form of definition by recursion
-over inductive objects. See Section~\ref{Function} for more advanced
-constructions. The command:
-\begin{center}
-  \texttt{Fixpoint {\ident} {\params} {\tt \{struct}
-  \ident$_0$ {\tt \}} : type$_0$ := \term$_0$ 
-  \comindex{Fixpoint}\label{Fixpoint}}
-\end{center}
-allows defining functions by pattern-matching over inductive objects 
-using a fixed point construction.
-The meaning of this declaration is to define {\it ident} a recursive
-function with arguments specified by the binders in {\params} such
-that {\it ident} applied to arguments corresponding to these binders
-has type \type$_0$, and is equivalent to the expression \term$_0$. The
-type of the {\ident} is consequently {\tt forall {\params} {\tt,}
-  \type$_0$} and the value is equivalent to {\tt fun {\params} {\tt
-    =>} \term$_0$}.
-
-To be accepted, a {\tt Fixpoint} definition has to satisfy some
-syntactical constraints on a special argument called the decreasing
-argument. They are needed to ensure that the {\tt Fixpoint} definition
-always terminates. The point of the {\tt \{struct \ident {\tt \}}}
-annotation is to let the user tell the system which argument decreases
-along the recursive calls. For instance, one can define the addition 
-function as :
-
-\begin{coq_example}
-Fixpoint add (n m:nat) {struct n} : nat :=
-  match n with
-  | O => m
-  | S p => S (add p m)
-  end.
-\end{coq_example}
-
-The {\tt \{struct \ident {\tt \}}} annotation may be left implicit, in
-this case the system try successively arguments from left to right
-until it finds one that satisfies the decreasing condition. Note that
-some fixpoints may have several arguments that fit as decreasing
-arguments, and this choice influences the reduction of the
-fixpoint. Hence an explicit annotation must be used if the leftmost
-decreasing argument is not the desired one. Writing explicit
-annotations can also speed up type-checking of large mutual fixpoints.
-
-The {\tt match} operator matches a value (here \verb:n:) with the
-various constructors of its (inductive) type. The remaining arguments
-give the respective values to be returned, as functions of the
-parameters of the corresponding constructor. Thus here when \verb:n:
-equals \verb:O: we return \verb:m:, and when \verb:n: equals 
-\verb:(S p): we return \verb:(S (add p m)):.
-
-The {\tt match} operator is formally described
-in detail in Section~\ref{Caseexpr}.  The system recognizes that in
-the inductive call {\tt (add p m)} the first argument actually
-decreases because it is a {\em pattern variable} coming from {\tt match
-  n with}.
-
-\Example The following definition is not correct and generates an
-error message:
-
-\begin{coq_eval}
-Set Printing Depth 50.
-\end{coq_eval}
-% (********** The following is not correct and should produce **********)
-% (*********      Error: Recursive call to wrongplus ...      **********)
-\begin{coq_example}
-Fail Fixpoint wrongplus (n m:nat) {struct n} : nat :=
-  match m with
-  | O => n
-  | S p => S (wrongplus n p)
-  end.
-\end{coq_example}
-
-because the declared decreasing argument {\tt n} actually does not
-decrease in the recursive call.  The function computing the addition
-over the second argument should rather be written:
-
-\begin{coq_example*}
-Fixpoint plus (n m:nat) {struct m} : nat :=
-  match m with
-  | O => n
-  | S p => S (plus n p)
-  end.
-\end{coq_example*}
-
-The ordinary match operation on natural numbers can be mimicked in the
-following way.
-\begin{coq_example*}
-Fixpoint nat_match 
-  (C:Set) (f0:C) (fS:nat -> C -> C) (n:nat) {struct n} : C :=
-  match n with
-  | O => f0
-  | S p => fS p (nat_match C f0 fS p)
-  end.
-\end{coq_example*}
-The recursive call may not only be on direct subterms of the recursive
-variable {\tt n} but also on a deeper subterm and we can directly
-write the function {\tt mod2} which gives the remainder modulo 2 of a
-natural number.
-\begin{coq_example*}
-Fixpoint mod2 (n:nat) : nat :=
-  match n with
-  | O => O
-  | S p => match p with
-           | O => S O
-           | S q => mod2 q
-           end
-  end.
-\end{coq_example*}
-In order to keep the strong normalization property, the fixed point
-reduction will only be performed when the argument in position of the
-decreasing argument (which type should be in an inductive definition)
-starts with a constructor.
-
-The {\tt Fixpoint} construction enjoys also the {\tt with} extension
-to define functions over mutually defined inductive types or more
-generally any mutually recursive definitions.
-
-\begin{Variants}
-\item {\tt Fixpoint} {\ident$_1$} {\params$_1$} {\tt :} {\type$_1$} {\tt :=} {\term$_1$}\\
-        {\tt with} {\ldots} \\
-        {\tt with} {\ident$_m$} {\params$_m$} {\tt :} {\type$_m$} {\tt :=} {\term$_m$}\\
-        Allows to define simultaneously {\ident$_1$}, {\ldots},
-        {\ident$_m$}.
-\end{Variants}
-
-\Example 
-The size of trees and forests can be defined the following way: 
-\begin{coq_eval}
-Reset Initial.
-Variables A B : Set.
-Inductive tree : Set :=
-    node : A -> forest -> tree
-with forest : Set :=
-  | leaf : B -> forest
-  | cons : tree -> forest -> forest.
-\end{coq_eval}
-\begin{coq_example*}
-Fixpoint tree_size (t:tree) : nat :=
-  match t with
-  | node a f => S (forest_size f)
-  end
- with forest_size (f:forest) : nat :=
-  match f with
-  | leaf b => 1
-  | cons t f' => (tree_size t + forest_size f')
-  end.
-\end{coq_example*}
-A generic command {\tt Scheme} is useful to build automatically various
-mutual induction principles. It is described in Section~\ref{Scheme}.
-
-\subsubsection{Definitions of recursive objects in co-inductive types}
-
-The command:
-\begin{center}
-  \texttt{CoFixpoint {\ident} : \type$_0$ := \term$_0$}
-  \comindex{CoFixpoint}\label{CoFixpoint}
-\end{center}
-introduces a method for constructing an infinite object of a
-coinduc\-tive type. For example, the stream containing all natural
-numbers can be introduced applying the following method to the number
-\texttt{O} (see Section~\ref{CoInductiveTypes} for the definition of
-{\tt Stream}, {\tt hd} and {\tt tl}):
-\begin{coq_eval}
-Reset Initial.
-CoInductive Stream : Set :=
-    Seq : nat -> Stream -> Stream.
-Definition hd (x:Stream) := match x with
-                            | Seq a s => a
-                            end.
-Definition tl (x:Stream) := match x with
-                            | Seq a s => s
-                            end.
-\end{coq_eval}
-\begin{coq_example}
-CoFixpoint from (n:nat) : Stream := Seq n (from (S n)).
-\end{coq_example}
-
-Oppositely to recursive ones, there is no decreasing argument in a
-co-recursive definition. To be admissible, a method of construction
-must provide at least one extra constructor of the infinite object for
-each iteration. A syntactical guard condition is imposed on
-co-recursive definitions in order to ensure this: each recursive call
-in the definition must be protected by at least one constructor, and
-only by constructors. That is the case in the former definition, where
-the single recursive call of \texttt{from} is guarded by an
-application of \texttt{Seq}. On the contrary, the following recursive
-function does not satisfy the guard condition:
-
-\begin{coq_eval}
-Set Printing Depth 50.
-\end{coq_eval}
-% (********** The following is not correct and should produce **********)
-% (***************** Error: Unguarded recursive call *******************)
-\begin{coq_example}
-Fail CoFixpoint filter (p:nat -> bool) (s:Stream) : Stream :=
-  if p (hd s) then Seq (hd s) (filter p (tl s)) else filter p (tl s).
-\end{coq_example}
-
-The elimination of co-recursive definition is done lazily, i.e. the
-definition is expanded only when it occurs at the head of an
-application which is the argument of a case analysis expression.  In
-any other context, it is considered as a canonical expression which is
-completely evaluated. We can test this using the command
-\texttt{Eval}, which computes the normal forms of a term:
-
-\begin{coq_example}
-Eval compute in (from 0).
-Eval compute in (hd (from 0)).
-Eval compute in (tl (from 0)).
-\end{coq_example}
-
-\begin{Variants}
-\item{\tt CoFixpoint {\ident$_1$} {\params} :{\type$_1$} :=
-  {\term$_1$}}\\ As for most constructions, arguments of co-fixpoints
-  expressions can be introduced before the {\tt :=} sign.
-\item{\tt CoFixpoint} {\ident$_1$} {\tt :} {\type$_1$} {\tt :=} {\term$_1$}\\
-     {\tt with}\\
-        \mbox{}\hspace{0.1cm} {\ldots} \\
-        {\tt with} {\ident$_m$} {\tt :} {\type$_m$} {\tt :=} {\term$_m$}\\
-As in the \texttt{Fixpoint} command (see Section~\ref{Fixpoint}), it
-is possible to introduce a block of mutually dependent methods.
-\end{Variants}
-
-%%
-%% Theorems & Lemmas
-%%
-\subsection{Assertions and proofs}
-\label{Assertions}
-
-An assertion states a proposition (or a type) of which the proof (or
-an inhabitant of the type) is interactively built using tactics. The
-interactive proof mode is described in
-Chapter~\ref{Proof-handling} and the tactics in Chapter~\ref{Tactics}.
-The basic assertion command is:
-
-\subsubsection{\tt Theorem {\ident} \zeroone{\binders} : {\type}.
-\comindex{Theorem}}
-
-After the statement is asserted, {\Coq} needs a proof. Once a proof of
-{\type} under the assumptions represented by {\binders} is given and
-validated, the proof is generalized into a proof of {\tt forall
-  \zeroone{\binders}, {\type}} and the theorem is bound to the name
-{\ident} in the environment.
-
-\begin{ErrMsgs}
-
-\item \errindex{The term {\form} has type {\ldots} which should be Set,
-    Prop or Type}
-
-\item \errindexbis{{\ident} already exists}{already exists}
- 
-  The name you provided is already defined. You have then to choose
-  another name.
-
-\end{ErrMsgs}
-
-\begin{Variants} 
-\item {\tt Lemma {\ident} \zeroone{\binders} : {\type}.}\comindex{Lemma}\\
-  {\tt Remark {\ident} \zeroone{\binders} : {\type}.}\comindex{Remark}\\
-  {\tt Fact {\ident} \zeroone{\binders} : {\type}.}\comindex{Fact}\\
-  {\tt Corollary {\ident} \zeroone{\binders} : {\type}.}\comindex{Corollary}\\
-  {\tt Proposition {\ident} \zeroone{\binders} : {\type}.}\comindex{Proposition}
-
-These commands are synonyms of \texttt{Theorem {\ident} \zeroone{\binders} : {\type}}.
-
-\item {\tt Theorem \nelist{{\ident} \zeroone{\binders}: {\type}}{with}.}
-
-This command is useful for theorems that are proved by simultaneous
-induction over a mutually inductive assumption, or that assert mutually
-dependent statements in some mutual co-inductive type. It is equivalent
-to {\tt Fixpoint} or {\tt CoFixpoint}
-(see Section~\ref{CoFixpoint}) but using tactics to build the proof of
-the statements (or the body of the specification, depending on the
-point of view). The inductive or co-inductive types on which the
-induction or coinduction has to be done is assumed to be non ambiguous
-and is guessed by the system. 
-
-Like in a {\tt Fixpoint} or {\tt CoFixpoint} definition, the induction
-hypotheses have to be used on {\em structurally smaller} arguments
-(for a {\tt Fixpoint}) or be {\em guarded by a constructor} (for a {\tt
-  CoFixpoint}).  The verification that recursive proof arguments are
-correct is done only at the time of registering the lemma in the
-environment. To know if the use of induction hypotheses is correct at
-some time of the interactive development of a proof, use the command
-{\tt Guarded} (see Section~\ref{Guarded}).
-
-The command can be used also with {\tt Lemma},
-{\tt Remark}, etc. instead of {\tt Theorem}.
-
-\item {\tt Definition {\ident} \zeroone{\binders} : {\type}.}
-
-This allows defining a term of type {\type} using the proof editing mode. It
-behaves as {\tt Theorem} but is intended to be used in conjunction with
-  {\tt Defined} (see \ref{Defined}) in order to define a
- constant of which the computational behavior is relevant.
-
-The command can be used also with {\tt Example} instead
-of {\tt Definition}.
-
-\SeeAlso Sections~\ref{Opaque} and~\ref{Transparent} ({\tt Opaque}
-and {\tt Transparent}) and~\ref{unfold} (tactic {\tt unfold}).
-
-\item {\tt Let {\ident} \zeroone{\binders} : {\type}.}
-
-Like {\tt Definition {\ident} \zeroone{\binders} : {\type}.} except
-that the definition is turned into a let-in definition generalized over
-the declarations depending on it after closing the current section.
-
-\item {\tt Fixpoint \nelist{{\ident} {\binders} \zeroone{\annotation} {\typecstr} \zeroone{{\tt :=} {\term}}}{with}.}
-\comindex{Fixpoint}
-
-This generalizes the syntax of {\tt Fixpoint} so that one or more
-bodies can be defined interactively using the proof editing mode (when
-a body is omitted, its type is mandatory in the syntax). When the
-block of proofs is completed, it is intended to be ended by {\tt
-  Defined}.
-
-\item {\tt CoFixpoint \nelist{{\ident} \zeroone{\binders} {\typecstr} \zeroone{{\tt :=} {\term}}}{with}.}
-\comindex{CoFixpoint}
-
-This generalizes the syntax of {\tt CoFixpoint} so that one or more bodies
-can be defined interactively using the proof editing mode.
-
-\end{Variants}
-
-\subsubsection{{\tt Proof.} {\dots} {\tt Qed.}
-\comindex{Proof}
-\comindex{Qed}}
-
-A proof starts by the keyword {\tt Proof}.  Then {\Coq} enters the
-proof editing mode until the proof is completed. The proof editing
-mode essentially contains tactics that are described in chapter
-\ref{Tactics}. Besides tactics, there are commands to manage the proof
-editing mode. They are described in Chapter~\ref{Proof-handling}. When
-the proof is completed it should be validated and put in the
-environment using the keyword {\tt Qed}.
-\medskip
-
-\ErrMsg
-\begin{enumerate}
-\item \errindex{{\ident} already exists}
-\end{enumerate}
-
-\begin{Remarks}
-\item Several statements can be simultaneously asserted.
-\item Not only other assertions but any vernacular command can be given
-while in the process of proving a given assertion. In this case, the command is
-understood as if it would have been given before the statements still to be
-proved. 
-\item {\tt Proof} is recommended but can currently be omitted. On the
-opposite side, {\tt Qed} (or {\tt Defined}, see below) is mandatory to
-validate a proof.
-\item Proofs ended by {\tt Qed} are declared opaque. Their content
-  cannot be unfolded (see \ref{Conversion-tactics}), thus realizing
-  some form of {\em proof-irrelevance}. To be able to unfold a proof,
-  the proof should be ended by {\tt Defined} (see below).
-\end{Remarks}
-
-\begin{Variants}
-\item \comindex{Defined}
-  {\tt Proof.} {\dots} {\tt Defined.}\\
-  Same as {\tt Proof.} {\dots} {\tt Qed.} but the proof is
-  then declared transparent, which means that its
-  content can be explicitly used for type-checking and that it
-  can be unfolded in conversion tactics (see
-  \ref{Conversion-tactics}, \ref{Opaque}, \ref{Transparent}).
-%Not claimed to be part of Gallina...
-%\item {\tt Proof.} {\dots} {\tt Save.}\\
-%  Same as {\tt Proof.} {\dots} {\tt Qed.}
-%\item {\tt Goal} \type {\dots} {\tt Save} \ident \\
-%  Same as {\tt Lemma} \ident {\tt :} \type \dots {\tt Save.}
-%  This is intended to be used in the interactive mode.
-\item \comindex{Admitted}
-  {\tt Proof.} {\dots} {\tt Admitted.}\\
-  Turns the current asserted statement into an axiom and exits the
-  proof mode.
-\end{Variants}
-
-% Local Variables: 
-% mode: LaTeX
-% TeX-master: "Reference-Manual"
-% End: 
-
diff --git a/doc/refman/RefMan-ltac.tex b/doc/refman/RefMan-ltac.tex
deleted file mode 100644
index 3ed697d8be..0000000000
--- a/doc/refman/RefMan-ltac.tex
+++ /dev/null
@@ -1,1829 +0,0 @@
-\chapter[The tactic language]{The tactic language\label{TacticLanguage}}
-%HEVEA\cutname{ltac.html}
-
-%\geometry{a4paper,body={5in,8in}}
-
-This chapter gives a compact documentation of Ltac, the tactic
-language available in {\Coq}. We start by giving the syntax, and next,
-we present the informal semantics. If you want to know more regarding
-this language and especially about its foundations, you can refer
-to~\cite{Del00}. Chapter~\ref{Tactics-examples} is devoted to giving
-examples of use of this language on small but also with non-trivial
-problems.
-
-
-\section{Syntax}
-
-\def\tacexpr{\textrm{\textsl{expr}}}
-\def\tacexprlow{\textrm{\textsl{tacexpr$_1$}}}
-\def\tacexprinf{\textrm{\textsl{tacexpr$_2$}}}
-\def\tacexprpref{\textrm{\textsl{tacexpr$_3$}}}
-\def\atom{\textrm{\textsl{atom}}}
-%%\def\recclause{\textrm{\textsl{rec\_clause}}}
-\def\letclause{\textrm{\textsl{let\_clause}}}
-\def\matchrule{\textrm{\textsl{match\_rule}}}
-\def\contextrule{\textrm{\textsl{context\_rule}}}
-\def\contexthyp{\textrm{\textsl{context\_hyp}}}
-\def\tacarg{\nterm{tacarg}}
-\def\cpattern{\nterm{cpattern}}
-\def\selector{\textrm{\textsl{selector}}}
-\def\toplevelselector{\textrm{\textsl{toplevel\_selector}}}
-
-The syntax of the tactic language is given Figures~\ref{ltac}
-and~\ref{ltac-aux}. See Chapter~\ref{BNF-syntax} for a description of
-the BNF metasyntax used in these grammar rules. Various already
-defined entries will be used in this chapter: entries
-{\naturalnumber}, {\integer}, {\ident}, {\qualid}, {\term},
-{\cpattern} and {\atomictac} represent respectively the natural and
-integer numbers, the authorized identificators and qualified names,
-{\Coq}'s terms and patterns and all the atomic tactics described in
-Chapter~\ref{Tactics}. The syntax of {\cpattern} is the same as that
-of terms, but it is extended with pattern matching metavariables. In
-{\cpattern}, a pattern-matching metavariable is represented with the
-syntax {\tt ?id} where {\tt id} is an {\ident}. The notation {\tt \_}
-can also be used to denote metavariable whose instance is
-irrelevant. In the notation {\tt ?id}, the identifier allows us to
-keep instantiations and to make constraints whereas {\tt \_} shows
-that we are not interested in what will be matched. On the right hand
-side of pattern-matching clauses, the named metavariable are used
-without the question mark prefix. There is also a special notation for
-second-order pattern-matching problems: in an applicative pattern of
-the form {\tt @?id id$_1$ \ldots id$_n$}, the variable {\tt id}
-matches any complex expression with (possible) dependencies in the
-variables {\tt id$_1$ \ldots id$_n$} and returns a functional term of
-the form {\tt fun id$_1$ \ldots id$_n$ => {\term}}.
-
-
-The main entry of the grammar is {\tacexpr}. This language is used in
-proof mode but it can also be used in toplevel definitions as shown in
-Figure~\ref{ltactop}.
-
-\begin{Remarks}
-\item The infix tacticals ``\dots\ {\tt ||} \dots'', ``\dots\ {\tt +}
-  \dots'', and ``\dots\ {\tt ;} \dots'' are associative.
-
-\item In {\tacarg}, there is an overlap between {\qualid} as a
-direct tactic argument and {\qualid} as a particular case of
-{\term}. The resolution is done by first looking for a reference of
-the tactic language and if it fails, for a reference to a term. To
-force the resolution as a reference of the tactic language, use the
-form {\tt ltac :} {\qualid}. To force the resolution as a reference to
-a term, use the syntax {\tt ({\qualid})}.
-
-\item As shown by the figure, tactical {\tt ||} binds more than the
-prefix tacticals {\tt try}, {\tt repeat}, {\tt do} and
-{\tt abstract} which themselves bind more than the postfix tactical
-``{\tt \dots\ ;[ \dots\ ]}'' which binds more than ``\dots\ {\tt ;}
-\dots''.
-
-For instance
-\begin{quote}
-{\tt try repeat \tac$_1$ ||
-  \tac$_2$;\tac$_3$;[\tac$_{31}$|\dots|\tac$_{3n}$];\tac$_4$.}
-\end{quote}
-is understood as
-\begin{quote}
-{\tt (try (repeat (\tac$_1$ || \tac$_2$)));} \\
-{\tt ((\tac$_3$;[\tac$_{31}$|\dots|\tac$_{3n}$]);\tac$_4$).}
-\end{quote}
-\end{Remarks}
-
-
-\begin{figure}[htbp]
-\begin{centerframe}
-\begin{tabular}{lcl}
-{\tacexpr} & ::= &
-           {\tacexpr} {\tt ;} {\tacexpr}\\
-& | & {\tt [>} \nelist{\tacexpr}{|} {\tt ]}\\
-& | & {\tacexpr} {\tt ; [} \nelist{\tacexpr}{|} {\tt ]}\\
-& | & {\tacexprpref}\\
-\\
-{\tacexprpref} & ::= &
-           {\tt do} {\it (}{\naturalnumber} {\it |} {\ident}{\it )} {\tacexprpref}\\
-& | & {\tt progress} {\tacexprpref}\\
-& | & {\tt repeat} {\tacexprpref}\\
-& | & {\tt try} {\tacexprpref}\\
-& | & {\tt once} {\tacexprpref}\\
-& | & {\tt exactly\_once} {\tacexprpref}\\
-& | & {\tt timeout} {\it (}{\naturalnumber} {\it |} {\ident}{\it )} {\tacexprpref}\\
-& | & {\tt time} \zeroone{\qstring} {\tacexprpref}\\
-& | & {\tt only} {\selector} {\tt :} {\tacexprpref}\\
-& | & {\tacexprinf} \\
-\\
-{\tacexprinf} & ::= &
-           {\tacexprlow} {\tt ||} {\tacexprpref}\\
-& | &      {\tacexprlow} {\tt +} {\tacexprpref}\\
-& | &      {\tt tryif} {\tacexprlow} {\tt then} {\tacexprlow} {\tt else} {\tacexprlow}\\
-& | & {\tacexprlow}\\
-\\
-{\tacexprlow} & ::= &
-{\tt fun} \nelist{\name}{} {\tt =>} {\atom}\\
-& | &
-{\tt let} \zeroone{\tt rec} \nelist{\letclause}{\tt with} {\tt in}
-{\atom}\\
-& | &
-{\tt match goal with} \nelist{\contextrule}{\tt |} {\tt end}\\
-& | &
-{\tt match reverse goal with} \nelist{\contextrule}{\tt |} {\tt end}\\
-& | &
-{\tt match} {\tacexpr} {\tt with} \nelist{\matchrule}{\tt |} {\tt end}\\
-& | &
-{\tt lazymatch goal with} \nelist{\contextrule}{\tt |} {\tt end}\\
-& | &
-{\tt lazymatch reverse goal with} \nelist{\contextrule}{\tt |} {\tt end}\\
-& | &
-{\tt lazymatch} {\tacexpr} {\tt with} \nelist{\matchrule}{\tt |} {\tt end}\\
-& | &
-{\tt multimatch goal with} \nelist{\contextrule}{\tt |} {\tt end}\\
-& | &
-{\tt multimatch reverse goal with} \nelist{\contextrule}{\tt |} {\tt end}\\
-& | &
-{\tt multimatch} {\tacexpr} {\tt with} \nelist{\matchrule}{\tt |} {\tt end}\\
-& | & {\tt abstract} {\atom}\\
-& | & {\tt abstract} {\atom} {\tt using} {\ident} \\
-& | & {\tt first [} \nelist{\tacexpr}{\tt |} {\tt ]}\\
-& | & {\tt solve [} \nelist{\tacexpr}{\tt |} {\tt ]}\\
-& | & {\tt idtac} \sequence{\messagetoken}{}\\
-& | & {\tt fail} \zeroone{\naturalnumber} \sequence{\messagetoken}{}\\
-& | & {\tt gfail} \zeroone{\naturalnumber} \sequence{\messagetoken}{}\\
-& | & {\tt fresh} ~|~ {\tt fresh} {\qstring}|~ {\tt fresh} {\qualid}\\
-& | & {\tt context} {\ident} {\tt [} {\term} {\tt ]}\\
-& | & {\tt eval} {\nterm{redexpr}} {\tt in} {\term}\\
-& | & {\tt type of} {\term}\\
-& | & {\tt external} {\qstring} {\qstring} \nelist{\tacarg}{}\\
-& | & {\tt constr :} {\term}\\
-& | & {\tt uconstr :} {\term}\\
-& | & {\tt type\_term} {\term}\\
-& | & {\tt numgoals} \\
-& | & {\tt guard} {\it test}\\
-& | & {\tt assert\_fails} {\tacexprpref}\\
-& | & {\tt assert\_succeds} {\tacexprpref}\\
-& | & \atomictac\\
-& | & {\qualid} \nelist{\tacarg}{}\\
-& | & {\atom}
-\end{tabular}
-\end{centerframe}
-\caption{Syntax of the tactic language}
-\label{ltac}
-\end{figure}
-
-
-
-\begin{figure}[htbp]
-\begin{centerframe}
-\begin{tabular}{lcl}
-{\atom} & ::= &
-           {\qualid} \\
-& | & ()\\
-& | & {\integer}\\
-& | & {\tt (} {\tacexpr} {\tt )}\\
-\\
-{\messagetoken}\!\!\!\!\!\! & ::= & {\qstring} ~|~ {\ident} ~|~ {\integer} \\
-\\
-\tacarg & ::= &
-        {\qualid}\\
-& $|$ & {\tt ()} \\
-& $|$ & {\tt ltac :} {\atom}\\
-& $|$ & {\term}\\
-\\
-\letclause & ::= & {\ident} \sequence{\name}{} {\tt :=} {\tacexpr}\\
-\\
-\contextrule & ::= &
-  \nelist{\contexthyp}{\tt ,} {\tt |-}{\cpattern} {\tt =>} {\tacexpr}\\
-& $|$ & {\tt |-} {\cpattern} {\tt =>} {\tacexpr}\\
-& $|$ & {\tt \_ =>} {\tacexpr}\\
-\\
-\contexthyp & ::= & {\name} {\tt :} {\cpattern}\\
-             & $|$ & {\name} {\tt :=} {\cpattern} \zeroone{{\tt :} {\cpattern}}\\
-\\
-\matchrule & ::= &
-           {\cpattern} {\tt =>} {\tacexpr}\\
-& $|$ & {\tt context} {\zeroone{\ident}} {\tt [} {\cpattern} {\tt ]}
-           {\tt =>} {\tacexpr}\\
-& $|$ & {\tt \_ =>} {\tacexpr}\\
-\\
-{\it test} & ::= &
-        {\integer} {\tt \,=\,} {\integer}\\
-& $|$ & {\integer} {\tt \,<\,} {\integer}\\
-& $|$ & {\integer} {\tt <=} {\integer}\\
-& $|$ & {\integer} {\tt \,>\,} {\integer}\\
-& $|$ & {\integer} {\tt >=} {\integer}\\
-\\
-\selector & ::= &
-        [{\ident}]\\
-& $|$ & {\integer}\\
-& $|$ & \nelist{{\it (}{\integer} {\it |} {\integer} {\tt -} {\integer}{\it )}}
-          {\tt ,}\\
-\\
-\toplevelselector & ::= &
-        \selector\\
-& $|$ & {\tt all}\\
-& $|$ & {\tt par}
-\end{tabular}
-\end{centerframe}
-\caption{Syntax of the tactic language (continued)}
-\label{ltac-aux}
-\end{figure}
-
-\begin{figure}[ht]
-\begin{centerframe}
-\begin{tabular}{lcl}
-\nterm{top} & ::= & \zeroone{\tt Local} {\tt Ltac} \nelist{\nterm{ltac\_def}} {\tt with} \\
-\\
-\nterm{ltac\_def} & ::= & {\ident} \sequence{\ident}{} {\tt :=}
-{\tacexpr}\\
-& $|$ &{\qualid} \sequence{\ident}{} {\tt ::=}{\tacexpr}
-\end{tabular}
-\end{centerframe}
-\caption{Tactic toplevel definitions}
-\label{ltactop}
-\end{figure}
-
-
-%%
-%% Semantics
-%%
-\section{Semantics}
-%\index[tactic]{Tacticals}
-\index{Tacticals}
-%\label{Tacticals}
-
-Tactic expressions can only be applied in the context of a proof.  The
-evaluation yields either a term, an integer or a tactic. Intermediary
-results can be terms or integers but the final result must be a tactic
-which is then applied to the focused goals.
-
-There is a special case for {\tt match goal} expressions of which
-the clauses evaluate to tactics. Such expressions can only be used as
-end result of a tactic expression (never as argument of a non recursive local
-definition or of an application).
-
-The rest of this section explains the semantics of every construction
-of Ltac.
-
-
-%% \subsection{Values}
-
-%% Values are given by Figure~\ref{ltacval}. All these values are tactic values,
-%% i.e. to be applied to a goal, except {\tt Fun}, {\tt Rec} and $arg$ values.
-
-%% \begin{figure}[ht]
-%% \noindent{}\framebox[6in][l]
-%% {\parbox{6in}
-%% {\begin{center}
-%% \begin{tabular}{lp{0.1in}l}
-%% $vexpr$ & ::= & $vexpr$ {\tt ;} $vexpr$\\
-%% & | & $vexpr$ {\tt ; [} {\it (}$vexpr$ {\tt |}{\it )}$^*$ $vexpr$ {\tt
-%% ]}\\
-%% & | & $vatom$\\
-%% \\
-%% $vatom$ & ::= & {\tt Fun} \nelist{\inputfun}{}  {\tt ->} {\tacexpr}\\
-%% %& | & {\tt Rec} \recclause\\
-%% & | &
-%% {\tt Rec} \nelist{\recclause}{\tt And} {\tt In}
-%% {\tacexpr}\\
-%% & | &
-%% {\tt Match Context With} {\it (}$context\_rule$ {\tt |}{\it )}$^*$
-%% $context\_rule$\\
-%% & | & {\tt (} $vexpr$ {\tt )}\\
-%% & | & $vatom$ {\tt Orelse} $vatom$\\
-%% & | & {\tt Do} {\it (}{\naturalnumber} {\it |} {\ident}{\it )} $vatom$\\
-%% & | & {\tt Repeat} $vatom$\\
-%% & | & {\tt Try} $vatom$\\
-%% & | & {\tt First [} {\it (}$vexpr$ {\tt |}{\it )}$^*$ $vexpr$ {\tt ]}\\
-%% & | & {\tt Solve [} {\it (}$vexpr$ {\tt |}{\it )}$^*$ $vexpr$ {\tt ]}\\
-%% & | & {\tt Idtac}\\
-%% & | & {\tt Fail}\\
-%% & | & {\primitivetactic}\\
-%% & | & $arg$
-%% \end{tabular}
-%% \end{center}}}
-%% \caption{Values of ${\cal L}_{tac}$}
-%% \label{ltacval}
-%% \end{figure}
-
-%% \subsection{Evaluation}
-
-\subsubsection[Sequence]{Sequence\tacindex{;}
-\index{Tacticals!;@{\tt {\tac$_1$};\tac$_2$}}}
-
-A sequence is an expression of the following form:
-\begin{quote}
-{\tacexpr}$_1$ {\tt ;} {\tacexpr}$_2$
-\end{quote}
-The expression {\tacexpr}$_1$ is evaluated to $v_1$, which must be
-a tactic value. The tactic $v_1$ is applied to the current goal,
-possibly producing more goals. Then {\tacexpr}$_2$ is evaluated to
-produce $v_2$, which must be a tactic value. The tactic $v_2$ is applied to
-all the goals produced by the prior application. Sequence is associative.
-
-\subsubsection[Local application of tactics]{Local application of tactics\tacindex{[>\ldots$\mid$\ldots$\mid$\ldots]}\tacindex{;[\ldots$\mid$\ldots$\mid$\ldots]}\index{Tacticals![> \mid ]@{\tt {\tac$_0$};[{\tac$_1$}$\mid$\ldots$\mid$\tac$_n$]}}\index{Tacticals!; [ \mid ]@{\tt {\tac$_0$};[{\tac$_1$}$\mid$\ldots$\mid$\tac$_n$]}}}
-%\tacindex{; [ | ]}
-%\index{; [ | ]@{\tt ;[\ldots$\mid$\ldots$\mid$\ldots]}}
-
-Different tactics can be applied to the different goals using the following form:
-\begin{quote}
-{\tt [ >} {\tacexpr}$_1$ {\tt |} $...$ {\tt |} {\tacexpr}$_n$ {\tt ]}
-\end{quote}
-The expressions {\tacexpr}$_i$ are evaluated to $v_i$, for $i=0,...,n$
-and all have to be tactics. The $v_i$ is applied to the $i$-th goal,
-for $=1,...,n$. It fails if the number of focused goals is not exactly $n$.
-
-\begin{Variants}
-  \item If no tactic is given for the $i$-th goal, it behaves as if
-    the tactic {\tt idtac} were given. For instance, {\tt [~> | auto
-    ]} is a shortcut for {\tt [ > idtac | auto ]}.
-
-  \item {\tt [ >} {\tacexpr}$_1$ {\tt |} $...$ {\tt |}
-    {\tacexpr}$_i$ {\tt |} {\tacexpr} {\tt ..} {\tt |}
-    {\tacexpr}$_{i+1+j}$ {\tt |} $...$ {\tt |} {\tacexpr}$_n$ {\tt ]}
-
-  In this variant, {\tt expr} is used for each goal numbered from
-  $i+1$ to $i+j$ (assuming $n$ is the number of goals).
-
-  Note that {\tt ..} is part of the syntax, while $...$ is the meta-symbol used
-  to describe a list of {\tacexpr} of arbitrary length.
-  goals numbered from $i+1$ to $i+j$.
-
-  \item {\tt [ >} {\tacexpr}$_1$ {\tt |} $...$ {\tt |}
-    {\tacexpr}$_i$ {\tt |} {\tt ..} {\tt |} {\tacexpr}$_{i+1+j}$ {\tt |}
-    $...$ {\tt |} {\tacexpr}$_n$ {\tt ]}
-
-  In this variant, {\tt idtac} is used for the goals numbered from
-  $i+1$ to $i+j$.
-
-  \item {\tt [ >} {\tacexpr} {\tt ..} {\tt ]}
-
-    In this variant, the tactic {\tacexpr} is applied independently to
-    each of the goals, rather than globally. In particular, if there
-    are no goal, the tactic is not run at all. A tactic which
-    expects multiple goals, such as {\tt swap}, would act as if a single
-    goal is focused.
-
-  \item {\tacexpr} {\tt ; [ } {\tacexpr}$_1$ {\tt |} $...$ {\tt |} {\tacexpr}$_n$ {\tt ]}
-
-    This variant of local tactic application is paired with a
-    sequence.  In this variant, $n$ must be the number of goals
-    generated by the application of {\tacexpr} to each of the
-    individual goals independently. All the above variants work in
-    this form too. Formally, {\tacexpr} {\tt ; [} $...$ {\tt ]} is
-    equivalent to
-    \begin{quote}
-    {\tt [ >} {\tacexpr} {\tt ; [ >} $...$ {\tt ]} {\tt ..} {\tt ]}
-    \end{quote}
-
-\end{Variants}
-
-\subsubsection[Goal selectors]{Goal selectors\label{ltac:selector}
-\tacindex{\tt :}\index{Tacticals!:@{\tt :}}}
-
-We can restrict the application of a tactic to a subset of
-the currently focused goals with:
-\begin{quote}
-  {\toplevelselector} {\tt :} {\tacexpr}
-\end{quote}
-We can also use selectors as a tactical, which allows to use them nested in
-a tactic expression, by using the keyword {\tt only}:
-\begin{quote}
-  {\tt only} {\selector} {\tt :} {\tacexpr}
-\end{quote}
-When selecting several goals, the tactic {\tacexpr} is applied globally to
-all selected goals.
-
-\begin{Variants}
-  \item{} [{\ident}] {\tt :} {\tacexpr}
-
-    In this variant, {\tacexpr} is applied locally to a goal
-    previously named by the user (see~\ref{ExistentialVariables}).
-
-  \item {\num} {\tt :} {\tacexpr}
-
-    In this variant, {\tacexpr} is applied locally to the
-    {\num}-th goal.
-
-  \item $n_1$-$m_1$, \dots, $n_k$-$m_k$ {\tt :} {\tacexpr}
-
-    In this variant, {\tacexpr} is applied globally to the subset
-    of goals described by the given ranges. You can write a single
-    $n$ as a shortcut for $n$-$n$ when specifying multiple ranges.
-
-  \item {\tt all:} {\tacexpr}
-
-    In this variant, {\tacexpr} is applied to all focused goals.
-    {\tt all:} can only be used at the toplevel of a tactic expression.
-
-  \item {\tt par:} {\tacexpr}
-
-    In this variant, {\tacexpr} is applied to all focused goals
-    in parallel.  The number of workers can be controlled via the
-    command line option {\tt -async-proofs-tac-j} taking as argument
-    the desired number of workers.  Limitations:  {\tt par: } only works
-    on goals containing no existential variables and {\tacexpr} must
-    either solve the goal completely or do nothing (i.e. it cannot make
-    some progress).
-    {\tt par:} can only be used at the toplevel of a tactic expression.
-
-\end{Variants}
-
-\ErrMsg \errindex{No such goal}
-
-\subsubsection[For loop]{For loop\tacindex{do}
-\index{Tacticals!do@{\tt do}}}
-
-There is a for loop that repeats a tactic {\num} times:
-\begin{quote}
-{\tt do} {\num} {\tacexpr}
-\end{quote}
-{\tacexpr} is evaluated to $v$ which must be a tactic value.
-This tactic value $v$ is
-applied {\num} times. Supposing ${\num}>1$, after the first
-application of $v$, $v$ is applied, at least once, to the generated
-subgoals and so on. It fails if the application of $v$ fails before
-the {\num} applications have been completed.
-
-\subsubsection[Repeat loop]{Repeat loop\tacindex{repeat}
-\index{Tacticals!repeat@{\tt repeat}}}
-
-We have a repeat loop with:
-\begin{quote}
-{\tt repeat} {\tacexpr}
-\end{quote}
-{\tacexpr} is evaluated to $v$. If $v$ denotes a tactic, this tactic
-is applied to each focused goal independently. If the application
-succeeds, the tactic is applied recursively to all the generated subgoals
-until it eventually fails.  The recursion stops in a subgoal when the
-tactic has failed \emph{to make progress}.  The tactic {\tt repeat
-  {\tacexpr}} itself never fails.
-
-\subsubsection[Error catching]{Error catching\tacindex{try}
-\index{Tacticals!try@{\tt try}}}
-
-We can catch the tactic errors with:
-\begin{quote}
-{\tt try} {\tacexpr}
-\end{quote}
-{\tacexpr} is evaluated to $v$ which must be a tactic value.
-The tactic value $v$ is
-applied to each focused goal independently. If the application of $v$
-fails in a goal, it catches the error and leaves the goal
-unchanged. If the level of the exception is positive, then the
-exception is re-raised with its level decremented.
-
-\subsubsection[Detecting progress]{Detecting progress\tacindex{progress}}
-
-We can check if a tactic made progress with:
-\begin{quote}
-{\tt progress} {\tacexpr}
-\end{quote}
-{\tacexpr} is evaluated to $v$ which must be a tactic value.
-The tactic value $v$ is
-applied to each focued subgoal independently. If the application of
-$v$ to one of the focused subgoal produced subgoals equal to the
-initial goals (up to syntactical equality), then an error of level 0
-is raised.
-
-\ErrMsg \errindex{Failed to progress}
-
-\subsubsection[Backtracking branching]{Backtracking branching\tacindex{$+$}
-\index{Tacticals!or@{\tt $+$}}}
-
-We can branch with the following structure:
-\begin{quote}
-{\tacexpr}$_1$ {\tt +} {\tacexpr}$_2$
-\end{quote}
-{\tacexpr}$_1$ and {\tacexpr}$_2$ are evaluated to $v_1$ and
-$v_2$ which must be tactic values. The tactic value $v_1$ is applied to each
-focused goal independently and if it fails or a later tactic fails,
-then the proof backtracks to the current goal and $v_2$ is applied.
-
-Tactics can be seen as having several successes. When a tactic fails
-it asks for more successes of the prior tactics. {\tacexpr}$_1$ {\tt
-  +} {\tacexpr}$_2$ has all the successes of $v_1$ followed by all the
-successes of $v_2$. Algebraically, ({\tacexpr}$_1$ {\tt +}
-{\tacexpr}$_2$);{\tacexpr}$_3$ $=$ ({\tacexpr}$_1$;{\tacexpr}$_3$)
-{\tt +} ({\tacexpr}$_2$;{\tacexpr}$_3$).
-
-Branching is left-associative.
-
-\subsubsection[First tactic to work]{First tactic to work\tacindex{first}
-\index{Tacticals!first@{\tt first}}}
-
-Backtracking branching may be too expensive. In this case we may
-restrict to a local, left biased, branching and consider the first
-tactic to work (i.e. which does not fail) among a panel of tactics:
-\begin{quote}
-{\tt first [} {\tacexpr}$_1$ {\tt |} $...$ {\tt |} {\tacexpr}$_n$ {\tt ]}
-\end{quote}
-{\tacexpr}$_i$ are evaluated to $v_i$ and $v_i$ must be tactic values,
-for $i=1,...,n$. Supposing $n>1$, it applies, in each focused goal
-independently, $v_1$, if it works, it stops otherwise it tries to
-apply $v_2$ and so on. It fails when there is no applicable tactic. In
-other words, {\tt first [} {\tacexpr}$_1$ {\tt |} $...$ {\tt |}
-  {\tacexpr}$_n$ {\tt ]} behaves, in each goal, as the the first $v_i$
-to have \emph{at least} one success.
-
-\ErrMsg \errindex{No applicable tactic}
-
-\variant {\tt first {\tacexpr}}
-
-This is an Ltac alias that gives a primitive access to the {\tt first} tactical
-as a Ltac definition without going through a parsing rule. It expects to be
-given a list of tactics through a {\tt Tactic Notation}, allowing to write
-notations of the following form.
-
-\Example
-
-\begin{quote}
-{\tt Tactic Notation "{foo}" tactic\_list(tacs) := first tacs.}
-\end{quote}
-
-\subsubsection[Left-biased branching]{Left-biased branching\tacindex{$\mid\mid$}
-\index{Tacticals!orelse@{\tt $\mid\mid$}}}
-
-Yet another way of branching without backtracking is the following structure:
-\begin{quote}
-{\tacexpr}$_1$ {\tt ||} {\tacexpr}$_2$
-\end{quote}
-{\tacexpr}$_1$ and {\tacexpr}$_2$ are evaluated to $v_1$ and
-$v_2$ which must be tactic values. The tactic value $v_1$ is applied in each
-subgoal independently and if it fails \emph{to progress} then $v_2$ is
-applied. {\tacexpr}$_1$ {\tt ||} {\tacexpr}$_2$ is equivalent to {\tt
-  first [} {\tt progress} {\tacexpr}$_1$ {\tt |}
-  {\tacexpr}$_2$ {\tt ]} (except that if it fails, it fails like
-$v_2$). Branching is left-associative.
-
-\subsubsection[Generalized biased branching]{Generalized biased branching\tacindex{tryif}
-\index{Tacticals!tryif@{\tt tryif}}}
-
-The tactic
-\begin{quote}
-{\tt tryif {\tacexpr}$_1$ then {\tacexpr}$_2$ else {\tacexpr}$_3$}
-\end{quote}
-is a generalization of the biased-branching tactics above. The
-expression {\tacexpr}$_1$ is evaluated to $v_1$, which is then applied
-to each subgoal independently. For each goal where $v_1$ succeeds at
-least once, {\tacexpr}$_2$ is evaluated to $v_2$ which is then applied
-collectively to the generated subgoals. The $v_2$ tactic can trigger
-backtracking points in $v_1$: where $v_1$ succeeds at least once, {\tt
-  tryif {\tacexpr}$_1$ then {\tacexpr}$_2$ else {\tacexpr}$_3$} is
-equivalent to $v_1;v_2$. In each of the goals where $v_1$ does not
-succeed at least once, {\tacexpr}$_3$ is evaluated in $v_3$ which is
-is then applied to the goal.
-
-\subsubsection[Soft cut]{Soft cut\tacindex{once}\index{Tacticals!once@{\tt once}}}
-
-Another way of restricting backtracking is to restrict a tactic to a
-single success \emph{a posteriori}:
-\begin{quote}
-{\tt once} {\tacexpr}
-\end{quote}
-{\tacexpr} is evaluated to $v$ which must be a tactic value.
-The tactic value $v$ is
-applied but only its first success is used. If $v$ fails, {\tt once}
-{\tacexpr} fails like $v$. If $v$ has a least one success, {\tt once}
-{\tacexpr} succeeds once, but cannot produce more successes.
-
-\subsubsection[Checking the successes]{Checking the successes\tacindex{exactly\_once}\index{Tacticals!exactly\_once@{\tt exactly\_once}}}
-
-Coq provides an experimental way to check that a tactic has \emph{exactly one} success:
-\begin{quote}
-{\tt exactly\_once} {\tacexpr}
-\end{quote}
-{\tacexpr} is evaluated to $v$ which must be a tactic value.
-The tactic value $v$ is
-applied if it has at most one success. If $v$ fails, {\tt
-  exactly\_once} {\tacexpr} fails like $v$. If $v$ has a exactly one
-success, {\tt exactly\_once} {\tacexpr} succeeds like $v$. If $v$ has
-two or more successes, {\tt exactly\_once} {\tacexpr} fails.
-
-The experimental status of this tactic pertains to the fact if $v$ performs side effects, they may occur in a unpredictable way. Indeed, normally $v$ would only be executed up to the first success until backtracking is needed, however {\tt exactly\_once} needs to look ahead to see whether a second success exists, and may run further effects immediately.
-
-\ErrMsg \errindex{This tactic has more than one success}
-
-\subsubsection[Checking the failure]{Checking the failure\tacindex{assert\_fails}\index{Tacticals!assert\_fails@{\tt assert\_fails}}}
-
-Coq provides a derived tactic to check that a tactic \emph{fails}:
-\begin{quote}
-{\tt assert\_fails} {\tacexpr}
-\end{quote}
-This behaves like {\tt tryif {\tacexpr} then fail 0 tac "succeeds" else idtac}.
-
-\subsubsection[Checking the success]{Checking the success\tacindex{assert\_succeeds}\index{Tacticals!assert\_succeeds@{\tt assert\_succeeds}}}
-
-Coq provides a derived tactic to check that a tactic has \emph{at least one} success:
-\begin{quote}
-{\tt assert\_succeeds} {\tacexpr}
-\end{quote}
-This behaves like {\tt tryif (assert\_fails tac) then fail 0 tac "fails" else idtac}.
-
-\subsubsection[Solving]{Solving\tacindex{solve}
-\index{Tacticals!solve@{\tt solve}}}
-
-We may consider the first to solve (i.e. which generates no subgoal) among a
-panel of tactics:
-\begin{quote}
-{\tt solve [} {\tacexpr}$_1$ {\tt |} $...$ {\tt |} {\tacexpr}$_n$ {\tt ]}
-\end{quote}
-{\tacexpr}$_i$ are evaluated to $v_i$ and $v_i$ must be tactic values,
-for $i=1,...,n$. Supposing $n>1$, it applies $v_1$ to each goal
-independently, if it doesn't solve the goal then it tries to apply
-$v_2$ and so on. It fails if there is no solving tactic.
-
-\ErrMsg \errindex{Cannot solve the goal}
-
-\variant {\tt solve {\tacexpr}}
-
-This is an Ltac alias that gives a primitive access to the {\tt solve} tactical.
-See the {\tt first} tactical for more information.
-
-\subsubsection[Identity]{Identity\label{ltac:idtac}\tacindex{idtac}
-\index{Tacticals!idtac@{\tt idtac}}}
-
-The constant {\tt idtac} is the identity tactic: it leaves any goal
-unchanged but it appears in the proof script.
-
-\variant {\tt idtac \nelist{\messagetoken}{}}
-
-This prints the given tokens. Strings and integers are printed
-literally. If a (term) variable is given, its contents are printed.
-
-
-\subsubsection[Failing]{Failing\tacindex{fail}
-\index{Tacticals!fail@{\tt fail}}
-\tacindex{gfail}\index{Tacticals!gfail@{\tt gfail}}}
-
-The tactic {\tt fail} is the always-failing tactic: it does not solve
-any goal. It is useful for defining other tacticals since it can be
-caught by {\tt try}, {\tt repeat}, {\tt match goal}, or the branching
-tacticals. The {\tt fail} tactic will, however, succeed if all the
-goals have already been solved.
-
-\begin{Variants}
-\item {\tt fail $n$}\\ The number $n$ is the failure level. If no
-  level is specified, it defaults to $0$.  The level is used by {\tt
-    try}, {\tt repeat}, {\tt match goal} and the branching tacticals.
-  If $0$, it makes {\tt match goal} considering the next clause
-  (backtracking). If non zero, the current {\tt match goal} block,
-  {\tt try}, {\tt repeat}, or branching command is aborted and the
-  level is decremented. In the case of {\tt +}, a non-zero level skips
-  the first backtrack point, even if the call to {\tt fail $n$} is not
-  enclosed in a {\tt +} command, respecting the algebraic identity.
-
-\item {\tt fail \nelist{\messagetoken}{}}\\
-The given tokens are used for printing the failure message.
-
-\item {\tt fail $n$ \nelist{\messagetoken}{}}\\
-This is a combination of the previous variants.
-
-\item {\tt gfail}\\
-This variant fails even if there are no goals left.
-
-\item {\tt gfail \nelist{\messagetoken}{}}\\
-{\tt gfail $n$ \nelist{\messagetoken}{}}\\
-These variants fail with an error message or an error level even if
-there are no goals left. Be careful however if Coq terms have to be
-printed as part of the failure: term construction always forces the
-tactic into the goals, meaning that if there are no goals when it is
-evaluated, a tactic call like {\tt let x:=H in fail 0 x} will succeed.
-
-\end{Variants}
-
-\ErrMsg \errindex{Tactic Failure {\it message} (level $n$)}.
-
-\subsubsection[Timeout]{Timeout\tacindex{timeout}
-\index{Tacticals!timeout@{\tt timeout}}}
-
-We can force a tactic to stop if it has not finished after a certain
-amount of time:
-\begin{quote}
-{\tt timeout} {\num} {\tacexpr}
-\end{quote}
-{\tacexpr} is evaluated to $v$ which must be a tactic value.
-The tactic value $v$ is
-applied normally, except that it is interrupted after ${\num}$ seconds
-if it is still running. In this case the outcome is a failure.
-
-Warning: For the moment, {\tt timeout} is based on elapsed time in
-seconds, which is very
-machine-dependent: a script that works on a quick machine may fail
-on a slow one. The converse is even possible if you combine a
-{\tt timeout} with some other tacticals. This tactical is hence
-proposed only for convenience during debug or other development
-phases, we strongly advise you to not leave any {\tt timeout} in
-final scripts. Note also that this tactical isn't available on
-the native Windows port of Coq.
-
-\subsubsection{Timing a tactic\tacindex{time}
-\index{Tacticals!time@{\tt time}}}
-
-A tactic execution can be timed:
-\begin{quote}
- {\tt time} {\qstring} {\tacexpr}
-\end{quote}
-evaluates {\tacexpr}
-and displays the time the tactic expression ran, whether it fails or
-successes. In case of several successes, the time for each successive
-runs is displayed. Time is in seconds and is machine-dependent. The
-{\qstring} argument is optional. When provided, it is used to identify
-this particular occurrence of {\tt time}.
-
-\subsubsection{Timing a tactic that evaluates to a term\tacindex{time\_constr}\tacindex{restart\_timer}\tacindex{finish\_timing}
-\index{Tacticals!time\_constr@{\tt time\_constr}}}
-\index{Tacticals!restart\_timer@{\tt restart\_timer}}
-\index{Tacticals!finish\_timing@{\tt finish\_timing}}
-
-Tactic expressions that produce terms can be timed with the experimental tactic
-\begin{quote}
- {\tt time\_constr} {\tacexpr}
-\end{quote}
-which evaluates {\tacexpr\tt{ ()}}
-and displays the time the tactic expression evaluated, assuming successful evaluation.
-Time is in seconds and is machine-dependent.
-
-This tactic currently does not support nesting, and will report times based on the innermost execution.
-This is due to the fact that it is implemented using the tactics
-\begin{quote}
- {\tt restart\_timer} {\qstring}
-\end{quote}
-and
-\begin{quote}
- {\tt finish\_timing} ({\qstring}) {\qstring}
-\end{quote}
-which (re)set and display an optionally named timer, respectively.
-The parenthesized {\qstring} argument to {\tt finish\_timing} is also
-optional, and determines the label associated with the timer for
-printing.
-
-By copying the definition of {\tt time\_constr} from the standard
-library, users can achive support for a fixed pattern of nesting by
-passing different {\qstring} parameters to {\tt restart\_timer} and
-{\tt finish\_timing} at each level of nesting.  For example:
-
-\begin{coq_example}
-Ltac time_constr1 tac :=
-  let eval_early := match goal with _ => restart_timer "(depth 1)" end in
-  let ret := tac () in
-  let eval_early := match goal with _ => finish_timing ( "Tactic evaluation" ) "(depth 1)" end in
-  ret.
-
-Goal True.
-  let v := time_constr
-             ltac:(fun _ =>
-                     let x := time_constr1 ltac:(fun _ => constr:(10 * 10)) in
-                     let y := time_constr1 ltac:(fun _ => eval compute in x) in
-                     y) in
-  pose v.
-Abort.
-\end{coq_example}
-
-\subsubsection[Local definitions]{Local definitions\index{Ltac!let@\texttt{let}}
-\index{Ltac!let rec@\texttt{let rec}}
-\index{let@\texttt{let}!in Ltac}
-\index{let rec@\texttt{let rec}!in Ltac}}
-
-Local definitions can be done as follows:
-\begin{quote}
-{\tt let} {\ident}$_1$ {\tt :=} {\tacexpr}$_1$\\
-{\tt with} {\ident}$_2$ {\tt :=} {\tacexpr}$_2$\\
-...\\
-{\tt with} {\ident}$_n$ {\tt :=} {\tacexpr}$_n$ {\tt in}\\
-{\tacexpr}
-\end{quote}
-each {\tacexpr}$_i$ is evaluated to $v_i$, then, {\tacexpr} is
-evaluated by substituting $v_i$ to each occurrence of {\ident}$_i$,
-for $i=1,...,n$. There is no dependencies between the {\tacexpr}$_i$
-and the {\ident}$_i$.
-
-Local definitions can be recursive by using {\tt let rec} instead of
-{\tt let}. In this latter case, the definitions are evaluated lazily
-so that the {\tt rec} keyword can be used also in non recursive cases
-so as to avoid the eager evaluation of local definitions.
-
-\subsubsection{Application}
-
-An application is an expression of the following form:
-\begin{quote}
-{\qualid} {\tacarg}$_1$ ... {\tacarg}$_n$
-\end{quote}
-The reference {\qualid} must be bound to some defined tactic
-definition expecting at least $n$ arguments.  The expressions
-{\tacexpr}$_i$ are evaluated to $v_i$, for $i=1,...,n$.
-%If {\tacexpr} is a {\tt Fun} or {\tt Rec} value then the body is evaluated by
-%substituting $v_i$ to the formal parameters, for $i=1,...,n$. For recursive
-%clauses, the bodies are lazily substituted (when an identifier to be evaluated
-%is the name of a recursive clause).
-
-%\subsection{Application of tactic values}
-
-\subsubsection[Function construction]{Function construction\index{fun@\texttt{fun}!in Ltac}
-\index{Ltac!fun@\texttt{fun}}}
-
-A parameterized tactic can be built anonymously (without resorting to
-local definitions) with:
-\begin{quote}
-{\tt fun} {\ident${}_1$} ... {\ident${}_n$} {\tt =>} {\tacexpr}
-\end{quote}
-Indeed, local definitions of functions are a syntactic sugar for
-binding a {\tt fun} tactic to an identifier.
-
-\subsubsection[Pattern matching on terms]{Pattern matching on terms\index{Ltac!match@\texttt{match}}
-\index{match@\texttt{match}!in Ltac}}
-
-We can carry out pattern matching on terms with:
-\begin{quote}
-{\tt match} {\tacexpr} {\tt with}\\
-~~~{\cpattern}$_1$ {\tt =>} {\tacexpr}$_1$\\
-~{\tt |} {\cpattern}$_2$ {\tt =>} {\tacexpr}$_2$\\
-~...\\
-~{\tt |} {\cpattern}$_n$ {\tt =>} {\tacexpr}$_n$\\
-~{\tt |} {\tt \_} {\tt =>} {\tacexpr}$_{n+1}$\\
-{\tt end}
-\end{quote}
-The expression {\tacexpr} is evaluated and should yield a term which
-is matched against {\cpattern}$_1$. The matching is non-linear: if a
-metavariable occurs more than once, it should match the same
-expression every time. It is first-order except on the
-variables of the form {\tt @?id} that occur in head position of an
-application. For these variables, the matching is second-order and
-returns a functional term.
-
-Alternatively, when a metavariable of the form {\tt ?id} occurs under
-binders, say $x_1$, \ldots, $x_n$ and the expression matches, the
-metavariable is instantiated by a term which can then be used in any
-context which also binds the variables $x_1$, \ldots, $x_n$ with
-same types. This provides with a primitive form of matching
-under context which does not require manipulating a functional term.
-
-If the matching with {\cpattern}$_1$ succeeds, then {\tacexpr}$_1$ is
-evaluated into some value by substituting the pattern matching
-instantiations to the metavariables. If {\tacexpr}$_1$ evaluates to a
-tactic and the {\tt match} expression is in position to be applied to
-a goal (e.g. it is not bound to a variable by a {\tt let in}), then
-this tactic is applied. If the tactic succeeds, the list of resulting
-subgoals is the result of the {\tt match} expression. If
-{\tacexpr}$_1$ does not evaluate to a tactic or if the {\tt match}
-expression is not in position to be applied to a goal, then the result
-of the evaluation of {\tacexpr}$_1$ is the result of the {\tt match}
-expression.
-
-If the matching with {\cpattern}$_1$ fails, or if it succeeds but the
-evaluation of {\tacexpr}$_1$ fails, or if the evaluation of
-{\tacexpr}$_1$ succeeds but returns a tactic in execution position
-whose execution fails, then {\cpattern}$_2$ is used and so on.  The
-pattern {\_} matches any term and shunts all remaining patterns if
-any. If all clauses fail (in particular, there is no pattern {\_})
-then a no-matching-clause error is raised.
-
-Failures in subsequent tactics do not cause backtracking to select new
-branches or inside the right-hand side of the selected branch even if
-it has backtracking points.
-
-\begin{ErrMsgs}
-
-\item \errindex{No matching clauses for match}
-
-  No pattern can be used and, in particular, there is no {\tt \_} pattern.
-
-\item \errindex{Argument of match does not evaluate to a term}
-
-  This happens when {\tacexpr} does not denote a term.
-
-\end{ErrMsgs}
-
-\begin{Variants}
-
-\item \index{multimatch@\texttt{multimatch}!in Ltac}
-\index{Ltac!multimatch@\texttt{multimatch}}
-Using {\tt multimatch} instead of {\tt match} will allow subsequent
-tactics to backtrack into a right-hand side tactic which has
-backtracking points left and trigger the selection of a new matching
-branch when all the backtracking points of the right-hand side have
-been consumed.
-
-The syntax {\tt match \ldots} is, in fact, a shorthand for
-{\tt once multimatch \ldots}.
-
-\item \index{lazymatch@\texttt{lazymatch}!in Ltac}
-\index{Ltac!lazymatch@\texttt{lazymatch}}
-Using {\tt lazymatch} instead of {\tt match} will perform the same
-pattern matching procedure but will commit to the first matching
-branch rather than trying a new matching if the right-hand side
-fails. If the right-hand side of the selected branch is a tactic with
-backtracking points, then subsequent failures cause this tactic to
-backtrack.
-
-\item \index{context@\texttt{context}!in pattern}
-There is a special form of patterns to match a subterm against the
-pattern:
-\begin{quote}
-{\tt context} {\ident} {\tt [} {\cpattern} {\tt ]}
-\end{quote}
-It matches any term with a subterm matching {\cpattern}. If there is
-a match, the optional {\ident} is assigned the ``matched context'', i.e.
-the initial term where the matched subterm is replaced by a
-hole. The example below will show how to use such term contexts.
-
-If the evaluation of the right-hand-side of a valid match fails, the
-next matching subterm is tried. If no further subterm matches, the
-next clause is tried. Matching subterms are considered top-bottom and
-from left to right (with respect to the raw printing obtained by
-setting option {\tt Printing All}, see Section~\ref{SetPrintingAll}).
-
-\begin{coq_example}
-Ltac f x :=
-  match x with
-    context f [S ?X] =>
-    idtac X;                    (* To display the evaluation order *)
-    assert (p := eq_refl 1 : X=1);    (* To filter the case X=1 *)
-    let x:= context f[O] in assert (x=O) (* To observe the context *)
-  end.
-Goal True.
-f (3+4).
-\end{coq_example}
-
-\end{Variants}
-
-\subsubsection[Pattern matching on goals]{Pattern matching on goals\index{Ltac!match goal@\texttt{match goal}}\label{ltac-match-goal}
-\index{Ltac!match reverse goal@\texttt{match reverse goal}}
-\index{match goal@\texttt{match goal}!in Ltac}
-\index{match reverse goal@\texttt{match reverse goal}!in Ltac}}
-
-We can make pattern matching on goals using the following expression:
-\begin{quote}
-\begin{tabbing}
-{\tt match goal with}\\
-~~\={\tt |} $hyp_{1,1}${\tt ,}...{\tt ,}$hyp_{1,m_1}$
-   ~~{\tt |-}{\cpattern}$_1${\tt =>} {\tacexpr}$_1$\\
-  \>{\tt |} $hyp_{2,1}${\tt ,}...{\tt ,}$hyp_{2,m_2}$
-   ~~{\tt |-}{\cpattern}$_2${\tt =>} {\tacexpr}$_2$\\
-~~...\\
-  \>{\tt |} $hyp_{n,1}${\tt ,}...{\tt ,}$hyp_{n,m_n}$
-   ~~{\tt |-}{\cpattern}$_n${\tt =>} {\tacexpr}$_n$\\
-  \>{\tt |\_}~~~~{\tt =>} {\tacexpr}$_{n+1}$\\
-{\tt end}
-\end{tabbing}
-\end{quote}
-
-If each hypothesis pattern $hyp_{1,i}$, with $i=1,...,m_1$
-is matched (non-linear first-order unification) by an hypothesis of
-the goal and if {\cpattern}$_1$ is matched by the conclusion of the
-goal, then {\tacexpr}$_1$ is evaluated to $v_1$ by substituting the
-pattern matching to the metavariables and the real hypothesis names
-bound to the possible hypothesis names occurring in the hypothesis
-patterns. If $v_1$ is a tactic value, then it is applied to the
-goal. If this application fails, then another combination of
-hypotheses is tried with the same proof context pattern. If there is
-no other combination of hypotheses then the second proof context
-pattern is tried and so on. If the next to last proof context pattern
-fails then {\tacexpr}$_{n+1}$ is evaluated to $v_{n+1}$ and $v_{n+1}$
-is applied. Note also that matching against subterms (using the {\tt
-context} {\ident} {\tt [} {\cpattern} {\tt ]}) is available and is
-also subject to yielding several matchings.
-
-Failures in subsequent tactics do not cause backtracking to select new
-branches or combinations of hypotheses, or inside the right-hand side
-of the selected branch even if it has backtracking points.
-
-\ErrMsg \errindex{No matching clauses for match goal}
-
-No clause succeeds, i.e. all matching patterns, if any,
-fail at the application of the right-hand-side.
-
-\medskip
-
-It is important to know that each hypothesis of the goal can be
-matched by at most one hypothesis pattern. The order of matching is
-the following: hypothesis patterns are examined from the right to the
-left (i.e. $hyp_{i,m_i}$ before $hyp_{i,1}$). For each hypothesis
-pattern, the goal hypothesis are matched in order (fresher hypothesis
-first), but it possible to reverse this order (older first) with
-the {\tt match reverse goal with} variant.
-
-\variant
-
-\index{multimatch goal@\texttt{multimatch goal}!in Ltac}
-\index{Ltac!multimatch goal@\texttt{multimatch goal}}
-\index{multimatch reverse goal@\texttt{multimatch reverse goal}!in Ltac}
-\index{Ltac!multimatch reverse goal@\texttt{multimatch reverse goal}}
-
-Using {\tt multimatch} instead of {\tt match} will allow subsequent
-tactics to backtrack into a right-hand side tactic which has
-backtracking points left and trigger the selection of a new matching
-branch or combination of hypotheses when all the backtracking points
-of the right-hand side have been consumed.
-
-The syntax {\tt match [reverse] goal \ldots} is, in fact, a shorthand for
-{\tt once multimatch [reverse] goal \ldots}.
-
-\index{lazymatch goal@\texttt{lazymatch goal}!in Ltac}
-\index{Ltac!lazymatch goal@\texttt{lazymatch goal}}
-\index{lazymatch reverse goal@\texttt{lazymatch reverse goal}!in Ltac}
-\index{Ltac!lazymatch reverse goal@\texttt{lazymatch reverse goal}}
-Using {\tt lazymatch} instead of {\tt match} will perform the same
-pattern matching procedure but will commit to the first matching
-branch with the first matching combination of hypotheses rather than
-trying a new matching if the right-hand side fails. If the right-hand
-side of the selected branch is a tactic with backtracking points, then
-subsequent failures cause this tactic to backtrack.
-
-\subsubsection[Filling a term context]{Filling a term context\index{context@\texttt{context}!in expression}}
-
-The following expression is not a tactic in the sense that it does not
-produce subgoals but generates a term to be used in tactic
-expressions:
-\begin{quote}
-{\tt context} {\ident} {\tt [} {\tacexpr} {\tt ]}
-\end{quote}
-{\ident} must denote a context variable bound by a {\tt context}
-pattern of a {\tt match} expression. This expression evaluates
-replaces the hole of the value of {\ident} by the value of
-{\tacexpr}.
-
-\ErrMsg \errindex{not a context variable}
-
-
-\subsubsection[Generating fresh hypothesis names]{Generating fresh hypothesis names\index{Ltac!fresh@\texttt{fresh}}
-\index{fresh@\texttt{fresh}!in Ltac}}
-
-Tactics sometimes have to generate new names for hypothesis. Letting
-the system decide a name with the {\tt intro} tactic is not so good
-since it is very awkward to retrieve the name the system gave.
-The following expression returns an identifier:
-\begin{quote}
-{\tt fresh} \nelist{\textrm{\textsl{component}}}{}
-\end{quote}
-It evaluates to an identifier unbound in the goal. This fresh
-identifier is obtained by concatenating the value of the
-\textrm{\textsl{component}}'s (each of them is, either an {\qualid} which
-has to refer to a (unqualified) name, or directly a name denoted by a
-{\qstring}). If the resulting name is already used, it is padded
-with a number so that it becomes fresh. If no component is
-given, the name is a fresh derivative of the name {\tt H}.
-
-\subsubsection[Computing in a constr]{Computing in a constr\index{Ltac!eval@\texttt{eval}}
-\index{eval@\texttt{eval}!in Ltac}}
-
-Evaluation of a term can be performed with:
-\begin{quote}
-{\tt eval} {\nterm{redexpr}} {\tt in} {\term}
-\end{quote}
-where \nterm{redexpr} is a reduction tactic among {\tt red}, {\tt
-hnf}, {\tt compute}, {\tt simpl}, {\tt cbv}, {\tt lazy}, {\tt unfold},
-{\tt fold}, {\tt pattern}.
-
-\subsubsection{Recovering the type of a term}
-%\tacindex{type of}
-\index{Ltac!type of@\texttt{type of}}
-\index{type of@\texttt{type of}!in Ltac}
-
-The following returns the type of {\term}:
-
-\begin{quote}
-{\tt type of} {\term}
-\end{quote}
-
-\subsubsection[Manipulating untyped terms]{Manipulating untyped terms\index{Ltac!uconstr@\texttt{uconstr}}
-\index{uconstr@\texttt{uconstr}!in Ltac}
-\index{Ltac!type\_term@\texttt{type\_term}}
-\index{type\_term@\texttt{type\_term}!in Ltac}}
-
-The terms built in Ltac are well-typed by default. It may not be
-appropriate for building large terms using a recursive Ltac function:
-the term has to be entirely type checked at each step, resulting in
-potentially very slow behavior. It is possible to build untyped terms
-using Ltac with the syntax
-
-\begin{quote}
-{\tt uconstr :} {\term}
-\end{quote}
-
-An untyped term, in Ltac, can contain references to hypotheses or to
-Ltac variables containing typed or untyped terms. An untyped term can
-be type-checked using the function {\tt type\_term} whose argument is
-parsed as an untyped term and returns a well-typed term which can be
-used in tactics.
-
-\begin{quote}
-{\tt type\_term} {\term}
-\end{quote}
-
-Untyped terms built using {\tt uconstr :} can also be used as
-arguments to the {\tt refine} tactic~\ref{refine}. In that case the
-untyped term is type checked against the conclusion of the goal, and
-the holes which are not solved by the typing procedure are turned into
-new subgoals.
-
-\subsubsection[Counting the goals]{Counting the goals\index{Ltac!numgoals@\texttt{numgoals}}\index{numgoals@\texttt{numgoals}!in Ltac}}
-
-The number of goals under focus can be recovered using the {\tt
-  numgoals} function. Combined with the {\tt guard} command below, it
-can be used to branch over the number of goals produced by previous tactics.
-
-\begin{coq_example*}
-Ltac pr_numgoals := let n := numgoals in idtac "There are" n "goals".
-
-Goal True /\ True /\ True.
-split;[|split].
-\end{coq_example*}
-\begin{coq_example}
-all:pr_numgoals.
-\end{coq_example}
-
-\subsubsection[Testing boolean expressions]{Testing boolean expressions\index{Ltac!guard@\texttt{guard}}\index{guard@\texttt{guard}!in Ltac}}
-
-The {\tt guard} tactic tests a boolean expression, and fails if the expression evaluates to false. If the expression evaluates to true, it succeeds without affecting the proof.
-
-\begin{quote}
-{\tt guard} {\it test}
-\end{quote}
-
-The accepted tests are simple integer comparisons.
-
-\begin{coq_example*}
-Goal True /\ True /\ True.
-split;[|split].
-\end{coq_example*}
-\begin{coq_example}
-all:let n:= numgoals in guard n<4.
-Fail all:let n:= numgoals in guard n=2.
-\end{coq_example}
-\begin{ErrMsgs}
-
-\item \errindex{Condition not satisfied}
-
-\end{ErrMsgs}
-
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-
-\subsubsection[Proving a subgoal as a separate lemma]{Proving a subgoal as a separate lemma\tacindex{abstract}\tacindex{transparent\_abstract}
-\index{Tacticals!abstract@{\tt abstract}}\index{Tacticals!transparent\_abstract@{\tt transparent\_abstract}}}
-
-From the outside ``\texttt{abstract \tacexpr}'' is the same as
-{\tt solve \tacexpr}. Internally it saves an auxiliary lemma called
-{\ident}\texttt{\_subproof}\textit{n} where {\ident} is the name of the
-current goal and \textit{n} is chosen so that this is a fresh name.
-Such an auxiliary lemma is inlined in the final proof term.
-
-This tactical is useful with tactics such as \texttt{omega} or
-\texttt{discriminate} that generate huge proof terms. With that tool
-the user can avoid the explosion at time of the \texttt{Save} command
-without having to cut manually the proof in smaller lemmas.
-
-It may be useful to generate lemmas minimal w.r.t. the assumptions they depend
-on. This can be obtained thanks to the option below.
-
-\begin{Variants}
-\item \texttt{abstract {\tacexpr} using {\ident}}.\\
-  Give explicitly the name of the auxiliary lemma.
-  Use this feature at your own risk; explicitly named and reused subterms
-  don't play well with asynchronous proofs.
-\item \texttt{transparent\_abstract {\tacexpr}}.\\
-  Save the subproof in a transparent lemma rather than an opaque one.
-  Use this feature at your own risk; building computationally relevant terms
-  with tactics is fragile.
-\item \texttt{transparent\_abstract {\tacexpr} using {\ident}}.\\
-  Give explicitly the name of the auxiliary transparent lemma.
-  Use this feature at your own risk; building computationally relevant terms
-  with tactics is fragile, and explicitly named and reused subterms
-  don't play well with asynchronous proofs.
-\end{Variants}
-
-\ErrMsg \errindex{Proof is not complete}
-
-\section[Tactic toplevel definitions]{Tactic toplevel definitions\comindex{Ltac}}
-
-\subsection{Defining {\ltac} functions}
-
-Basically, {\ltac} toplevel definitions are made as follows:
-%{\tt Tactic Definition} {\ident} {\tt :=} {\tacexpr}\\
-%
-%{\tacexpr} is evaluated to $v$ and $v$ is associated to {\ident}. Next, every
-%script is evaluated by substituting $v$ to {\ident}.
-%
-%We can define functional definitions by:\\
-\begin{quote}
-{\tt Ltac} {\ident} {\ident}$_1$ ... {\ident}$_n$ {\tt :=}
-{\tacexpr}
-\end{quote}
-This defines a new {\ltac} function that can be used in any tactic
-script or new {\ltac} toplevel definition.
-
-\Rem The preceding definition can equivalently be written:
-\begin{quote}
-{\tt Ltac} {\ident} {\tt := fun} {\ident}$_1$ ... {\ident}$_n$
-{\tt =>} {\tacexpr}
-\end{quote}
-Recursive and mutual recursive function definitions are also
-possible with the syntax:
-\begin{quote}
-{\tt Ltac} {\ident}$_1$ {\ident}$_{1,1}$ ...
-{\ident}$_{1,m_1}$~~{\tt :=} {\tacexpr}$_1$\\
-{\tt with} {\ident}$_2$ {\ident}$_{2,1}$ ... {\ident}$_{2,m_2}$~~{\tt :=}
-{\tacexpr}$_2$\\
-...\\
-{\tt with} {\ident}$_n$ {\ident}$_{n,1}$ ... {\ident}$_{n,m_n}$~~{\tt :=}
-{\tacexpr}$_n$
-\end{quote}
-\medskip
-It is also possible to \emph{redefine} an existing user-defined tactic
-using the syntax:
-\begin{quote}
-{\tt Ltac} {\qualid} {\ident}$_1$ ... {\ident}$_n$ {\tt ::=}
-{\tacexpr}
-\end{quote}
-A previous definition of {\qualid} must exist in the environment.
-The new definition will always be used instead of the old one and
-it goes across module boundaries.
-
-If preceded by the keyword {\tt Local} the tactic definition will not
-be exported outside the current module.
-
-\subsection[Printing {\ltac} tactics]{Printing {\ltac} tactics\comindex{Print Ltac}}
-
-Defined {\ltac} functions can be displayed using the command
-
-\begin{quote}
-{\tt Print Ltac {\qualid}.}
-\end{quote}
-
-The command {\tt Print Ltac Signatures\comindex{Print Ltac Signatures}} displays a list of all user-defined tactics, with their arguments.
-
-\section{Debugging {\ltac} tactics}
-
-\subsection[Info trace]{Info trace\comindex{Info}\optindex{Info Level}}
-
-It is possible to print the trace of the path eventually taken by an {\ltac} script. That is, the list of executed tactics, discarding all the branches which have failed. To that end the {\tt Info} command can be used with the following syntax.
-
-\begin{quote}
-{\tt Info} {\num} {\tacexpr}.
-\end{quote}
-
-The number {\num} is the unfolding level of tactics in the trace. At level $0$, the trace contains a sequence of tactics in the actual script, at level $1$, the trace will be the concatenation of the traces of these tactics, etc\ldots
-
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-\begin{coq_example*}
-Ltac t x := exists x; reflexivity.
-
-Goal exists n, n=0.
-\end{coq_example*}
-\begin{coq_example}
-Info 0 t 1||t 0.
-\end{coq_example}
-\begin{coq_example*}
-Undo.
-\end{coq_example*}
-\begin{coq_example}
-Info 1 t 1||t 0.
-\end{coq_example}
-
-The trace produced by {\tt Info} tries its best to be a reparsable {\ltac} script, but this goal is not achievable in all generality. So some of the output traces will contain oddities.
-
-As an additional help for debugging, the trace produced by {\tt Info} contains (in comments) the messages produced by the {\tt idtac} tacticals~\ref{ltac:idtac} at the right possition in the script. In particular, the calls to {\tt idtac} in branches which failed are not printed.
-
-An alternative to the {\tt Info} command is to use the {\tt Info Level} option as follows:
-
-\begin{quote}
-{\tt Set Info Level} \num.
-\end{quote}
-
-This will automatically print the same trace as {\tt Info \num} at each tactic call. The unfolding level can be overridden by a call to the {\tt Info} command. And this option can be turned off with:
-
-\begin{quote}
-{\tt Unset Info Level} \num.
-\end{quote}
-
-The current value for the {\tt Info Level} option can be checked using the {\tt Test Info Level} command.
-
-\subsection[Interactive debugger]{Interactive debugger\optindex{Ltac Debug}\optindex{Ltac Batch Debug}}
-
-The {\ltac} interpreter comes with a step-by-step debugger. The
-debugger can be activated using the command
-
-\begin{quote}
-{\tt Set Ltac Debug.}
-\end{quote}
-
-\noindent and deactivated using the command
-
-\begin{quote}
-{\tt Unset Ltac Debug.}
-\end{quote}
-
-To know if the debugger is on, use the command \texttt{Test Ltac Debug}.
-When the debugger is activated, it stops at every step of the
-evaluation of the current {\ltac} expression and it prints information
-on what it is doing. The debugger stops, prompting for a command which
-can be one of the following:
-
-\medskip
-\begin{tabular}{ll}
-simple newline: & go to the next step\\
-h: & get help\\
-x: & exit current evaluation\\
-s: & continue current evaluation without stopping\\
-r $n$: & advance $n$ steps further\\
-r {\qstring}: & advance up to the next call to ``{\tt idtac} {\qstring}''\\
-\end{tabular}
-
-A non-interactive mode for the debugger is available via the command
-
-\begin{quote}
-{\tt Set Ltac Batch Debug.}
-\end{quote}
-
-This option has the effect of presenting a newline at every prompt,
-when the debugger is on.  The debug log thus created, which does not
-require user input to generate when this option is set, can then be
-run through external tools such as \texttt{diff}.
-
-\subsection[Profiling {\ltac} tactics]{Profiling {\ltac} tactics\optindex{Ltac Profiling}\comindex{Show Ltac Profile}\comindex{Reset Ltac Profile}}
-
-It is possible to measure the time spent in invocations of primitive tactics as well as tactics defined in {\ltac} and their inner invocations. The primary use is the development of complex tactics, which can sometimes be so slow as to impede interactive usage. The reasons for the performence degradation can be intricate, like a slowly performing {\ltac} match or a sub-tactic whose performance only degrades in certain situations. The profiler generates a call tree and indicates the time spent in a tactic depending its calling context. Thus it allows to locate the part of a tactic definition that contains the performance bug.
-
-\begin{quote}
-{\tt Set Ltac Profiling}.
-\end{quote}
-Enables the profiler
-
-\begin{quote}
-{\tt Unset Ltac Profiling}.
-\end{quote}
-Disables the profiler
-
-\begin{quote}
-{\tt Show Ltac Profile}.
-\end{quote}
-Prints the profile
-
-\begin{quote}
-{\tt Show Ltac Profile} {\qstring}.
-\end{quote}
-Prints a profile for all tactics that start with {\qstring}. Append a period (.) to the string if you only want exactly that name.
-
-\begin{quote}
-{\tt Reset Ltac Profile}.
-\end{quote}
-Resets the profile, that is, deletes all accumulated information.  Note that backtracking across a {\tt Reset Ltac Profile} will not restore the information.
-
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-\begin{coq_example*}
-Require Import Coq.omega.Omega.
-
-Ltac mytauto := tauto.
-Ltac tac := intros; repeat split; omega || mytauto.
-
-Notation max x y := (x + (y - x)) (only parsing).
-\end{coq_example*}
-\begin{coq_example*}
-Goal forall x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z,
-    max x (max y z) = max (max x y) z /\ max x (max y z) = max (max x y) z
-    /\ (A /\ B /\ C /\ D /\ E /\ F /\ G /\ H /\ I /\ J /\ K /\ L /\ M /\ N /\ O /\ P /\ Q /\ R /\ S /\ T /\ U /\ V /\ W /\ X /\ Y /\ Z
-        -> Z /\ Y /\ X /\ W /\ V /\ U /\ T /\ S /\ R /\ Q /\ P /\ O /\ N /\ M /\ L /\ K /\ J /\ I /\ H /\ G /\ F /\ E /\ D /\ C /\ B /\ A).
-Proof.
-\end{coq_example*}
-\begin{coq_example}
-  Set Ltac Profiling.
-  tac.
-\end{coq_example}
-{\let\textit\texttt% use tt mode for the output of ltacprof
-\begin{coq_example}
-  Show Ltac Profile.
-\end{coq_example}
-\begin{coq_example}
-  Show Ltac Profile "omega".
-\end{coq_example}
-}
-\begin{coq_example*}
-Abort.
-Unset Ltac Profiling.
-\end{coq_example*}
-
-\tacindex{start ltac profiling}\tacindex{stop ltac profiling}
-The following two tactics behave like {\tt idtac} but enable and disable the profiling. They allow you to exclude parts of a proof script from profiling.
-
-\begin{quote}
-{\tt start ltac profiling}.
-\end{quote}
-
-\begin{quote}
-{\tt stop ltac profiling}.
-\end{quote}
-
-\tacindex{reset ltac profile}\tacindex{show ltac profile}
-The following tactics behave like the corresponding vernacular commands and allow displaying and resetting the profile from tactic scripts for benchmarking purposes.
-
-\begin{quote}
-{\tt reset ltac profile}.
-\end{quote}
-
-\begin{quote}
-{\tt show ltac profile}.
-\end{quote}
-
-\begin{quote}
-{\tt show ltac profile} {\qstring}.
-\end{quote}
-
-You can also pass the {\tt -profile-ltac} command line option to {\tt coqc}, which performs a {\tt Set Ltac Profiling} at the beginning of each document, and a {\tt Show Ltac Profile} at the end.
-
-Note that the profiler currently does not handle backtracking into multi-success tactics, and issues a warning to this effect in many cases when such backtracking occurs.
-
-\subsection[Run-time optimization tactic]{Run-time optimization tactic\label{tactic-optimizeheap}}.
-
-The following tactic behaves like {\tt idtac}, and running it compacts the heap in the
-OCaml run-time system. It is analogous to the Vernacular command {\tt Optimize Heap} (see~\ref{vernac-optimizeheap}).
-
-\tacindex{optimize\_heap}
-\begin{quote}
-{\tt optimize\_heap}.
-\end{quote}
-
-\endinput
-
-\subsection{Permutation on closed lists}
-
-\begin{figure}[b]
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-\begin{coq_example*}
-Require Import List.
-Section Sort.
-Variable A : Set.
-Inductive permut : list A -> list A -> Prop :=
-  | permut_refl   : forall l, permut l l
-  | permut_cons   :
-      forall a l0 l1, permut l0 l1 -> permut (a :: l0) (a :: l1)
-  | permut_append : forall a l, permut (a :: l) (l ++ a :: nil)
-  | permut_trans  :
-      forall l0 l1 l2, permut l0 l1 -> permut l1 l2 -> permut l0 l2.
-End Sort.
-\end{coq_example*}
-\end{center}
-\caption{Definition of the permutation predicate}
-\label{permutpred}
-\end{figure}
-
-
-Another more complex example is the problem of permutation on closed
-lists. The aim is to show that a closed list is a permutation of
-another one.  First, we define the permutation predicate as shown on
-Figure~\ref{permutpred}.
-
-\begin{figure}[p]
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_example}
-Ltac Permut n :=
-  match goal with
-  | |- (permut _ ?l ?l) => apply permut_refl
-  | |- (permut _ (?a :: ?l1) (?a :: ?l2)) =>
-      let newn := eval compute in (length l1) in
-      (apply permut_cons; Permut newn)
-  | |- (permut ?A (?a :: ?l1) ?l2) =>
-      match eval compute in n with
-      | 1 => fail
-      | _ =>
-          let l1' := constr:(l1 ++ a :: nil) in
-          (apply (permut_trans A (a :: l1) l1' l2);
-            [ apply permut_append | compute; Permut (pred n) ])
-      end
-  end.
-Ltac PermutProve :=
-  match goal with
-  | |- (permut _ ?l1 ?l2) =>
-      match eval compute in (length l1 = length l2) with
-      | (?n = ?n) => Permut n
-      end
-  end.
-\end{coq_example}
-\end{minipage}}
-\end{center}
-\caption{Permutation tactic}
-\label{permutltac}
-\end{figure}
-
-\begin{figure}[p]
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_example*}
-Lemma permut_ex1 :
-  permut nat (1 :: 2 :: 3 :: nil) (3 :: 2 :: 1 :: nil).
-Proof.
-PermutProve.
-Qed.
-
-Lemma permut_ex2 :
-  permut nat
-    (0 :: 1 :: 2 :: 3 :: 4 :: 5 :: 6 :: 7 :: 8 :: 9 :: nil)
-    (0 :: 2 :: 4 :: 6 :: 8 :: 9 :: 7 :: 5 :: 3 :: 1 :: nil).
-Proof.
-PermutProve.
-Qed.
-\end{coq_example*}
-\end{minipage}}
-\end{center}
-\caption{Examples of {\tt PermutProve} use}
-\label{permutlem}
-\end{figure}
-
-Next, we can write naturally the tactic and the result can be seen on
-Figure~\ref{permutltac}. We can notice that we use two toplevel
-definitions {\tt PermutProve} and {\tt Permut}. The function to be
-called is {\tt PermutProve} which computes the lengths of the two
-lists and calls {\tt Permut} with the length if the two lists have the
-same length. {\tt Permut} works as expected.  If the two lists are
-equal, it concludes. Otherwise, if the lists have identical first
-elements, it applies {\tt Permut} on the tail of the lists.  Finally,
-if the lists have different first elements, it puts the first element
-of one of the lists (here the second one which appears in the {\tt
-  permut} predicate) at the end if that is possible, i.e., if the new
-first element has been at this place previously. To verify that all
-rotations have been done for a list, we use the length of the list as
-an argument for {\tt Permut} and this length is decremented for each
-rotation down to, but not including, 1 because for a list of length
-$n$, we can make exactly $n-1$ rotations to generate at most $n$
-distinct lists. Here, it must be noticed that we use the natural
-numbers of {\Coq} for the rotation counter. On Figure~\ref{ltac}, we
-can see that it is possible to use usual natural numbers but they are
-only used as arguments for primitive tactics and they cannot be
-handled, in particular, we cannot make computations with them. So, a
-natural choice is to use {\Coq} data structures so that {\Coq} makes
-the computations (reductions) by {\tt eval compute in} and we can get
-the terms back by {\tt match}.
-
-With {\tt PermutProve}, we can now prove lemmas such those shown on
-Figure~\ref{permutlem}.
-
-
-\subsection{Deciding intuitionistic propositional logic}
-
-\begin{figure}[tbp]
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_example}
-Ltac Axioms :=
-  match goal with
-  | |- True => trivial
-  | _:False |- _  => elimtype False; assumption
-  | _:?A |- ?A  => auto
-  end.
-Ltac DSimplif :=
-  repeat
-   (intros;
-    match goal with
-     | id:(~ _) |- _ => red in id
-     | id:(_ /\ _) |- _ =>
-         elim id; do 2 intro; clear id
-     | id:(_ \/ _) |- _ =>
-         elim id; intro; clear id
-     | id:(?A /\ ?B -> ?C) |- _ =>
-         cut (A -> B -> C);
-          [ intro | intros; apply id; split; assumption ]
-     | id:(?A \/ ?B -> ?C) |- _ =>
-         cut (B -> C);
-          [ cut (A -> C);
-             [ intros; clear id
-             | intro; apply id; left; assumption ]
-          | intro; apply id; right; assumption ]
-     | id0:(?A -> ?B),id1:?A |- _ =>
-         cut B; [ intro; clear id0 | apply id0; assumption ]
-     | |- (_ /\ _) => split
-     | |- (~ _) => red
-     end).
-\end{coq_example}
-\end{minipage}}
-\end{center}
-\caption{Deciding intuitionistic propositions (1)}
-\label{tautoltaca}
-\end{figure}
-
-\begin{figure}
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_example}
-Ltac TautoProp :=
-  DSimplif;
-   Axioms ||
-     match goal with
-     | id:((?A -> ?B) -> ?C) |- _ =>
-          cut (B -> C);
-          [ intro; cut (A -> B);
-             [ intro; cut C;
-                [ intro; clear id | apply id; assumption ]
-             | clear id ]
-          | intro; apply id; intro; assumption ]; TautoProp
-     | id:(~ ?A -> ?B) |- _ =>
-         cut (False -> B);
-          [ intro; cut (A -> False);
-             [ intro; cut B;
-                [ intro; clear id | apply id; assumption ]
-             | clear id ]
-          | intro; apply id; red; intro; assumption ]; TautoProp
-     | |- (_ \/ _) => (left; TautoProp) || (right; TautoProp)
-     end.
-\end{coq_example}
-\end{minipage}}
-\end{center}
-\caption{Deciding intuitionistic propositions (2)}
-\label{tautoltacb}
-\end{figure}
-
-The pattern matching on goals allows a complete and so a powerful
-backtracking when returning tactic values. An interesting application
-is the problem of deciding intuitionistic propositional logic.
-Considering the contraction-free sequent calculi {\tt LJT*} of
-Roy~Dyckhoff (\cite{Dyc92}), it is quite natural to code such a tactic
-using the tactic language. On Figure~\ref{tautoltaca}, the tactic {\tt
-  Axioms} tries to conclude using usual axioms. The {\tt DSimplif}
-tactic applies all the reversible rules of Dyckhoff's system.
-Finally, on Figure~\ref{tautoltacb}, the {\tt TautoProp} tactic (the
-main tactic to be called) simplifies with {\tt DSimplif}, tries to
-conclude with {\tt Axioms} and tries several paths using the
-backtracking rules (one of the four Dyckhoff's rules for the left
-implication to get rid of the contraction and the right or).
-
-\begin{figure}[tb]
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_example*}
-Lemma tauto_ex1 : forall A B:Prop, A /\ B -> A \/ B.
-Proof.
-TautoProp.
-Qed.
-
-Lemma tauto_ex2 :
-   forall A B:Prop, (~ ~ B -> B) -> (A -> B) -> ~ ~ A -> B.
-Proof.
-TautoProp.
-Qed.
-\end{coq_example*}
-\end{minipage}}
-\end{center}
-\caption{Proofs of tautologies with {\tt TautoProp}}
-\label{tautolem}
-\end{figure}
-
-For example, with {\tt TautoProp}, we can prove tautologies like those of
-Figure~\ref{tautolem}.
-
-
-\subsection{Deciding type isomorphisms}
-
-A more tricky problem is to decide equalities between types and modulo
-isomorphisms. Here, we choose to use the isomorphisms of the simply typed
-$\lb{}$-calculus with Cartesian product and $unit$ type (see, for example,
-\cite{RC95}). The axioms of this $\lb{}$-calculus are given by
-Figure~\ref{isosax}.
-
-\begin{figure}
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-\begin{coq_example*}
-Open Scope type_scope.
-Section Iso_axioms.
-Variables A B C : Set.
-Axiom Com : A * B = B * A.
-Axiom Ass : A * (B * C) = A * B * C.
-Axiom Cur : (A * B -> C) = (A -> B -> C).
-Axiom Dis : (A -> B * C) = (A -> B) * (A -> C).
-Axiom P_unit : A * unit = A.
-Axiom AR_unit : (A -> unit) = unit.
-Axiom AL_unit : (unit -> A) = A.
-Lemma Cons : B = C -> A * B = A * C.
-Proof.
-intro Heq; rewrite Heq; reflexivity.
-Qed.
-End Iso_axioms.
-\end{coq_example*}
-\end{minipage}}
-\end{center}
-\caption{Type isomorphism axioms}
-\label{isosax}
-\end{figure}
-
-The tactic to judge equalities modulo this axiomatization can be written as
-shown on Figures~\ref{isosltac1} and~\ref{isosltac2}. The algorithm is quite
-simple. Types are reduced using axioms that can be oriented (this done by {\tt
-MainSimplif}). The normal forms are sequences of Cartesian
-products without Cartesian product in the left component. These normal forms
-are then compared modulo permutation of the components (this is done by {\tt
-CompareStruct}). The main tactic to be called and realizing this algorithm is
-{\tt IsoProve}.
-
-\begin{figure}
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_example}
-Ltac DSimplif trm :=
-  match trm with
-  | (?A * ?B * ?C) =>
-      rewrite <- (Ass A B C); try MainSimplif
-  | (?A * ?B -> ?C) =>
-      rewrite (Cur A B C); try MainSimplif
-  | (?A -> ?B * ?C) =>
-      rewrite (Dis A B C); try MainSimplif
-  | (?A * unit) =>
-      rewrite (P_unit A); try MainSimplif
-  | (unit * ?B) =>
-      rewrite (Com unit B); try MainSimplif
-  | (?A -> unit) =>
-      rewrite (AR_unit A); try MainSimplif
-  | (unit -> ?B) =>
-      rewrite (AL_unit B); try MainSimplif
-  | (?A * ?B) =>
-      (DSimplif A; try MainSimplif) || (DSimplif B; try MainSimplif)
-  | (?A -> ?B) =>
-      (DSimplif A; try MainSimplif) || (DSimplif B; try MainSimplif)
-  end
- with MainSimplif :=
-  match goal with
-  | |- (?A = ?B) => try DSimplif A; try DSimplif B
-  end.
-Ltac Length trm :=
-  match trm with
-  | (_ * ?B) => let succ := Length B in constr:(S succ)
-  | _ => constr:1
-  end.
-Ltac assoc := repeat rewrite <- Ass.
-\end{coq_example}
-\end{minipage}}
-\end{center}
-\caption{Type isomorphism tactic (1)}
-\label{isosltac1}
-\end{figure}
-
-\begin{figure}
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_example}
-Ltac DoCompare n :=
-  match goal with
-  | [ |- (?A = ?A) ] => reflexivity
-  | [ |- (?A * ?B = ?A * ?C) ] =>
-    apply Cons; let newn := Length B in DoCompare newn
-  | [ |- (?A * ?B = ?C) ] =>
-    match eval compute in n with
-    | 1 => fail
-    | _ =>
-      pattern (A * B) at 1; rewrite Com; assoc; DoCompare (pred n)
-    end
-  end.
-Ltac CompareStruct :=
-  match goal with
-  | [ |- (?A = ?B) ] =>
-      let l1 := Length A
-      with l2 := Length B in
-      match eval compute in (l1 = l2) with
-      | (?n = ?n) => DoCompare n
-      end
-  end.
-Ltac IsoProve := MainSimplif; CompareStruct.
-\end{coq_example}
-\end{minipage}}
-\end{center}
-\caption{Type isomorphism tactic (2)}
-\label{isosltac2}
-\end{figure}
-
-Figure~\ref{isoslem} gives examples of what can be solved by {\tt IsoProve}.
-
-\begin{figure}
-\begin{center}
-\fbox{\begin{minipage}{0.95\textwidth}
-\begin{coq_example*}
-Lemma isos_ex1 :
-  forall A B:Set, A * unit * B = B * (unit * A).
-Proof.
-intros; IsoProve.
-Qed.
-
-Lemma isos_ex2 :
-  forall A B C:Set,
-    (A * unit -> B * (C * unit)) =
-    (A * unit -> (C -> unit) * C) * (unit -> A -> B).
-Proof.
-intros; IsoProve.
-Qed.
-\end{coq_example*}
-\end{minipage}}
-\end{center}
-\caption{Type equalities solved by {\tt IsoProve}}
-\label{isoslem}
-\end{figure}
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: "Reference-Manual"
-%%% End:
diff --git a/doc/refman/RefMan-oth.tex b/doc/refman/RefMan-oth.tex
deleted file mode 100644
index bef31d3fa5..0000000000
--- a/doc/refman/RefMan-oth.tex
+++ /dev/null
@@ -1,1224 +0,0 @@
-\chapter[Vernacular commands]{Vernacular commands\label{Vernacular-commands}
-\label{Other-commands}}
-%HEVEA\cutname{vernacular.html}
-
-\section{Displaying}
-
-\subsection[\tt Print {\qualid}.]{\tt Print {\qualid}.\comindex{Print}}
-This command displays on the screen information about the declared or
-defined object referred by {\qualid}.
-
-\begin{ErrMsgs}
-\item {\qualid} \errindex{not a defined object}
-\item \errindex{Universe instance should have length} $n$.
-\item \errindex{This object does not support universe names.}
-\end{ErrMsgs}
-
-\begin{Variants}
-\item {\tt Print Term {\qualid}.}
-\comindex{Print Term}\\ 
-This is a synonym to {\tt Print {\qualid}} when {\qualid} denotes a
-global constant. 
-
-\item {\tt About {\qualid}.}
-\label{About}
-\comindex{About}\\ 
-This displays various information about the object denoted by {\qualid}:
-its kind (module, constant, assumption, inductive,
-constructor, abbreviation, \ldots), long name, type, implicit
-arguments and argument scopes. It does not print the body of
-definitions or proofs.
-
-\item {\tt Print {\qualid}@\{names\}.}\\
-This locally renames the polymorphic universes of {\qualid}.
-An underscore means the raw universe is printed.
-This form can be used with {\tt Print Term} and {\tt About}.
-
-%\item {\tt Print Proof {\qualid}.}\comindex{Print Proof}\\
-%In case \qualid\ denotes an opaque theorem defined in a section,
-%it is stored on a special unprintable form and displayed as 
-%{\tt <recipe>}. {\tt Print Proof} forces the printable form of \qualid\
-%to be computed and displays it.
-\end{Variants}
-
-\subsection[\tt Print All.]{\tt Print All.\comindex{Print All}}
-This command displays information about the current state of the
-environment, including sections and modules.
-
-\begin{Variants}
-\item {\tt Inspect \num.}\comindex{Inspect}\\
-This command displays the {\num} last objects of the current
-environment, including sections and modules.
-\item {\tt Print Section {\ident}.}\comindex{Print Section}\\
-should correspond to a currently open section, this command
-displays the objects defined since the beginning of this section.
-% Discontinued
-%% \item {\tt Print.}\comindex{Print}\\
-%% This command displays the axioms and variables declarations in the
-%% environment as well as the constants defined since the last variable
-%% was introduced.
-\end{Variants}
-
-\section{Flags, Options and Tables}
-
-{\Coq} configurability is based on flags (e.g. {\tt Set Printing All} in
-Section~\ref{SetPrintingAll}), options (e.g. {\tt Set Printing Width
-  {\integer}} in Section~\ref{SetPrintingWidth}), or tables (e.g. {\tt
-  Add Printing Record {\ident}}, in Section~\ref{AddPrintingLet}). The
-names of flags, options and tables are made of non-empty sequences of
-identifiers (conventionally with capital initial letter). The general
-commands handling flags, options and tables are given below.
-
-\subsection[\tt Set {\rm\sl flag}.]{\tt Set {\rm\sl flag}.\comindex{Set}}
-This command switches {\rm\sl flag} on. The original state of
-{\rm\sl flag} is restored when the current module ends.
-
-\begin{Variants}
-\item {\tt Local Set {\rm\sl flag}.}\\
-This command switches {\rm\sl flag} on. The original state of
-{\rm\sl flag} is restored when the current \emph{section} ends.
-\item {\tt Global Set {\rm\sl flag}.}\\
-This command switches {\rm\sl flag} on. The original state of
-{\rm\sl flag} is \emph{not} restored at the end of the module. Additionally,
-if set in a file, {\rm\sl flag} is switched on when the file is
-{\tt Require}-d.
-\end{Variants}
-
-\subsection[\tt Unset {\rm\sl flag}.]{\tt Unset {\rm\sl flag}.\comindex{Unset}}
-This command switches {\rm\sl flag} off. The original state of {\rm\sl flag}
-is restored when the current module ends.
-
-\begin{Variants}
-\item {\tt Local Unset {\rm\sl flag}.\comindex{Local Unset}}\\
-This command switches {\rm\sl flag} off. The original state of {\rm\sl flag}
-is restored when the current \emph{section} ends.
-\item {\tt Global Unset {\rm\sl flag}.\comindex{Global Unset}}\\
-This command switches {\rm\sl flag} off.  The original state of
-{\rm\sl flag} is \emph{not} restored at the end of the module. Additionally,
-if set in a file, {\rm\sl flag} is switched off when the file is
-{\tt Require}-d.
-\end{Variants}
-
-\subsection[\tt Test {\rm\sl flag}.]{\tt Test {\rm\sl flag}.\comindex{Test}}
-This command prints whether {\rm\sl flag} is on or off.
-
-\subsection[\tt Set {\rm\sl option} {\rm\sl value}.]{\tt Set {\rm\sl option} {\rm\sl value}.\comindex{Set}}
-This command sets {\rm\sl option} to {\rm\sl value}. The original value of
-{\rm\sl option} is restored when the current module ends.
-
-\begin{Variants}
-\item {\tt Local Set {\rm\sl option} {\rm\sl value}.\comindex{Local Set}}
-This command sets {\rm\sl option} to {\rm\sl value}. The original value of
-{\rm\sl option} is restored at the end of the module.
-\item {\tt Global Set {\rm\sl option} {\rm\sl value}.\comindex{Global Set}}
-This command sets {\rm\sl option} to {\rm\sl value}. The original value of
-{\rm\sl option} is \emph{not} restored at the end of the module. Additionally,
-if set in a file, {\rm\sl option} is set to {\rm\sl value} when the file is
-{\tt Require}-d.
-\end{Variants}
-
-\subsection[\tt Unset {\rm\sl option}.]{\tt Unset {\rm\sl option}.\comindex{Unset}}
-This command resets {\rm\sl option} to its default value.
-
-\begin{Variants}
-\item {\tt Local Unset {\rm\sl option}.\comindex{Local Unset}}\\
-This command resets {\rm\sl option} to its default value. The original state of {\rm\sl option}
-is restored when the current \emph{section} ends.
-\item {\tt Global Unset {\rm\sl option}.\comindex{Global Unset}}\\
-This command resets {\rm\sl option} to its default value.  The original state of
-{\rm\sl option} is \emph{not} restored at the end of the module. Additionally,
-if unset in a file, {\rm\sl option} is reset to its default value when the file is
-{\tt Require}-d.
-\end{Variants}
-
-\subsection[\tt Test {\rm\sl option}.]{\tt Test {\rm\sl option}.\comindex{Test}}
-This command prints the current value of {\rm\sl option}.
-
-\subsection{Tables}
-The general commands for tables are {\tt Add {\rm\sf table} {\rm\sl
-    value}}, {\tt Remove {\rm\sf table} {\rm\sl value}}, {\tt Test
-    {\rm\sf table}}, {\tt Test {\rm\sf table} for {\rm\sl value}} and
-  {\tt Print Table {\rm\sf table}}.
-
-\subsection[\tt Print Options.]{\tt Print Options.\comindex{Print Options}}
-This command lists all available flags, options and tables.
-
-\begin{Variants}
-\item {\tt Print Tables}.\comindex{Print Tables}\\
-This is a synonymous of {\tt Print Options.}
-\end{Variants}
-
-\section{Requests to the environment}
-
-\subsection[\tt Check {\term}.]{\tt Check {\term}.\label{Check}
-\comindex{Check}}
-This command displays the type of {\term}. When called in proof mode, 
-the term is checked in the local context of the current subgoal.
-
-\begin{Variants}
-\item {\tt selector: Check {\term}}.\\
-specifies on which subgoal to perform typing (see
-  Section~\ref{tactic-syntax}).
-\end{Variants}
-
-
-\subsection[\tt Eval {\rm\sl convtactic} in {\term}.]{\tt Eval {\rm\sl convtactic} in {\term}.\comindex{Eval}}
-
-This command performs the specified reduction on {\term}, and displays
-the resulting term with its type. The term to be reduced may depend on
-hypothesis introduced in the first subgoal (if a proof is in
-progress).
-
-\SeeAlso Section~\ref{Conversion-tactics}.
-
-\subsection[\tt Compute {\term}.]{\tt Compute {\term}.\comindex{Compute}}
-
-This command performs a call-by-value evaluation of {\term} by using
-the bytecode-based virtual machine. It is a shortcut for
-{\tt Eval vm\_compute in {\term}}.
-
-\SeeAlso Section~\ref{Conversion-tactics}.
-
-\subsection[\tt Extraction \term.]{\tt Extraction \term.\label{ExtractionTerm}
-\comindex{Extraction}} 
-This command displays the extracted term from
-{\term}. The extraction is processed according to the distinction
-between {\Set} and {\Prop}; that is to say, between logical and
-computational content (see Section~\ref{Sorts}). The extracted term is
-displayed in {\ocaml} syntax, where global identifiers are still
-displayed as in \Coq\ terms.
-
-\begin{Variants}
-\item \texttt{Recursive Extraction} {\qualid$_1$} \ldots{} {\qualid$_n$}{\tt .}\\
-  Recursively extracts all the material needed for the extraction of 
-  global {\qualid$_1$}, \ldots, {\qualid$_n$}.
-\end{Variants}
-
-\SeeAlso Chapter~\ref{Extraction}.
-
-\subsection[\tt Print Assumptions {\qualid}.]{\tt Print Assumptions {\qualid}.\comindex{Print Assumptions}}
-\label{PrintAssumptions}
-
-This commands display all the assumptions (axioms, parameters and
-variables) a theorem or definition depends on.  Especially, it informs
-on the assumptions with respect to which the validity of a theorem
-relies.
-
-\begin{Variants}
-\item \texttt{\tt Print Opaque Dependencies {\qualid}.
-  \comindex{Print Opaque Dependencies}}\\
-  Displays the set of opaque constants {\qualid} relies on in addition
-  to the assumptions.
-\item \texttt{\tt Print Transparent Dependencies {\qualid}.
-  \comindex{Print Transparent Dependencies}}\\
-  Displays the set of transparent constants {\qualid} relies on in addition
-  to the assumptions.
-\item \texttt{\tt Print All Dependencies {\qualid}.
-  \comindex{Print All Dependencies}}\\
-  Displays all assumptions and constants {\qualid} relies on.
-\end{Variants}
-
-\subsection[\tt Search {\qualid}.]{\tt Search {\qualid}.\comindex{Search}}
-This command displays the name and type of all objects (hypothesis of
-the current goal, theorems, axioms, etc) of the current context whose
-statement contains \qualid. This command is useful to remind the user
-of the name of library lemmas.
-
-\begin{ErrMsgs}
-\item \errindex{The reference \qualid\ was not found in the current
-environment}\\
-    There is no constant in the environment named \qualid.
-\end{ErrMsgs}
-
-\newcommand{\termpatternorstr}{{\termpattern}\textrm{\textsl{-}}{\str}}
-
-\begin{Variants}
-\item {\tt Search {\str}.}
-
-If {\str} is a valid identifier, this command displays the name and type
-of all objects (theorems, axioms, etc) of the current context whose
-name contains {\str}. If {\str} is a notation's string denoting some
-reference {\qualid} (referred to by its main symbol as in \verb="+"=
-or by its notation's string as in \verb="_ + _"= or \verb="_ 'U' _"=, see
-Section~\ref{Notation}), the command works like {\tt Search
-{\qualid}}.
-
-\item {\tt Search {\str}\%{\delimkey}.}
-
-The string {\str} must be a notation or the main symbol of a notation
-which is then interpreted in the scope bound to the delimiting key
-{\delimkey} (see Section~\ref{scopechange}).
-
-\item {\tt Search {\termpattern}.}
-
-This searches for all statements or types of definition that contains
-a subterm that matches the pattern {\termpattern} (holes of the
-pattern are either denoted by ``{\texttt \_}'' or
-by ``{\texttt ?{\ident}}'' when non linear patterns are expected).
-
-\item {\tt Search \nelist{\zeroone{-}{\termpatternorstr}}{}.}\\
-
-\noindent where {\termpatternorstr} is a
-{\termpattern} or a {\str}, or a {\str} followed by a scope
-delimiting key {\tt \%{\delimkey}}.
-
-This generalization of {\tt Search} searches for all objects
-whose statement or type contains a subterm matching {\termpattern} (or
-{\qualid} if {\str} is the notation for a reference {\qualid}) and
-whose name contains all {\str} of the request that correspond to valid
-identifiers. If a {\termpattern} or a {\str} is prefixed by ``-'', the
-search excludes the objects that mention that {\termpattern} or that
-{\str}.
-
-\item
-  {\tt Search} \nelist{{\termpatternorstr}}{}
-    {\tt inside} {\module$_1$} \ldots{} {\module$_n$}{\tt .}
-
-This restricts the search to constructions defined in modules
-{\module$_1$} \ldots{} {\module$_n$}.
-
-\item
-  {\tt Search \nelist{{\termpatternorstr}}{}
-     outside {\module$_1$}...{\module$_n$}.}
-
-This restricts the search to constructions not defined in modules
-{\module$_1$} \ldots{} {\module$_n$}.
-
-\item {\tt selector: Search \nelist{\zeroone{-}{\termpatternorstr}}{}.}
-
-  This specifies the goal on which to search hypothesis (see
-  Section~\ref{tactic-syntax}). By default the 1st goal is searched.
-  This variant can be combined with other variants presented here.
-\end{Variants}
-
-\examples
-
-\begin{coq_example*}
-Require Import ZArith.
-\end{coq_example*}
-\begin{coq_example}
-Search Z.mul Z.add "distr".
-Search "+"%Z "*"%Z "distr" -positive -Prop.
-Search (?x * _ + ?x * _)%Z outside OmegaLemmas.
-\end{coq_example}
-
-\Warning \comindex{SearchAbout} Up to {\Coq} version 8.4, {\tt Search}
-had the behavior of current {\tt SearchHead} and the behavior of
-current {\tt Search} was obtained with command {\tt SearchAbout}. For
-compatibility, the deprecated name {\tt SearchAbout} can still be used
-as a synonym of {\tt Search}. For compatibility, the list of objects to
-search when using {\tt SearchAbout} may also be enclosed by optional
-{\tt [ ]} delimiters.
-
-\subsection[\tt SearchHead {\term}.]{\tt SearchHead {\term}.\comindex{SearchHead}}
-This command displays the name and type of all hypothesis of the
-current goal (if any) and theorems of the current context whose
-statement's conclusion has the form {\tt ({\term} t1 ..
-  tn)}.  This command is useful to remind the user of the name of
-library lemmas.
-
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-
-\begin{coq_example}
-SearchHead le.
-SearchHead (@eq bool).
-\end{coq_example}
-
-\begin{Variants}
-\item
-{\tt SearchHead} {\term} {\tt inside} {\module$_1$} \ldots{} {\module$_n$}{\tt .}
-
-This restricts the search to constructions defined in modules
-{\module$_1$} \ldots{} {\module$_n$}.
-
-\item {\tt SearchHead} {\term} {\tt outside} {\module$_1$} \ldots{} {\module$_n$}{\tt .}
-
-This restricts the search to constructions not defined in modules
-{\module$_1$} \ldots{} {\module$_n$}.
-
-\begin{ErrMsgs}
-\item \errindex{Module/section \module{} not found}
-No module \module{} has been required (see Section~\ref{Require}).
-\end{ErrMsgs}
-
-\item {\tt selector: SearchHead {\term}.}
-
-  This specifies the goal on which to search hypothesis (see
-  Section~\ref{tactic-syntax}). By default the 1st goal is searched.
-  This variant can be combined with other variants presented here.
-
-\end{Variants}
-
-\Warning Up to {\Coq} version 8.4, {\tt SearchHead} was named {\tt Search}.
-
-\subsection[\tt SearchPattern {\termpattern}.]{\tt SearchPattern {\term}.\comindex{SearchPattern}}
-
-This command displays the name and type of all hypothesis of the
-current goal (if any) and theorems of the current context whose statement's
-conclusion or last hypothesis and conclusion matches the expression
-{\term} where holes in the latter are denoted by ``{\texttt \_}''. It
-is a variant of {\tt Search
-  {\termpattern}} that does not look for subterms but searches for
-statements whose conclusion has exactly the expected form, or whose
-statement finishes by the given series of hypothesis/conclusion.
-
-\begin{coq_example*}
-Require Import Arith.
-\end{coq_example*}
-\begin{coq_example}
-SearchPattern (_ + _ = _ + _).
-SearchPattern (nat -> bool).
-SearchPattern (forall l : list _, _ l l).
-\end{coq_example}
-
-Patterns need not be linear: you can express that the same expression
-must occur in two places by using pattern variables `{\texttt
-?{\ident}}''.
-
-\begin{coq_example}
-SearchPattern (?X1 + _ = _ + ?X1).
-\end{coq_example}
-
-\begin{Variants}
-\item {\tt SearchPattern {\term} inside
-{\module$_1$} \ldots{} {\module$_n$}.}
-
-This restricts the search to constructions defined in modules
-{\module$_1$} \ldots{} {\module$_n$}.
-
-\item {\tt SearchPattern {\term} outside {\module$_1$} \ldots{} {\module$_n$}.}
-
-This restricts the search to constructions not defined in modules
-{\module$_1$} \ldots{} {\module$_n$}.
-
-\item {\tt selector: SearchPattern {\term}.}
-
-  This specifies the goal on which to search hypothesis (see
-  Section~\ref{tactic-syntax}). By default the 1st goal is searched.
-  This variant can be combined with other variants presented here.
-
-\end{Variants}
-
-\subsection[\tt SearchRewrite {\term}.]{\tt SearchRewrite {\term}.\comindex{SearchRewrite}}
-
-This command displays the name and type of all hypothesis of the
-current goal (if any) and theorems of the current context whose
-statement's conclusion is an equality of which one side matches the
-expression {\term}. Holes in {\term} are denoted by ``{\texttt \_}''.
-
-\begin{coq_example}
-Require Import Arith.
-SearchRewrite (_ + _ + _).
-\end{coq_example}
-
-\begin{Variants}
-\item {\tt SearchRewrite {\term} inside
-{\module$_1$} \ldots{} {\module$_n$}.}
-
-This restricts the search to constructions defined in modules
-{\module$_1$} \ldots{} {\module$_n$}.
-
-\item {\tt SearchRewrite {\term} outside {\module$_1$} \ldots{} {\module$_n$}.}
-
-This restricts the search to constructions not defined in modules
-{\module$_1$} \ldots{} {\module$_n$}.
-
-\item {\tt selector: SearchRewrite {\term}.}
-
-  This specifies the goal on which to search hypothesis (see
-  Section~\ref{tactic-syntax}). By default the 1st goal is searched.
-  This variant can be combined with other variants presented here.
-
-\end{Variants}
-
-\subsubsection{Nota Bene:}
-For the {\tt Search}, {\tt SearchHead}, {\tt SearchPattern} and
-{\tt SearchRewrite} queries, it is possible to globally filter
-the search results via the command
-{\tt Add Search Blacklist "substring1"}.
-A lemma whose fully-qualified name contains any of the declared substrings
-will be removed from the search results.
-The default blacklisted substrings are {\tt 
-  "\_subproof" "Private\_"}. The command {\tt Remove Search Blacklist
-  ...} allows expunging this blacklist.
-
-% \begin{tabbing}
-% \ \ \ \ \=11.\ \=\kill
-% \>1.\>$A=B\mx{ if }A\stackrel{\bt{}\io{}}{\lra{}}B$\\
-% \>2.\>$\sa{}x:A.B=\sa{}y:A.B[x\la{}y]\mx{ if }y\not\in{}FV(\sa{}x:A.B)$\\
-% \>3.\>$\Pi{}x:A.B=\Pi{}y:A.B[x\la{}y]\mx{ if }y\not\in{}FV(\Pi{}x:A.B)$\\
-% \>4.\>$\sa{}x:A.B=\sa{}x:B.A\mx{ if }x\not\in{}FV(A,B)$\\
-% \>5.\>$\sa{}x:(\sa{}y:A.B).C=\sa{}x:A.\sa{}y:B[y\la{}x].C[x\la{}(x,y)]$\\
-% \>6.\>$\Pi{}x:(\sa{}y:A.B).C=\Pi{}x:A.\Pi{}y:B[y\la{}x].C[x\la{}(x,y)]$\\
-% \>7.\>$\Pi{}x:A.\sa{}y:B.C=\sa{}y:(\Pi{}x:A.B).(\Pi{}x:A.C[y\la{}(y\sm{}x)]$\\
-% \>8.\>$\sa{}x:A.unit=A$\\
-% \>9.\>$\sa{}x:unit.A=A[x\la{}tt]$\\
-% \>10.\>$\Pi{}x:A.unit=unit$\\
-% \>11.\>$\Pi{}x:unit.A=A[x\la{}tt]$
-% \end{tabbing}
-
-% For more informations about the exact working of this command, see
-% \cite{Del97}.
-
-\subsection[\tt Locate {\qualid}.]{\tt Locate {\qualid}.\comindex{Locate}
-\label{Locate}}
-This command displays the full name of objects whose name is a prefix of the
-qualified identifier {\qualid}, and consequently the \Coq\ module in which they
-are defined. It searches for objects from the different qualified name spaces of
-{\Coq}: terms, modules, Ltac, etc.
-
-\begin{coq_eval}
-(*************** The last line should produce **************************)
-(*********** Error: I.Dont.Exist not a defined object ******************)
-\end{coq_eval}
-\begin{coq_eval}
-Set Printing Depth 50.
-\end{coq_eval}
-\begin{coq_example}
-Locate nat.
-Locate Datatypes.O.
-Locate Init.Datatypes.O.
-Locate Coq.Init.Datatypes.O.
-Locate I.Dont.Exist.
-\end{coq_example}
-
-\begin{Variants}
-\item {\tt Locate Term {\qualid}.}\comindex{Locate Term}\\
-  As {\tt Locate} but restricted to terms.
-
-\item {\tt Locate Module {\qualid}.}
-  As {\tt Locate} but restricted to modules.
-
-\item {\tt Locate Ltac {\qualid}.}\comindex{Locate Ltac}\\
-  As {\tt Locate} but restricted to tactics.
-\end{Variants}
-
-
-\SeeAlso Section \ref{LocateSymbol}
-
-\section{Loading files}
-
-\Coq\ offers the possibility of loading different
-parts of a whole development stored in separate files. Their contents
-will be loaded as if they were entered from the keyboard. This means
-that the loaded files are ASCII files containing sequences of commands
-for \Coq's toplevel. This kind of file is called a {\em script} for
-\Coq\index{Script file}. The standard (and default) extension of
-\Coq's script files is {\tt .v}.
-
-\subsection[\tt Load {\ident}.]{\tt Load {\ident}.\comindex{Load}\label{Load}}
-This command loads the file named {\ident}{\tt .v}, searching
-successively in each of the directories specified in the {\em
-  loadpath}. (see Section~\ref{loadpath})
-
-Files loaded this way cannot leave proofs open, and neither the {\tt
-  Load} command can be use inside a proof.
-
-\begin{Variants}
-\item {\tt Load {\str}.}\label{Load-str}\\
-  Loads the file denoted by the string {\str}, where {\str} is any
-  complete filename. Then the \verb.~. and {\tt ..}
-  abbreviations are allowed as well as shell variables. If no
-  extension is specified, \Coq\ will use the default extension {\tt
-    .v}
-\item {\tt Load Verbose {\ident}.}, 
-  {\tt Load Verbose {\str}}\\
-  \comindex{Load Verbose}
-  Display, while loading, the answers of \Coq\ to each command
-  (including tactics) contained in the loaded file
-  \SeeAlso Section~\ref{Begin-Silent}
-\end{Variants}
-
-\begin{ErrMsgs}
-\item \errindex{Can't find file {\ident} on loadpath}
-\item \errindex{Load is not supported inside proofs}
-\item \errindex{Files processed by Load cannot leave open proofs}
-\end{ErrMsgs}
-
-\section[Compiled files]{Compiled files\label{compiled}\index{Compiled files}}
-
-This section describes the commands used to load compiled files (see
-Chapter~\ref{Addoc-coqc} for documentation on how to compile a file).
-A compiled file is a particular case of module called {\em library file}.
-
-%%%%%%%%%%%%
-% Import and Export described in RefMan-mod.tex
-% the minor difference (to avoid multiple Exporting of libraries) in
-% the treatment of normal modules and libraries by Export omitted
-
-\subsection[\tt Require {\qualid}.]{\tt Require {\qualid}.\label{Require}
-\comindex{Require}}
-
-This command looks in the loadpath for a file containing
-module {\qualid} and adds the corresponding module to the environment
-of {\Coq}. As library files have dependencies in other library files,
-the command {\tt Require {\qualid}} recursively requires all library
-files the module {\qualid} depends on and adds the corresponding modules to the
-environment of {\Coq} too. {\Coq} assumes that the compiled files have
-been produced by a valid {\Coq} compiler and their contents are then not
-replayed nor rechecked.
-
-To locate the file in the file system, {\qualid} is decomposed under
-the form {\dirpath}{\tt .}{\textsl{ident}} and the file {\ident}{\tt
-.vo} is searched in the physical directory of the file system that is
-mapped in {\Coq} loadpath to the logical path {\dirpath} (see
-Section~\ref{loadpath}). The mapping between physical directories and
-logical names at the time of requiring the file must be consistent
-with the mapping used to compile the file. If several files match, one of them
-is picked in an unspecified fashion.
-
-\begin{Variants}
-\item {\tt Require Import {\qualid}.} \comindex{Require Import}
-
-  This loads and declares the module {\qualid} and its dependencies
-  then imports the contents of {\qualid} as described in
-  Section~\ref{Import}.
-
-  It does not import the modules on which {\qualid} depends unless
-  these modules were itself required in module {\qualid} using {\tt
-  Require Export}, as described below, or recursively required through
-  a sequence of {\tt Require Export}.
-
-  If the module required has already been loaded, {\tt Require Import
-  {\qualid}} simply imports it, as {\tt Import {\qualid}} would.
-
-\item {\tt Require Export {\qualid}.}
-  \comindex{Require Export}
-
-  This command acts as {\tt Require Import} {\qualid}, but if a
-  further module, say {\it A}, contains a command {\tt Require
-  Export} {\it B}, then the command {\tt Require Import} {\it A}
-  also imports the module {\it B}.
-
-\item {\tt Require \zeroone{Import {\sl |} Export}} {\qualid}$_1$ {\ldots} {\qualid}$_n${\tt .}
-
-  This loads the modules {\qualid}$_1$, \ldots, {\qualid}$_n$ and
-  their recursive dependencies. If {\tt Import} or {\tt Export} is
-  given, it also imports {\qualid}$_1$, \ldots, {\qualid}$_n$ and all
-  the recursive dependencies that were marked or transitively marked
-  as {\tt Export}.
-
-\item {\tt From {\dirpath} Require {\qualid}.}
-  \comindex{From Require}
-
-  This command acts as {\tt Require}, but picks any library whose absolute name
-  is of the form {\tt{\dirpath}.{\dirpath'}.{\qualid}} for some {\dirpath'}.
-  This is useful to ensure that the {\qualid} library comes from a given
-  package by making explicit its absolute root.
-
-\end{Variants}
-
-\begin{ErrMsgs}
-
-\item \errindex{Cannot load {\qualid}: no physical path bound to {\dirpath}}
-
-\item \errindex{Cannot find library foo in loadpath}
-
-  The command did not find the file {\tt foo.vo}. Either {\tt
-    foo.v} exists but is not compiled or {\tt foo.vo} is in a directory
-  which is not in your {\tt LoadPath} (see Section~\ref{loadpath}).
-
-\item \errindex{Compiled library {\ident}.vo makes inconsistent assumptions over library {\qualid}}
-
-  The command tried to load library file {\ident}.vo that depends on
-  some specific version of library {\qualid} which is not the one
-  already loaded in the current {\Coq} session. Probably {\ident}.v
-  was not properly recompiled with the last version of the file
-  containing module {\qualid}.
-
-\item \errindex{Bad magic number}
-
-  \index{Bad-magic-number@{\tt Bad Magic Number}}
-  The file {\tt{\ident}.vo} was found but either it is not a \Coq\
-  compiled module, or it was compiled with an older and incompatible
-  version of {\Coq}.
-
-\item \errindex{The file {\ident}.vo contains library {\dirpath} and not
-  library {\dirpath'}}
-
-  The library file {\dirpath'} is indirectly required by the {\tt
-  Require} command but it is bound in the current loadpath to the file
-  {\ident}.vo which was bound to a different library name {\dirpath}
-  at the time it was compiled.
-
-\item \errindex{Require is not allowed inside a module or a module type}
-
-  This command is not allowed inside a module or a module type being defined.
-  It is meant to describe a dependency between compilation units. Note however
-  that the commands {\tt Import} and {\tt Export} alone can be used inside
-  modules (see Section~\ref{Import}).
-
-\end{ErrMsgs}
-
-\SeeAlso Chapter~\ref{Addoc-coqc}
-
-\subsection[\tt Print Libraries.]{\tt Print Libraries.\comindex{Print Libraries}}
-
-This command displays the list of library files loaded in the current
-{\Coq} session. For each of these libraries, it also tells if it is
-imported.
-
-\subsection[\tt Declare ML Module {\str$_1$} .. {\str$_n$}.]{\tt Declare ML Module {\str$_1$} .. {\str$_n$}.\comindex{Declare ML Module}}
-This commands loads the {\ocaml} compiled files {\str$_1$} {\ldots}
-{\str$_n$} (dynamic link). It is mainly used to load tactics
-dynamically.
-% (see Chapter~\ref{WritingTactics}).
- The files are
-searched into the current {\ocaml} loadpath (see the command {\tt
-Add ML Path} in the Section~\ref{loadpath}).  Loading of {\ocaml}
-files is only possible under the bytecode version of {\tt coqtop}
-(i.e. {\tt coqtop.byte}, see chapter 
-\ref{Addoc-coqc}), or when {\Coq} has been compiled with a version of
-{\ocaml} that supports native {\tt Dynlink} ($\ge$ 3.11).
-
-\begin{Variants}
-\item {\tt Local Declare ML Module {\str$_1$} .. {\str$_n$}.}\\
-  This variant is not exported to the modules that import the module
-  where they occur, even if outside a section.
-\end{Variants}
-
-\begin{ErrMsgs}
-\item \errindex{File not found on loadpath : \str}
-\item \errindex{Loading of ML object file forbidden in a native {\Coq}}
-\end{ErrMsgs}
-
-\subsection[\tt Print ML Modules.]{\tt Print ML Modules.\comindex{Print ML Modules}}
-This print the name of all \ocaml{} modules loaded with \texttt{Declare
-  ML Module}. To know from where these module were loaded, the user
-should use the command \texttt{Locate File} (see Section~\ref{Locate File})
-
-\section[Loadpath]{Loadpath}
-
-Loadpaths are preferably managed using {\Coq} command line options
-(see Section~\ref{loadpath}) but there remain vernacular commands to
-manage them for practical purposes. Such commands are only meant to be issued in
-the toplevel, and using them in source files is discouraged.
-
-\subsection[\tt Pwd.]{\tt Pwd.\comindex{Pwd}\label{Pwd}}
-This command displays the current working directory.
-
-\subsection[\tt Cd {\str}.]{\tt Cd {\str}.\comindex{Cd}}
-This command changes the current directory according to {\str} 
-which can be any valid path.
-
-\begin{Variants}
-\item {\tt Cd.}\\
-  Is equivalent to {\tt Pwd.}
-\end{Variants}
-
-\subsection[\tt Add LoadPath {\str} as {\dirpath}.]{\tt Add LoadPath {\str} as {\dirpath}.\comindex{Add LoadPath}\label{AddLoadPath}}
-
-This command is equivalent to the command line option {\tt -Q {\str}
-  {\dirpath}}. It adds the physical directory {\str} to the current {\Coq}
-loadpath and maps it to the logical directory {\dirpath}.
-
-\begin{Variants}
-\item {\tt Add LoadPath {\str}.}\\
-Performs as {\tt Add LoadPath {\str} as {\dirpath}} but for the empty directory path.
-\end{Variants}
-
-\subsection[\tt Add Rec LoadPath {\str} as {\dirpath}.]{\tt Add Rec LoadPath {\str} as {\dirpath}.\comindex{Add Rec LoadPath}\label{AddRecLoadPath}}
-This command is equivalent to the command line option {\tt -R {\str}
-  {\dirpath}}. It adds the physical directory {\str} and all its
-subdirectories to the current {\Coq} loadpath.
-
-\begin{Variants}
-\item {\tt Add Rec LoadPath {\str}.}\\
-Works as {\tt Add Rec LoadPath {\str} as {\dirpath}} but for the empty logical directory path.
-\end{Variants}
-
-\subsection[\tt Remove LoadPath {\str}.]{\tt Remove LoadPath {\str}.\comindex{Remove LoadPath}}
-This command removes the path {\str} from the current \Coq\ loadpath.
-
-\subsection[\tt Print LoadPath.]{\tt Print LoadPath.\comindex{Print LoadPath}}
-This command displays the current \Coq\ loadpath.
-
-\begin{Variants}
-\item {\tt Print LoadPath {\dirpath}.}\\
-Works as {\tt Print LoadPath} but displays only the paths that extend the {\dirpath} prefix.
-\end{Variants}
-
-\subsection[\tt Add ML Path {\str}.]{\tt Add ML Path {\str}.\comindex{Add ML Path}}
-This command adds the path {\str} to the current {\ocaml} loadpath (see
-the command {\tt Declare ML Module} in the Section~\ref{compiled}).
-
-\subsection[\tt Add Rec ML Path {\str}.]{\tt Add Rec ML Path {\str}.\comindex{Add Rec ML Path}}
-This command adds the directory {\str} and all its subdirectories 
-to the current {\ocaml} loadpath (see
-the command {\tt Declare ML Module} in the Section~\ref{compiled}).
-
-\subsection[\tt Print ML Path {\str}.]{\tt Print ML Path {\str}.\comindex{Print ML Path}}
-This command displays the current {\ocaml} loadpath.
-This command makes sense only under the bytecode version of {\tt
-coqtop}, i.e. {\tt coqtop.byte} (see the
-command {\tt Declare ML Module} in the section
-\ref{compiled}).
-
-\subsection[\tt Locate File {\str}.]{\tt Locate File {\str}.\comindex{Locate
-  File}\label{Locate File}}
-This command displays the location of file {\str} in the current loadpath.
-Typically, {\str} is a \texttt{.cmo} or \texttt{.vo} or \texttt{.v} file.
-
-\subsection[\tt Locate Library {\dirpath}.]{\tt Locate Library {\dirpath}.\comindex{Locate Library}\label{Locate Library}}
-This command gives the status of the \Coq\ module {\dirpath}. It tells if the
-module is loaded and if not searches in the load path for a module
-of logical name {\dirpath}.
-
-\section{Backtracking}
-
-The backtracking commands described in this section can only be used
-interactively, they cannot be part of a vernacular file loaded via
-{\tt Load} or compiled by {\tt coqc}.
-
-\subsection[\tt Reset \ident.]{\tt Reset \ident.\comindex{Reset}}
-This command removes all the objects in the environment since \ident\ 
-was introduced, including \ident. \ident\ may be the name of a defined
-or declared object as well as the name of a section. One cannot reset
-over the name of a module or of an object inside a module.
-
-\begin{ErrMsgs}
-\item \ident: \errindex{no such entry}
-\end{ErrMsgs}
-
-\begin{Variants}
- \item {\tt Reset Initial.}\comindex{Reset Initial}\\
-   Goes back to the initial state, just after the start of the
-   interactive session.
-\end{Variants}
-
-\subsection[\tt Back.]{\tt Back.\comindex{Back}}
-
-This commands undoes all the effects of the last vernacular
-command. Commands read from a vernacular file via a {\tt Load} are
-considered as a single command. Proof management commands
-are also handled by this command (see Chapter~\ref{Proof-handling}).
-For that, {\tt Back} may have to undo more than one command in order
-to reach a state where the proof management information is available.
-For instance, when the last command is a {\tt Qed}, the management
-information about the closed proof has been discarded. In this case,
-{\tt Back} will then undo all the proof steps up to the statement of
-this proof.
-
-\begin{Variants}
-\item {\tt Back $n$} \\
-  Undoes $n$ vernacular commands. As for {\tt Back}, some extra
-  commands may be undone in order to reach an adequate state.
-  For instance {\tt Back n} will not re-enter a closed proof,
-  but rather go just before that proof.
-\end{Variants}
-
-\begin{ErrMsgs}
-\item \errindex{Invalid backtrack} \\
-  The user wants to undo more commands than available in the history.
-\end{ErrMsgs}
-
-\subsection[\tt BackTo $\num$.]{\tt BackTo $\num$.\comindex{BackTo}}
-\label{sec:statenums}
-
-This command brings back the system to the state labeled $\num$,
-forgetting the effect of all commands executed after this state.
-The state label is an integer which grows after each successful command.
-It is displayed in the prompt when in \texttt{-emacs} mode.
-Just as {\tt Back} (see above), the {\tt BackTo} command now handles
-proof states. For that, it may have to undo some
-extra commands and end on a state $\num' \leq \num$ if necessary.
-
-\begin{Variants}
-\item {\tt Backtrack $\num_1$ $\num_2$ $\num_3$}.\comindex{Backtrack}\\
-  {\tt Backtrack} is a \emph{deprecated} form of {\tt BackTo} which
-  allows explicitly manipulating the proof environment. The three
-  numbers $\num_1$, $\num_2$ and $\num_3$ represent the following:
-\begin{itemize}
-\item $\num_3$: Number of \texttt{Abort} to perform, i.e. the number
-  of currently opened nested proofs that must be canceled (see
-  Chapter~\ref{Proof-handling}).
-\item $\num_2$: \emph{Proof state number} to unbury once aborts have
-  been done. {\Coq} will compute the number of \texttt{Undo} to perform
-  (see Chapter~\ref{Proof-handling}).
-\item $\num_1$: State label to reach, as for {\tt BackTo}.
-\end{itemize}
-\end{Variants}
-
-\begin{ErrMsgs}
-\item \errindex{Invalid backtrack} \\
-  The destination state label is unknown.
-\end{ErrMsgs}
-
-\section{Quitting and debugging}
-
-\subsection[\tt Quit.]{\tt Quit.\comindex{Quit}}
-This command permits to quit \Coq.
-
-\subsection[\tt Drop.]{\tt Drop.\comindex{Drop}\label{Drop}}
-
-This is used mostly as a debug facility by \Coq's implementors
-and does not concern the casual user.
-This command permits to leave {\Coq} temporarily and enter the
-{\ocaml} toplevel. The {\ocaml} command:
-
-\begin{flushleft}
-\begin{verbatim}
-#use "include";;
-\end{verbatim}
-\end{flushleft}
-
-\noindent add the right loadpaths and loads some toplevel printers for
-all abstract types of \Coq - section\_path, identifiers, terms, judgments,
-\dots. You can also use the file \texttt{base\_include} instead,
-that loads only the pretty-printers for section\_paths and
-identifiers.
-% See Section~\ref{test-and-debug} more information on the
-% usage of the toplevel.
-You can return back to \Coq{} with the command: 
-
-\begin{flushleft}
-\begin{verbatim}
-go();;
-\end{verbatim}
-\end{flushleft}
-
-\begin{Warnings}
-\item It only works with the bytecode version of {\Coq} (i.e. {\tt coqtop} called with option {\tt -byte}, see the contents of Section~\ref{binary-images}).
-\item You must have compiled {\Coq} from the source package and set the
-  environment variable \texttt{COQTOP} to the root of your copy of the sources (see Section~\ref{EnvVariables}).
-\end{Warnings}
-
-\subsection[\tt Time \textrm{\textsl{command}}.]{\tt Time \textrm{\textsl{command}}.\comindex{Time}
-\label{time}}
-This command executes the vernacular command \textrm{\textsl{command}}
-and display the time needed to execute it.
-
-\subsection[\tt Redirect "\textrm{\textsl{file}}" \textrm{\textsl{command}}.]{\tt Redirect "\textrm{\textsl{file}}" \textrm{\textsl{command}}.\comindex{Redirect}
-\label{redirect}}
-This command executes the vernacular command \textrm{\textsl{command}}, redirecting its output to ``\textrm{\textsl{file}}.out''.
-
-\subsection[\tt Timeout \textrm{\textsl{int}} \textrm{\textsl{command}}.]{\tt Timeout \textrm{\textsl{int}} \textrm{\textsl{command}}.\comindex{Timeout}
-\label{timeout}}
-
-This command executes the vernacular command \textrm{\textsl{command}}. If
-the command has not terminated after the time specified by the integer
-(time expressed in seconds), then it is interrupted and an error message
-is displayed.
-
-\subsection[\tt Set Default Timeout \textrm{\textsl{int}}.]{\tt Set
-  Default Timeout \textrm{\textsl{int}}.\optindex{Default Timeout}}
-
-After using this command, all subsequent commands behave as if they
-were passed to a {\tt Timeout} command. Commands already starting by
-a {\tt Timeout} are unaffected.
-
-\subsection[\tt Unset Default Timeout.]{\tt Unset Default Timeout.\optindex{Default Timeout}}
-
-This command turns off the use of a default timeout.
-
-\subsection[\tt Test Default Timeout.]{\tt Test Default Timeout.\optindex{Default Timeout}}
-
-This command displays whether some default timeout has be set or not.
-
-\subsection[\tt Fail \textrm{\textsl{command-or-tactic}}.]{\tt Fail \textrm{\textsl{command-or-tactic}}.\comindex{Fail}\label{Fail}}
-
-For debugging {\Coq} scripts, sometimes it is desirable to know
-whether a command or a tactic fails. If the given command or tactic
-fails, the {\tt Fail} statement succeeds, without changing the proof
-state, and in interactive mode, {\Coq} prints a message confirming the failure.
-If the command or tactic succeeds, the statement is an error, and
-{\Coq} prints a message indicating that the failure did not occur.
-
-\section{Controlling display}
-
-\subsection[\tt Set Silent.]{\tt Set Silent.\optindex{Silent}
-\label{Begin-Silent}
-\index{Silent mode}}
-This command turns off the normal displaying.
-
-\subsection[\tt Unset Silent.]{\tt Unset Silent.\optindex{Silent}}
-This command turns the normal display on.
-
-\subsection[\tt Set Warnings ``(\nterm{w}$_1$,\ldots,%
-  \nterm{w}$_n$)''.]{{\tt Set Warnings ``(\nterm{w}$_1$,\ldots,%
-  \nterm{w}$_n$)''}.\optindex{Warnings}}
-\label{SetWarnings}
-This command configures the display of warnings. It is experimental, and
-expects, between quotes, a comma-separated list of warning names or
-categories. Adding~\texttt{-} in front of a warning or category disables it,
-adding~\texttt{+} makes it an error. It is possible to use the special
-categories \texttt{all} and \texttt{default}, the latter containing the warnings
-enabled by default. The flags are interpreted from left to right, so in case of
-an overlap, the flags on the right have higher priority, meaning that
-\texttt{A,-A} is equivalent to \texttt{-A}.
-
-\subsection[\tt Set Search Output Name Only.]{\tt Set Search Output Name Only.\optindex{Search Output Name Only}
-\label{Search-Output-Name-Only}
-\index{Search Output Name Only mode}}
-This command restricts the output of search commands to identifier names; turning it on causes invocations of {\tt Search}, {\tt SearchHead}, {\tt SearchPattern}, {\tt SearchRewrite} etc. to omit types from their output, printing only identifiers.
-
-\subsection[\tt Unset Search Output Name Only.]{\tt Unset Search Output Name Only.\optindex{Search Output Name Only}}
-This command turns type display in search results back on.
-
-\subsection[\tt Set Printing Width {\integer}.]{\tt Set Printing Width {\integer}.\optindex{Printing Width}}
-\label{SetPrintingWidth}
-This command sets which left-aligned part of the width of the screen
-is used for display. 
-
-\subsection[\tt Unset Printing Width.]{\tt Unset Printing Width.\optindex{Printing Width}}
-This command resets the width of the screen used for display to its
-default value (which is 78 at the time of writing this documentation).
-
-\subsection[\tt Test Printing Width.]{\tt Test Printing Width.\optindex{Printing Width}}
-This command displays the current screen width used for display.
-
-\subsection[\tt Set Printing Depth {\integer}.]{\tt Set Printing Depth {\integer}.\optindex{Printing Depth}}
-This command sets the nesting depth of the formatter used for
-pretty-printing. Beyond this depth, display of subterms is replaced by
-dots. 
-
-\subsection[\tt Unset Printing Depth.]{\tt Unset Printing Depth.\optindex{Printing Depth}}
-This command resets the nesting depth of the formatter used for
-pretty-printing to its default value (at the
-time of writing this documentation, the default value is 50).
-
-\subsection[\tt Test Printing Depth.]{\tt Test Printing Depth.\optindex{Printing Depth}}
-This command displays the current nesting depth used for display.
-
-\subsection[\tt Unset Printing Compact Contexts.]{\tt Unset Printing Compact Contexts.\optindex{Printing Compact Contexts}}
-This command resets the displaying of goals contexts to non compact
-mode (default at the time of writing this documentation). Non compact
-means that consecutive variables of different types are printed on
-different lines.
-
-\subsection[\tt Set Printing Compact Contexts.]{\tt Set Printing Compact Contexts.\optindex{Printing Compact Contexts}}
-This command sets the displaying of goals contexts to compact mode.
-The printer tries to reduce the vertical size of goals contexts by
-putting several variables (even if of different types) on the same
-line provided it does not exceed the printing width (See {\tt Set
-  Printing Width} above).
-
-\subsection[\tt Test Printing Compact Contexts.]{\tt Test Printing Compact Contexts.\optindex{Printing Compact Contexts}}
-This command displays the current state of compaction of goal.
-
-
-\subsection[\tt Unset Printing Unfocused.]{\tt Unset Printing Unfocused.\optindex{Printing Unfocused}}
-This command resets the displaying of goals to focused goals only
-(default). Unfocused goals are created by focusing other goals with
-bullets(see~\ref{bullets}) or curly braces (see~\ref{curlybacket}).
-
-\subsection[\tt Set Printing Unfocused.]{\tt Set Printing Unfocused.\optindex{Printing Unfocused}}
-This command enables the displaying of unfocused goals. The goals are
-displayed after the focused ones and are distinguished by a separator.
-
-\subsection[\tt Test Printing Unfocused.]{\tt Test Printing Unfocused.\optindex{Printing Unfocused}}
-This command displays the current state of unfocused goals display.
-
-\subsection[\tt Set Printing Dependent Evars Line.]{\tt Set Printing Dependent Evars Line.\optindex{Printing Dependent Evars Line}}
-This command enables the printing of the ``{\tt (dependent evars: \ldots)}''
-line when {\tt -emacs} is passed.
-
-\subsection[\tt Unset Printing Dependent Evars Line.]{\tt Unset Printing Dependent Evars Line.\optindex{Printing Dependent Evars Line}}
-This command disables the printing of the ``{\tt (dependent evars: \ldots)}''
-line when {\tt -emacs} is passed.
-
-%\subsection{\tt Abstraction ...}
-%Not yet documented.
-
-\section{Controlling the reduction strategies and the conversion algorithm}
-\label{Controlling_reduction_strategy}
-
-{\Coq} provides reduction strategies that the tactics can invoke and
-two different algorithms to check the convertibility of types.
-The first conversion algorithm lazily
-compares applicative terms while the other is a brute-force but efficient
-algorithm that first normalizes the terms before comparing them.  The
-second algorithm is based on a bytecode representation of terms
-similar to the bytecode representation used in the ZINC virtual
-machine~\cite{Leroy90}. It is especially useful for intensive
-computation of algebraic values, such as numbers, and for reflection-based
-tactics. The commands to fine-tune the reduction strategies and the
-lazy conversion algorithm are described first.
-
-\subsection[{\tt Opaque} \qualid$_1$ {\ldots} \qualid$_n${\tt .}]{{\tt Opaque} \qualid$_1$ {\ldots} \qualid$_n${\tt .}\comindex{Opaque}\label{Opaque}}
-This command has an effect on unfoldable constants, i.e. 
-on constants defined by {\tt Definition} or {\tt Let} (with an explicit
-body), or by a command assimilated to a definition such as {\tt
-Fixpoint}, {\tt Program Definition}, etc, or by a proof ended by {\tt
-Defined}. The command tells not to unfold
-the constants {\qualid$_1$} {\ldots} {\qualid$_n$} in tactics using
-$\delta$-conversion (unfolding a constant is replacing it by its
-definition).
-
-{\tt Opaque} has also an effect on the conversion algorithm of {\Coq},
-telling it to delay the unfolding of a constant as much as possible when
-{\Coq} has to check the conversion (see Section~\ref{conv-rules})
-of two distinct applied constants.
-
-The scope of {\tt Opaque} is limited to the current section, or
-current file, unless the variant {\tt Global Opaque \qualid$_1$ {\ldots}
-\qualid$_n$} is used.
-
-\SeeAlso sections \ref{Conversion-tactics}, \ref{Automatizing},
-\ref{Theorem}
-
-\begin{ErrMsgs}
-\item \errindex{The reference \qualid\ was not found in the current
-environment}\\
-    There is no constant referred by {\qualid} in the environment.
-    Nevertheless, if you asked \texttt{Opaque foo bar}
-    and if \texttt{bar} does not exist, \texttt{foo} is set opaque.
-\end{ErrMsgs}
-
-\subsection[{\tt Transparent} \qualid$_1$ {\ldots} \qualid$_n${\tt .}]{{\tt Transparent} \qualid$_1$ {\ldots} \qualid$_n${\tt .}\comindex{Transparent}\label{Transparent}}
-This command is the converse of {\tt Opaque} and it applies on
-unfoldable constants to restore their unfoldability after an {\tt
-Opaque} command.
-
-Note in particular that constants defined by a proof ended by {\tt
-Qed} are not unfoldable and {\tt Transparent} has no effect on
-them. This is to keep with the usual mathematical practice of {\em
-proof irrelevance}: what matters in a mathematical development is the
-sequence of lemma statements, not their actual proofs. This
-distinguishes lemmas from the usual defined constants, whose actual
-values are of course relevant in general.
-
-The scope of {\tt Transparent} is limited to the current section, or
-current file, unless the variant {\tt Global Transparent} \qualid$_1$
-{\ldots} \qualid$_n$ is used.
-
-\begin{ErrMsgs}
-% \item \errindex{Can not set transparent.}\\
-%     It is a constant from a required module or a parameter.
-\item \errindex{The reference \qualid\ was not found in the current
-environment}\\
-    There is no constant referred by {\qualid} in the environment.
-\end{ErrMsgs}
-
-\SeeAlso sections \ref{Conversion-tactics}, \ref{Automatizing},
-\ref{Theorem}
-
-\subsection{{\tt Strategy} {\it level} {\tt [} \qualid$_1$ {\ldots} \qualid$_n$
-  {\tt ].}\comindex{Strategy}\comindex{Local Strategy}\label{Strategy}}
-This command generalizes the behavior of {\tt Opaque} and {\tt
-  Transparent} commands. It is used to fine-tune the strategy for
-unfolding constants, both at the tactic level and at the kernel
-level. This command associates a level to \qualid$_1$ {\ldots}
-\qualid$_n$. Whenever two expressions with two distinct head
-constants are compared (for instance, this comparison can be triggered
-by a type cast), the one with lower level is expanded first. In case
-of a tie, the second one (appearing in the cast type) is expanded.
-
-Levels can be one of the following (higher to lower):
-\begin{description}
-\item[opaque]: level of opaque constants. They cannot be expanded by
-  tactics (behaves like $+\infty$, see next item).
-\item[\num]: levels indexed by an integer. Level $0$ corresponds
-  to the default behavior, which corresponds to transparent
-  constants. This level can also be referred to as {\bf transparent}.
-  Negative levels correspond to constants to be expanded before normal
-  transparent constants, while positive levels correspond to constants
-  to be expanded after normal transparent constants.
-\item[expand]: level of constants that should be expanded first
-  (behaves like $-\infty$)
-\end{description}
-
-These directives survive section and module closure, unless the
-command is prefixed by {\tt Local}. In the latter case, the behavior
-regarding sections and modules is the same as for the {\tt
-  Transparent} and {\tt Opaque} commands.
-
-\subsection{{\tt Print Strategy} \qualid{\tt .}\comindex{Print Strategy}\label{PrintStrategy}}
-
-This command prints the strategy currently associated to \qualid{}. It fails if
-\qualid{} is not an unfoldable reference, that is, neither a variable nor a
-constant.
-
-\begin{ErrMsgs}
-\item The reference is not unfoldable.
-\end{ErrMsgs}
-
-\begin{Variants}
-\item {\tt Print Strategies}\comindex{Print Strategies}\\
-  Print all the currently non-transparent strategies.
-\end{Variants}
-
-\subsection{\tt Declare Reduction \ident\ := {\rm\sl convtactic}.}
-
-This command allows giving a short name to a reduction expression,
-for instance {\tt lazy beta delta [foo bar]}. This short name can
-then be used in {\tt Eval \ident\ in ...} or {\tt eval} directives.
-This command accepts the {\tt Local} modifier, for discarding
-this reduction name at the end of the file or module. For the moment
-the name cannot be qualified. In particular declaring the same name
-in several modules or in several functor applications will be refused
-if these declarations are not local. The name \ident\ cannot be used
-directly as an Ltac tactic, but nothing prevent the user to also
-perform a {\tt Ltac \ident\ := {\rm\sl convtactic}}.
-
-\SeeAlso sections \ref{Conversion-tactics}
-
-\section{Controlling the locality of commands}
-
-\subsection{{\tt Local}, {\tt Global}
-\comindex{Local}
-\comindex{Global}
-}
-
-Some commands support a {\tt Local} or {\tt Global} prefix modifier to
-control the scope of their effect. There are four kinds of commands:
-
-\begin{itemize}
-\item Commands whose default is to extend their effect both outside the
-  section and the module or library file they occur in.
-
-  For these commands, the {\tt Local} modifier limits the effect of
-  the command to the current section or module it occurs in.
-
-  As an example, the {\tt Coercion} (see Section~\ref{Coercions})
-  and {\tt Strategy} (see Section~\ref{Strategy})
-  commands belong to this category.
-
-\item Commands whose default behavior is to stop their effect at the
-  end of the section they occur in but to extent their effect outside
-  the module or library file they occur in.
-
-  For these commands, the {\tt Local} modifier limits the effect of
-  the command to the current module if the command does not occur in a
-  section and the {\tt Global} modifier extends the effect outside the
-  current sections and current module if the command occurs in a
-  section.
-
-  As an example, the {\tt Implicit Arguments} (see
-  Section~\ref{Implicit Arguments}), {\tt Ltac} (see
-  Chapter~\ref{TacticLanguage}) or {\tt Notation} (see
-  Section~\ref{Notation}) commands belong to this category.
-
-  Notice that a subclass of these commands do not support extension of
-  their scope outside sections at all and the {\tt Global} is not
-  applicable to them.
-
-\item Commands whose default behavior is to stop their effect at the
-  end of the section or module they occur in.
-
-  For these commands, the {\tt Global} modifier extends their effect
-  outside the sections and modules they occurs in.
-
-  The {\tt Transparent} and {\tt Opaque} (see
-  Section~\ref{Controlling_reduction_strategy}) commands belong to
-  this category.
-
-\item Commands whose default behavior is to extend their effect
-  outside sections but not outside modules when they occur in a
-  section and to extend their effect outside the module or library
-  file they occur in when no section contains them.
-
-  For these commands, the {\tt Local} modifier limits the effect to
-  the current section or module while the {\tt Global} modifier extends
-  the effect outside the module even when the command occurs in a section.
-
-  The {\tt Set} and {\tt Unset} commands belong to this category.
-\end{itemize}
-
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "Reference-Manual"
-%%% End: 
diff --git a/doc/refman/RefMan-pro.tex b/doc/refman/RefMan-pro.tex
deleted file mode 100644
index bd74a40d7c..0000000000
--- a/doc/refman/RefMan-pro.tex
+++ /dev/null
@@ -1,581 +0,0 @@
-\chapter[Proof handling]{Proof handling\index{Proof editing}
-\label{Proof-handling}}
-%HEVEA\cutname{proof-handling.html}
-
-In \Coq's proof editing mode all top-level commands documented in 
-Chapter~\ref{Vernacular-commands} remain available
-and the user has access to specialized commands dealing with proof
-development pragmas documented in this section. He can also use some
-other specialized commands called {\em tactics}.  They are the very
-tools allowing the user to deal with logical reasoning. They are
-documented in Chapter~\ref{Tactics}.\\ 
-When switching in editing proof mode, the prompt
-\index{Prompt} 
-{\tt Coq <} is changed into {\tt {\ident} <} where {\ident} is the
-declared name of the theorem currently edited.
-
-At each stage of a proof development, one has a list of goals to
-prove. Initially, the list consists only in the theorem itself. After
-having applied some tactics, the list of goals contains the subgoals
-generated by the tactics.
-
-To each subgoal is associated  a number of
-hypotheses called the {\em \index*{local context}} of the goal.
-Initially, the local context contains the local variables and
-hypotheses of the current section (see Section~\ref{Variable}) and the
-local variables and hypotheses of the theorem statement.  It is
-enriched by the use of certain tactics (see e.g. {\tt intro} in
-Section~\ref{intro}).
-
-When a proof is completed, the message {\tt Proof completed} is
-displayed. One can then register this proof as a defined constant in the
-environment. Because there exists a correspondence between proofs and
-terms of $\lambda$-calculus, known as the {\em Curry-Howard
-isomorphism} \cite{How80,Bar91,Gir89,Hue89}, \Coq~ stores proofs as
-terms of {\sc Cic}. Those terms are called {\em proof
-  terms}\index{Proof term}.
-
-\ErrMsg When one attempts to use a proof editing command out of the
-proof editing mode, \Coq~ raises the error message : \errindex{No focused
-  proof}.
-
-\section{Switching on/off the proof editing mode}
-
-The proof editing mode is entered by asserting a statement, which
-typically is the assertion of a theorem:
-
-\begin{quote}
-{\tt Theorem {\ident} \zeroone{\binders} : {\form}.\comindex{Theorem}
-\label{Theorem}}
-\end{quote}
-
-The list of assertion commands is given in
-Section~\ref{Assertions}. The command {\tt Goal} can also be used.
-
-\subsection[Goal {\form}.]{\tt Goal {\form}.\comindex{Goal}\label{Goal}}
-
-This is intended for quick assertion of statements, without knowing in
-advance which name to give to the assertion, typically for quick
-testing of the provability of a statement. If the proof of the
-statement is eventually completed and validated, the statement is then
-bound to the name {\tt Unnamed\_thm} (or a variant of this name not
-already used for another statement).
-
-\subsection[\tt Qed.]{\tt Qed.\comindex{Qed}\label{Qed}}
-This command is available in interactive editing proof mode when the
-proof is completed.  Then {\tt Qed} extracts a proof term from the
-proof script, switches back to {\Coq} top-level and attaches the
-extracted proof term to the declared name of the original goal. This
-name is added to the environment as an {\tt Opaque} constant.
-
-\begin{ErrMsgs}
-\item \errindex{Attempt to save an incomplete proof}
-%\item \ident\ \errindex{already exists}\\ 
-%  The implicit name is already defined. You have then to provide
-%  explicitly a new name (see variant 3 below).
-\item Sometimes an error occurs when building the proof term,
-because tactics do not enforce completely the term construction
-constraints.
-
-The user should also be aware of the fact that since the proof term is
-completely rechecked at this point, one may have to wait a while when
-the proof is large. In some exceptional cases one may even incur a
-memory overflow.
-\end{ErrMsgs}
-
-\begin{Variants}
-
-\item {\tt Defined.}
-\comindex{Defined} 
-\label{Defined} 
-
-  Defines the proved term as a transparent constant.
-
-\item {\tt Save {\ident}.}
-  
-  Forces the name of the original goal to be {\ident}.  This command
-  (and the following ones) can only be used if the original goal has
-  been opened using the {\tt Goal} command.
-
-\end{Variants}
-
-\subsection[\tt Admitted.]{\tt Admitted.\comindex{Admitted}\label{Admitted}}
-This command is available in interactive editing proof mode to give up
-the current proof and declare the initial goal as an axiom.
-
-\subsection[\tt Proof {\term}.]{\tt Proof {\term}.\comindex{Proof}
-\label{BeginProof}}
-This command applies in proof editing mode. It is equivalent to {\tt
-  exact {\term}. Qed.} That is, you have to give the full proof in
-one gulp, as a proof term (see Section~\ref{exact}).
-
-\variant {\tt Proof.}
-  
-  Is a noop which is useful to delimit the sequence of tactic commands
-  which start a proof, after a {\tt Theorem} command.  It is a good
-  practice to use {\tt Proof.} as an opening parenthesis, closed in
-  the script with a closing {\tt Qed.}
-
-\SeeAlso {\tt Proof with {\tac}.} in Section~\ref{ProofWith}.
-
-\subsection[{\tt Proof using} {\ident$_1$} {\ldots} {\ident$_n$}{\tt .}]
-{{\tt Proof using} {\ident$_1$} {\ldots} {\ident$_n$}{\tt .}
-\comindex{Proof using} \label{ProofUsing}}
-
-This command applies in proof editing mode. 
-It declares the set of section variables (see~\ref{Variable}) 
-used by the proof. At {\tt Qed} time, the system will assert that 
-the set of section variables actually used in the proof is a subset of
-the declared one.
-
-The set of declared variables is closed under type dependency.
-For example if {\tt T} is variable and {\tt a} is a variable of
-type {\tt T}, the commands {\tt Proof using a} and
-{\tt Proof using T a} are actually equivalent.
-
-\variant {\tt Proof using} {\ident$_1$} {\ldots} {\ident$_n$} {\tt with} {\tac}{\tt .} 
-in Section~\ref{ProofWith}.
-
-\variant {\tt Proof using All.} 
-
-  Use all section variables.
-
-\variant {\tt Proof using Type.} 
-\variant {\tt Proof using.} 
-  
-  Use only section variables occurring in the statement.
-
-\variant {\tt Proof using Type*.} 
-  
-  The {\tt *} operator computes the forward transitive closure.
-  E.g. if the variable {\tt H} has type {\tt p < 5} then {\tt H} is
-  in {\tt p*} since {\tt p} occurs in the type of {\tt H}.
-  {\tt Type* } is the forward transitive closure of the entire set of
-  section variables occurring in the statement.
-
-\variant {\tt Proof using -( \ident$_1$} {\ldots} {\tt \ident$_n$  ).}
-  
-  Use all section variables except {\ident$_1$} {\ldots} {\ident$_n$}.
-
-\variant {\tt Proof using \nterm{collection}$_1$ + \nterm{collection}$_2$ .}
-
-\variant {\tt Proof using \nterm{collection}$_1$ - \nterm{collection}$_2$ .}
-
-\variant {\tt Proof using \nterm{collection} - ( \ident$_1$} {\ldots} {\tt \ident$_n$ ).}
-
-\variant {\tt Proof using \nterm{collection} * .}
-
-  Use section variables being, respectively, in the set union, set difference,
-  set complement, set forward transitive closure.
-  See Section~\ref{Collection} to know how to form a named
-  collection.
-  The {\tt *} operator binds stronger than {\tt +} and {\tt -}.
-
-\subsubsection{{\tt Proof using} options}
-\optindex{Default Proof Using}
-\optindex{Suggest Proof Using}
-% \optindex{Proof Using Clear Unused}
-
-The following options modify the behavior of {\tt Proof using}.
-
-\variant {\tt Set Default Proof Using "expression".} 
-
-  Use {\tt expression} as the default {\tt Proof using} value.
-  E.g. {\tt Set Default Proof Using "a b".} will complete all {\tt Proof }
-  commands not followed by a {\tt using} part with {\tt using a b}.
-
-\variant {\tt Set Suggest Proof Using.}
-
-  When {\tt Qed} is performed, suggest a {\tt using} annotation if
-  the user did not provide one.
-
-% \variant{\tt Unset Proof Using Clear Unused.}
-% 
-%   When {\tt Proof using a} all section variables but for {\tt a} and
-%   the variables used in the type of {\tt a} are cleared.
-%   This option can be used to turn off this behavior.
-% 
-\subsubsection[\tt Collection]{Name a set of section hypotheses for {\tt Proof using}}
-\comindex{Collection}\label{Collection}
-
-The command {\tt Collection} can be used to name a set of section hypotheses,
-with the purpose of making {\tt Proof using} annotations more compact.
-
-\variant {\tt Collection Some := x y z.}
-
-  Define the collection named "Some" containing {\tt x y} and {\tt z} 
-
-\variant {\tt Collection Fewer := Some - x.} 
-  
-  Define the collection named "Fewer" containing only {\tt x y} 
-
-\variant {\tt Collection Many := Fewer + Some.} 
-\variant {\tt Collection Many := Fewer - Some.} 
-  
-  Define the collection named "Many" containing the set union or set difference
-  of "Fewer" and "Some".
-
-\variant {\tt Collection Many := Fewer - (x y).}
-
-  Define the collection named "Many" containing the set difference
-  of "Fewer" and the unnamed collection {\tt x y}.
-
-\subsection[\tt Abort.]{\tt Abort.\comindex{Abort}}
-
-This command cancels the current proof development, switching back to
-the previous proof development, or to the \Coq\ toplevel if no other
-proof was edited.
-
-\begin{ErrMsgs}
-\item \errindex{No focused proof (No proof-editing in progress)}
-\end{ErrMsgs}
-
-\begin{Variants}
-
-\item {\tt Abort {\ident}.}
-
-  Aborts the editing of the proof named {\ident}.
-
-\item {\tt Abort All.}
-
-  Aborts all current goals, switching back to the \Coq\ toplevel.
-
-\end{Variants}
-
-%%%%
-\subsection[\tt Existential {\num} := {\term}.]{\tt Existential  {\num} := {\term}.\comindex{Existential}
-\label{Existential}}
-
-This command instantiates an existential variable. {\tt \num}
-is an index in the list of uninstantiated existential variables
-displayed by {\tt Show Existentials} (described in Section~\ref{Show}).
-
-This command is intended to be used to instantiate existential
-variables when the proof is completed but some uninstantiated
-existential variables remain. To instantiate existential variables
-during proof edition, you should use the tactic {\tt instantiate}.
-
-\SeeAlso {\tt instantiate (\num:= \term).} in Section~\ref{instantiate}.
-\SeeAlso {\tt Grab Existential Variables.} below.
-
-\subsection[\tt Grab Existential Variables.]{\tt Grab Existential Variables.\comindex{Grab Existential Variables}
-\label{GrabEvars}}
-
-This command can be run when a proof has no more goal to be solved but has remaining
-uninstantiated existential variables. It takes every uninstantiated existential variable
-and turns it into a goal.
-
-%%%%%%%%
-\section{Navigation in the proof tree}
-%%%%%%%%
-
-\subsection[\tt Undo.]{\tt Undo.\comindex{Undo}}
-
-This command cancels the effect of the last command.  Thus, it
-backtracks one step.
-
-\begin{Variants}
-
-\item {\tt Undo {\num}.}
-
-  Repeats {\tt Undo} {\num} times.
-
-\end{Variants}
-
-\subsection[\tt Restart.]{\tt Restart.\comindex{Restart}}
-This command restores the proof editing process to the original goal.
-
-\begin{ErrMsgs}
-\item \errindex{No focused proof to restart}
-\end{ErrMsgs}
-
-\subsection[\tt Focus.]{\tt Focus.\comindex{Focus}}
-This focuses the attention on the first subgoal to prove and the printing
-of the other subgoals is suspended until the focused subgoal is
-solved or unfocused. This is useful when there are many current
-subgoals which clutter your screen.
-
-\begin{Variant}
-\item {\tt Focus {\num}.}\\ 
-This focuses the attention on the $\num^{th}$ subgoal to prove.
-\end{Variant}
-
-\emph{This command is deprecated since 8.8: prefer the use of bullets or
-  focusing brackets instead, including {\tt {\num}: \{}}.
-
-\subsection[\tt Unfocus.]{\tt Unfocus.\comindex{Unfocus}}
-This command restores to focus the goal that were suspended by the
-last {\tt Focus} command.
-
-\emph{This command is deprecated since 8.8.}
-
-\subsection[\tt Unfocused.]{\tt Unfocused.\comindex{Unfocused}}
-Succeeds in the proof if fully unfocused, fails if there are some
-goals out of focus.
-
-\subsection[\tt \{ \textrm{and} \}]{\tt \{ \textrm{and} \}\comindex{\{}\comindex{\}}}\label{curlybacket}
-The command {\tt \{} (without a terminating period) focuses on the
-first goal, much like {\tt Focus.} does, however, the subproof can
-only be unfocused when it has been fully solved (\emph{i.e.} when
-there is no focused goal left). Unfocusing is then handled by {\tt \}}
-(again, without a terminating period). See also example in next section.
-
-Note that when a focused goal is proved a message is displayed
-together with a suggestion about the right bullet or {\tt \}} to
-unfocus it or focus the next one.
-
-\begin{Variants}
-
-\item {\tt {\num}: \{}\\
-This focuses on the $\num^{th}$ subgoal to prove.
-
-\end{Variants}
-
-\begin{ErrMsgs}
-\item \errindex{This proof is focused, but cannot be unfocused
-    this way} You are trying to use {\tt \}} but the current subproof
-  has not been fully solved.
-\item \errindex{No such goal}
-\item \errindex{Brackets only support the single numbered goal selector}
-\item see also error message about bullets below.
-\end{ErrMsgs}
-
-\subsection[Bullets]{Bullets\comindex{+ (command)}
-  \comindex{- (command)}\comindex{* (command)}\index{Bullets}}\label{bullets}
-Alternatively to {\tt \{} and {\tt \}}, proofs can be structured with
-bullets. The use of a bullet $b$ for the first time focuses on the
-first goal $g$, the same bullet cannot be used again until the proof
-of $g$ is completed, then it is mandatory to focus the next goal with $b$. The
-consequence is that $g$ and all goals present when $g$ was focused are
-focused with the same bullet $b$. See the example below.
-
-Different bullets can be used to nest levels. The scope of bullet does
-not go beyond enclosing {\tt \{} and {\tt \}}, so bullets can be
-reused as further nesting levels provided they are delimited by these.
-Available bullets are {\tt -}, {\tt +}, {\tt *}, {\tt --}, {\tt ++}, {\tt **},
-{\tt ---}, {\tt +++}, {\tt ***}, ... (without a
-terminating period).
-
-Note again that when a focused goal is proved a message is displayed
-together with a suggestion about the right bullet or {\tt \}} to
-unfocus it or focus the next one.
-
-Remark: In {\ProofGeneral} (Emacs interface to {\Coq}), you must use
-bullets with the priority ordering shown above to have a correct
-indentation. For example {\tt -} must be the outer bullet and {\tt **}
-the inner one in the example below.
-
-The following example script illustrates all these features:
-\begin{coq_example*}
-Goal (((True/\True)/\True)/\True)/\True.
-Proof.
-  split.
-  - split.
-    + split.
-      ** { split.
-          - trivial.
-          - trivial.
-        }
-      ** trivial.
-    + trivial.
-  - assert True.
-    { trivial. }
-    assumption.
-\end{coq_example*}
-
-
-\begin{ErrMsgs}
-\item \errindex{Wrong bullet {\abullet}1 : Current bullet
-    {\abullet}2 is not finished.}
-
-  Before using bullet {\abullet}1 again, you should first finish
-  proving the current focused goal. Note that {\abullet}1 and
-  {\abullet}2 may be the same.
-
-\item \errindex{Wrong bullet {\abullet}1 : Bullet {\abullet}2
-    is mandatory here.} You must put {\abullet}2 to focus next goal.
-  No other bullet is allowed here.
-
-
-\item \errindex{No such goal. Focus next goal with bullet
-    {\abullet}.}
-
-  You tried to applied a tactic but no goal where under focus. Using
-  {\abullet} is mandatory here.
-
-\item \errindex{No such goal. Try unfocusing with {"{\tt \}}"}.} You
-  just finished a goal focused by {\tt \{}, you must unfocus it with "{\tt \}}".
-
-\end{ErrMsgs}
-
-\subsection[\tt Set Bullet Behavior.]{\tt Set Bullet Behavior.\optindex{Bullet Behavior}}
-
-The bullet behavior can be controlled by the following commands.
-
-\begin{quote}
-Set Bullet Behavior "None".
-\end{quote}
-
-This makes bullets inactive.
-
-\begin{quote}
-Set Bullet Behavior "Strict Subproofs".
-\end{quote}
-
-This makes bullets active (this is the default behavior).
-
-\section{Requesting information}
-
-\subsection[\tt Show.]{\tt Show.\comindex{Show}\label{Show}}
-This command displays the current goals.
-
-\begin{Variants}
-\item {\tt Show {\num}.}\\ 
-  Displays only the {\num}-th subgoal.\\ 
-\begin{ErrMsgs}
-\item \errindex{No such goal}
-\item \errindex{No focused proof}
-\end{ErrMsgs}
-
-\item {\tt Show {\ident}.}\\
-  Displays the named goal {\ident}.
-  This is useful in particular to display a shelved goal but only works
-  if the corresponding existential variable has been named by the user
-  (see~\ref{ExistentialVariables}) as in the following example.
-
-\begin{coq_eval}
-Reset Initial.
-\end{coq_eval}
-
-\begin{coq_example*}
-Goal exists n, n = 0.
-  eexists ?[n].
-\end{coq_example*}
-\begin{coq_example}
-  Show n.
-\end{coq_example}
-
-\item {\tt Show Script.}\comindex{Show Script}\\
-  Displays the whole list of tactics applied from the beginning
-  of the current proof. 
-  This tactics script may contain some holes (subgoals not yet proved).
-  They are printed under the form \verb!<Your Tactic Text here>!.
-
-\item {\tt Show Proof.}\comindex{Show Proof}\\
-It displays the proof term generated by the 
-tactics that have been applied. 
-If the proof is not completed, this term contain holes,
-which correspond to the sub-terms which are still to be 
-constructed. These holes appear as a question mark indexed 
-by an integer, and applied to the list of variables in 
-the context, since it may depend on them. 
-The types obtained by abstracting away the context from the
-type of each hole-placer are also printed.
-
-\item {\tt Show Conjectures.}\comindex{Show Conjectures}\\
-It prints the list of the names of all the theorems that 
-are currently being proved.
-As it is possible to start proving a previous lemma during
-the proof of a theorem, this list may contain several 
-names. 
-
-\item{\tt Show Intro.}\comindex{Show Intro}\\
-If the current goal begins by at least one product, this command
-prints the name of the first product, as it would be generated by 
-an anonymous {\tt intro}. The aim of this command is to ease the
-writing of more robust scripts. For example, with an appropriate 
-{\ProofGeneral} macro, it is possible to transform any anonymous {\tt
-  intro} into a qualified one such as {\tt intro y13}.
-In the case of a non-product goal, it prints nothing. 
-
-\item{\tt Show Intros.}\comindex{Show Intros}\\
-This command is similar to the previous one, it simulates the naming 
-process of an {\tt intros}.
-
-\item{\tt Show Existentials.\label{ShowExistentials}}\comindex{Show Existentials}
-\\ It displays
-the set of all uninstantiated existential variables in the current proof tree, 
-along with the type and the context of each variable.
-
-\item{\tt Show Match {\ident}.\label{ShowMatch}}\comindex{Show Match}\\
-This variant displays a template of the Gallina {\tt match} construct 
-with a branch for each constructor of the type {\ident}.
-
-Example:
-
-\begin{coq_example}
-Show Match nat.  
-\end{coq_example}
-\begin{ErrMsgs}
-\item \errindex{Unknown inductive type}
-\end{ErrMsgs}
-
-\item{\tt Show Universes.\label{ShowUniverses}}\comindex{Show Universes}
-\\ It displays the set of all universe constraints and its
-normalized form at the current stage of the proof, useful for
-debugging universe inconsistencies.
-
-\end{Variants}
-
-
-\subsection[\tt Guarded.]{\tt Guarded.\comindex{Guarded}\label{Guarded}}
-
-Some tactics (e.g. refine \ref{refine}) allow to build proofs using
-fixpoint or co-fixpoint constructions. Due to the incremental nature
-of interactive proof construction, the check of the termination (or
-guardedness) of the recursive calls in the fixpoint or cofixpoint
-constructions is postponed to the time of the completion of the proof.
-
-The command \verb!Guarded! allows checking if the guard condition for
-fixpoint and cofixpoint is violated at some time of the construction
-of the proof without having to wait the completion of the proof."
-
-
-\section{Controlling the effect of proof editing commands}
-
-\subsection[\tt Set Hyps Limit {\num}.]{\tt Set Hyps Limit {\num}.\optindex{Hyps Limit}}
-This command sets the maximum number of hypotheses displayed in
-goals after the application of a tactic. 
-All the hypotheses remains usable in the proof development.
-
-
-\subsection[\tt Unset Hyps Limit.]{\tt Unset Hyps Limit.\optindex{Hyps Limit}}
-This command goes back to the default mode which is to print all
-available hypotheses.
-
-
-\subsection[\tt Set Automatic Introduction.]{\tt Set Automatic Introduction.\optindex{Automatic Introduction}\label{Set Automatic Introduction}}
-
-The option {\tt Automatic Introduction} controls the way binders are
-handled in assertion commands such as {\tt Theorem {\ident}
-  \zeroone{\binders} : {\form}}. When the option is set, which is the
-default, {\binders} are automatically put in the local context of the
-goal to prove.
-
-The option can be unset by issuing {\tt Unset Automatic Introduction}.
-When the option is unset, {\binders} are discharged on the statement
-to be proved and a tactic such as {\tt intro} (see
-Section~\ref{intro}) has to be used to move the assumptions to the
-local context.
-
-\section{Controlling memory usage\comindex{Optimize Proof}\comindex{Optimize Heap}}
-
-When experiencing high memory usage the following commands can be
-used to force Coq to optimize some of its internal data structures.
-
-\subsection[\tt Optimize Proof.]{\tt Optimize Proof.}
-
-This command forces Coq to shrink the data structure used to represent
-the ongoing proof.
-
-\subsection[\tt Optimize Heap.]{\tt Optimize Heap.\label{vernac-optimizeheap}}
-
-This command forces the OCaml runtime to perform a heap compaction.
-This is in general an expensive operation.  See: \\
-\ \url{http://caml.inria.fr/pub/docs/manual-ocaml/libref/Gc.html#VALcompact} \\
-There is also an analogous tactic {\tt optimize\_heap} (see~\ref{tactic-optimizeheap}).
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "Reference-Manual"
-%%% End: 
diff --git a/doc/refman/RefMan-uti.tex b/doc/refman/RefMan-uti.tex
deleted file mode 100644
index 962aa98b68..0000000000
--- a/doc/refman/RefMan-uti.tex
+++ /dev/null
@@ -1,482 +0,0 @@
-\chapter[Utilities]{Utilities\label{Utilities}}
-%HEVEA\cutname{tools.html}
-
-The distribution provides utilities to simplify some tedious works
-beside proof development, tactics writing or documentation.
-
-\section[Using Coq as a library]{Using Coq as a library}
-
-In previous versions, \texttt{coqmktop} was used to build custom
-toplevels --- for example for better debugging or custom static
-linking. Nowadays, the preferred method is to use \texttt{ocamlfind}.
-
-The most basic custom toplevel is built using:
-\begin{quotation}
-\texttt{\% ocamlfind ocamlopt -thread -rectypes -linkall -linkpkg
-  -package coq.toplevel toplevel/coqtop\_bin.ml -o my\_toplevel.native}
-\end{quotation}
-
-For example, to statically link LTAC, you can just do:
-\begin{quotation}
-\texttt{\% ocamlfind ocamlopt -thread -rectypes -linkall -linkpkg
-  -package coq.toplevel -package coq.ltac toplevel/coqtop\_bin.ml -o my\_toplevel.native}
-\end{quotation}
-and similarly for other plugins.
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\section[Building a \Coq\ project with {\tt coq\_makefile}]
-{Building a \Coq\ project with {\tt coq\_makefile}
-\label{Makefile}
-\ttindex{Makefile}
-\ttindex{coq\_Makefile}
-\ttindex{\_CoqProject}}
-
-The majority of \Coq\ projects are very similar: a collection of {\tt .v}
-files and eventually some {\tt .ml} ones (a \Coq\ plugin).  The main piece
-of metadata needed in order to build the project are the command
-line options to {\tt coqc} (e.g. {\tt -R, -I},
-\SeeAlso Section~\ref{coqoptions}). Collecting the list of files and
-options is the job of the {\tt \_CoqProject} file.
-
-A simple example of a {\tt \_CoqProject} file follows:
-
-\begin{verbatim}
--R theories/ MyCode
-theories/foo.v
-theories/bar.v
--I src/
-src/baz.ml4
-src/bazaux.ml
-src/qux_plugin.mlpack
-\end{verbatim}
-
-Currently, both \CoqIDE{} and Proof General (version $\geq$ 4.3pre) understand
-{\tt \_CoqProject} files and invoke \Coq\ with the desired options.
-
-The {\tt coq\_makefile} utility can be used to set up a build infrastructure
-for the \Coq\ project based on makefiles.  The recommended way of
-invoking {\tt coq\_makefile} is the following one:
-
-\begin{verbatim}
-coq_makefile -f _CoqProject -o CoqMakefile
-\end{verbatim}
-
-Such command generates the following files:
-\begin{description}
-	\item[{\tt CoqMakefile}] is a generic makefile for GNU Make that provides targets to build the project (both {\tt .v} and {\tt .ml*} files), to install it system-wide in the {\tt coq-contrib} directory (i.e. where \Coq\ is installed) as well as to invoke {\tt coqdoc} to generate html documentation.
-
-	\item[{\tt CoqMakefile.conf}] contains make variables assignments that reflect the contents of the {\tt \_CoqProject} file as well as the path relevant to \Coq{}.
-\end{description}
-
-An optional file {\bf {\tt CoqMakefile.local}} can be provided by the user in order to extend {\tt CoqMakefile}.  In particular one can declare custom actions to be performed before or after the build process. Similarly one can customize the install target or even provide new targets.  Extension points are documented in paragraph \ref{coqmakefile:local}.
-
-The extensions of the files listed in {\tt \_CoqProject} is
-used in order to decide how to build them.  In particular:
-
-\begin{itemize}
-\item {\Coq} files must use the \texttt{.v} extension
-\item {\ocaml} files must use the \texttt{.ml} or \texttt{.mli} extension
-\item {\ocaml} files that require pre processing for syntax extensions (like {\tt VERNAC EXTEND}) must use the \texttt{.ml4} extension
-\item In order to generate a plugin one has to list all {\ocaml} modules (i.e. ``Baz'' for ``baz.ml'') in a \texttt{.mlpack} file (or \texttt{.mllib} file).
-\end{itemize}
-
-The use of \texttt{.mlpack} files has to be preferred over \texttt{.mllib}
-files, since it results in a ``packed'' plugin: All auxiliary
-modules (as {\tt Baz} and {\tt Bazaux}) are hidden inside
-the plugin's ``name space'' ({\tt Qux\_plugin}).
-This reduces the chances of begin unable to load two distinct plugins
-because of a clash in their auxiliary module names.
-
-\paragraph{CoqMakefile.local} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\label{coqmakefile:local}
-
-The optional file {\tt CoqMakefile.local} is included by the generated file
-{\tt CoqMakefile}.  Such can contain two kinds of directives.
-
-\begin{description}
-  \item[Variable assignment] to the variables listed in the {\tt Parameters}
-	  section of the generated makefile.  Here we describe only few of them.
-  \begin{description}
-  \item[CAMLPKGS] can be used to specify third party findlib packages, and is
-	  passed to the OCaml compiler on building or linking of modules.
-          Eg: {\tt -package yojson}.
-  \item[CAMLFLAGS] can be used to specify additional flags to the OCaml
-	  compiler, like {\tt -bin-annot} or {\tt -w...}.
-  \item[COQC, COQDEP, COQDOC] can be set in order to use alternative 
-	  binaries (e.g. wrappers)
-  \item[COQ\_SRC\_SUBDIRS] can be extended by including other paths in which {\tt *.cm*} files are searched. For example {\tt COQ\_SRC\_SUBDIRS+=user-contrib/Unicoq} lets you build a plugin containing OCaml code that depends on the OCaml code of {\tt Unicoq}.
-  \end{description}
-\item[Rule extension]
-  The following makefile rules can be extended. For example
-\begin{verbatim}
-pre-all::
-        echo "This line is print before making the all target"
-install-extra::
-        cp ThisExtraFile /there/it/goes
-\end{verbatim}
-  \begin{description}
-  \item[pre-all::] run before the {\tt all} target.  One can use this
-	  to configure the project, or initialize sub modules or check
-	  dependencies are met.
-  \item[post-all::] run after the {\tt all} target.  One can use this
-	  to run a test suite, or compile extracted code.
-  \item[install-extra::] run after {\tt install}.  One can use this
-	  to install extra files.
-  \item[install-doc::]  One can use this to install extra doc.
-  \item[uninstall::] 
-  \item[uninstall-doc::]
-  \item[clean::]
-  \item[cleanall::]
-  \item[archclean::]
-  \item[merlin-hook::] One can append lines to the generated {\tt .merlin}
-	  file extending this target.
-  \end{description}
-\end{description}
-
-\paragraph{Timing targets and performance testing} %%%%%%%%%%%%%%%%%%%%%%%%%%%
-The generated \texttt{Makefile} supports the generation of two kinds
-of timing data: per-file build-times, and per-line times for an
-individual file.
-
-The following targets and \texttt{Makefile} variables allow collection
-of per-file timing data:
-\begin{itemize}
-\item \texttt{TIMED=1} --- passing this variable will cause
-  \texttt{make} to emit a line describing the user-space build-time
-  and peak memory usage for each file built.
-
-  \texttt{Note}: On Mac OS, this works best if you've installed
-  \texttt{gnu-time}.
-
-  \texttt{Example}: For example, the output of \texttt{make TIMED=1}
-  may look like this:
-\begin{verbatim}
-COQDEP Fast.v
-COQDEP Slow.v
-COQC Slow.v
-Slow (user: 0.34 mem: 395448 ko)
-COQC Fast.v
-Fast (user: 0.01 mem: 45184 ko)
-\end{verbatim}
-\item \texttt{pretty-timed} --- this target stores the output of
-  \texttt{make TIMED=1} into \texttt{time-of-build.log}, and displays
-  a table of the times, sorted from slowest to fastest, which is also
-  stored in \texttt{time-of-build-pretty.log}.  If you want to
-  construct the log for targets other than the default one, you can
-  pass them via the variable \texttt{TGTS}, e.g., \texttt{make
-    pretty-timed TGTS="a.vo b.vo"}.
-
-  \texttt{Note}: This target requires \texttt{python} to build the table.
-
-  \texttt{Note}: This target will \emph{append} to the timing log; if
-  you want a fresh start, you must remove the file
-  \texttt{time-of-build.log} or run \texttt{make cleanall}.
-
-  \texttt{Example}: For example, the output of \texttt{make
-    pretty-timed} may look like this:
-\begin{verbatim}
-COQDEP Fast.v
-COQDEP Slow.v
-COQC Slow.v
-Slow (user: 0.36 mem: 393912 ko)
-COQC Fast.v
-Fast (user: 0.05 mem: 45992 ko)
-Time     | File Name
---------------------
-0m00.41s | Total
---------------------
-0m00.36s | Slow
-0m00.05s | Fast
-\end{verbatim}
-\item \texttt{print-pretty-timed-diff} --- this target builds a table
-  of timing changes between two compilations; run \texttt{make
-    make-pretty-timed-before} to build the log of the ``before''
-  times, and run \texttt{make make-pretty-timed-after} to build the
-  log of the ``after'' times.  The table is printed on the command
-  line, and stored in \texttt{time-of-build-both.log}.  This target is
-  most useful for profiling the difference between two commits to a
-  repo.
-
-  \texttt{Note}: This target requires \texttt{python} to build the table.
-
-  \texttt{Note}: The \texttt{make-pretty-timed-before} and
-  \texttt{make-pretty-timed-after} targets will \emph{append} to the
-  timing log; if you want a fresh start, you must remove the files
-  \texttt{time-of-build-before.log} and
-  \texttt{time-of-build-after.log} or run \texttt{make cleanall}
-  \emph{before} building either the ``before'' or ``after'' targets.
-
-  \texttt{Note}: The table will be sorted first by absolute time
-  differences rounded towards zero to a whole-number of seconds, then
-  by times in the ``after'' column, and finally lexicographically by
-  file name.  This will put the biggest changes in either direction
-  first, and will prefer sorting by build-time over subsecond changes
-  in build time (which are frequently noise); lexicographic sorting
-  forces an order on files which take effectively no time to compile.
-
-  \texttt{Example}: For example, the output table from \texttt{make
-    print-pretty-timed-diff} may look like this:
-\begin{verbatim}
-After    | File Name | Before   || Change    | % Change
---------------------------------------------------------
-0m00.39s | Total     | 0m00.35s || +0m00.03s | +11.42%
---------------------------------------------------------
-0m00.37s | Slow      | 0m00.01s || +0m00.36s | +3600.00%
-0m00.02s | Fast      | 0m00.34s || -0m00.32s | -94.11%
-\end{verbatim}
-\end{itemize}
-
-The following targets and \texttt{Makefile} variables allow collection
-of per-line timing data:
-\begin{itemize}
-\item \texttt{TIMING=1} --- passing this variable will cause
-  \texttt{make} to use \texttt{coqc -time} to write to a
-  \texttt{.v.timing} file for each \texttt{.v} file compiled, which
-  contains line-by-line timing information.
-
-  \texttt{Example}: For example, running \texttt{make all TIMING=1} may
-  result in a file like this:
-\begin{verbatim}
-Chars 0 - 26 [Require~Coq.ZArith.BinInt.] 0.157 secs (0.128u,0.028s)
-Chars 27 - 68 [Declare~Reduction~comp~:=~vm_c...] 0. secs (0.u,0.s)
-Chars 69 - 162 [Definition~foo0~:=~Eval~comp~i...] 0.153 secs (0.136u,0.019s)
-Chars 163 - 208 [Definition~foo1~:=~Eval~comp~i...] 0.239 secs (0.236u,0.s)
-\end{verbatim}
-
-\item \texttt{print-pretty-single-time-diff
-  BEFORE=path/to/file.v.before-timing
-  AFTER=path/to/file.v.after-timing} --- this target will make a
-  sorted table of the per-line timing differences between the timing
-  logs in the \texttt{BEFORE} and \texttt{AFTER} files, display it,
-  and save it to the file specified by the
-  \texttt{TIME\_OF\_PRETTY\_BUILD\_FILE} variable, which defaults to
-  \texttt{time-of-build-pretty.log}.
-
-  To generate the \texttt{.v.before-timing} or
-  \texttt{.v.after-timing} files, you should pass
-  \texttt{TIMING=before} or \texttt{TIMING=after} rather than
-  \texttt{TIMING=1}.
-
-  \texttt{Note}: The sorting used here is the same as in the
-  \texttt{print-pretty-timed-diff} target.
-
-  \texttt{Note}: This target requires \texttt{python} to build the table.
-
-  \texttt{Example}: For example, running
-  \texttt{print-pretty-single-time-diff} might give a table like this:
-\begin{verbatim}
-After     | Code                                                | Before    || Change    | % Change
----------------------------------------------------------------------------------------------------
-0m00.50s  | Total                                               | 0m04.17s  || -0m03.66s | -87.96%
----------------------------------------------------------------------------------------------------
-0m00.145s | Chars 069 - 162 [Definition~foo0~:=~Eval~comp~i...] | 0m00.192s || -0m00.04s | -24.47%
-0m00.126s | Chars 000 - 026 [Require~Coq.ZArith.BinInt.]        | 0m00.143s || -0m00.01s | -11.88%
-   N/A    | Chars 027 - 068 [Declare~Reduction~comp~:=~nati...] | 0m00.s    || +0m00.00s | N/A
-0m00.s    | Chars 027 - 068 [Declare~Reduction~comp~:=~vm_c...] |    N/A    || +0m00.00s | N/A
-0m00.231s | Chars 163 - 208 [Definition~foo1~:=~Eval~comp~i...] | 0m03.836s || -0m03.60s | -93.97%
-\end{verbatim}
-
-\item \texttt{all.timing.diff}, \texttt{path/to/file.v.timing.diff}
-  --- The \texttt{path/to/file.v.timing.diff} target will make a
-  \texttt{.v.timing.diff} file for the corresponding \texttt{.v} file,
-  with a table as would be generated by the
-  \texttt{print-pretty-single-time-diff} target; it depends on having
-  already made the corresponding \texttt{.v.before-timing} and
-  \texttt{.v.after-timing} files, which can be made by passing
-  \texttt{TIMING=before} and \texttt{TIMING=after}.  The
-  \texttt{all.timing.diff} target will make such timing difference
-  files for all of the \texttt{.v} files that the \texttt{Makefile}
-  knows about.  It will fail if some \texttt{.v.before-timing} or
-  \texttt{.v.after-timing} files don't exist.
-
-  \texttt{Note}: This target requires \texttt{python} to build the table.
-\end{itemize}
-
-\paragraph{Reusing/extending the generated Makefile} %%%%%%%%%%%%%%%%%%%%%%%%%
-
-Including the generated makefile with an {\tt include} directive is discouraged.
-The contents of this file, including variable names
-and status of rules shall change in the future.  Users are advised to
-include {\tt Makefile.conf} or call a target of the generated Makefile
-as in {\tt make -f Makefile target} from another Makefile.
-
-One way to get access to all targets of the generated
-\texttt{CoqMakefile} is to have a generic target for invoking unknown
-targets.  For example:
-\begin{verbatim}
-# KNOWNTARGETS will not be passed along to CoqMakefile
-KNOWNTARGETS := CoqMakefile extra-stuff extra-stuff2
-# KNOWNFILES will not get implicit targets from the final rule, and so
-# depending on them won't invoke the submake
-# Warning: These files get declared as PHONY, so any targets depending
-# on them always get rebuilt
-KNOWNFILES   := Makefile _CoqProject
-
-.DEFAULT_GOAL := invoke-coqmakefile
-
-CoqMakefile: Makefile _CoqProject
-	$(COQBIN)coq_makefile -f _CoqProject -o CoqMakefile
-
-invoke-coqmakefile: CoqMakefile
-	$(MAKE) --no-print-directory -f CoqMakefile $(filter-out $(KNOWNTARGETS),$(MAKECMDGOALS))
-
-.PHONY: invoke-coqmakefile $(KNOWNFILES)
-
-####################################################################
-##                      Your targets here                         ##
-####################################################################
-
-# This should be the last rule, to handle any targets not declared above
-%: invoke-coqmakefile
-	@true
-\end{verbatim}
-
-\paragraph{Building a subset of the targets with -j} %%%%%%%%%%%%%%%%%%%%%%%%%
-
-To build, say, two targets \texttt{foo.vo} and \texttt{bar.vo}
-in parallel one can use \texttt{make only TGTS="foo.vo bar.vo" -j}.
-
-Note that \texttt{make foo.vo bar.vo -j} has a different meaning for
-the make utility, in particular it may build a shared prerequisite twice.
-
-\paragraph{Notes for users of {\tt coq\_makefile} with version $<$ 8.7} %%%%%%
-
-\begin{itemize}
-\item Support for ``sub-directory'' is deprecated.  To perform actions before
-	or after the build (like invoking make on a subdirectory) one can
-	hook in {\tt pre-all} and {\tt post-all} extension points
-\item \texttt{-extra-phony} and \texttt{-extra} are deprecated.  To provide
-	additional target ({\tt .PHONY} or not) please use
-	{\tt CoqMakefile.local}
-\end{itemize}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\section[Modules dependencies]{Modules dependencies\label{Dependencies}\index{Dependencies}
-  \ttindex{coqdep}}
-
-In order to compute modules dependencies (so to use {\tt make}),
-\Coq\ comes with an appropriate tool, {\tt coqdep}.
-
-{\tt coqdep} computes inter-module dependencies for \Coq\ and
-\ocaml\ programs, and prints the dependencies on the standard
-output in a format readable by make.  When a directory is given as
-argument, it is recursively looked at.
-
-Dependencies of \Coq\ modules are computed by looking at {\tt Require}
-commands ({\tt Require}, {\tt Requi\-re Export}, {\tt Require Import},
-but also at the command {\tt Declare ML Module}.
-
-Dependencies of \ocaml\ modules are computed by looking at
-\verb!open! commands and the dot notation {\em module.value}. However,
-this is done approximately and you are advised to use {\tt ocamldep}
-instead for the \ocaml\ modules dependencies.
-
-See the man page of {\tt coqdep} for more details and options.
-
-The build infrastructure generated by {\tt coq\_makefile}
-uses {\tt coqdep} to automatically compute the dependencies
-among the files part of the project.
-
-\section[Documenting \Coq\ files with coqdoc]{Documenting \Coq\ files with coqdoc\label{coqdoc}
-\ttindex{coqdoc}}
-
-\input{./coqdoc}
-
-\section[Embedded \Coq\ phrases inside \LaTeX\ documents]{Embedded \Coq\ phrases inside \LaTeX\ documents\label{Latex}
-  \ttindex{coq-tex}\index{Latex@{\LaTeX}}}
-
-When writing a documentation about a proof development, one may want
-to insert \Coq\ phrases inside a \LaTeX\ document, possibly together with
-the corresponding answers of the system. We provide a
-mechanical way to process such \Coq\ phrases embedded in \LaTeX\ files: the
-{\tt coq-tex} filter.  This filter extracts Coq phrases embedded in
-LaTeX files, evaluates them, and insert the outcome of the evaluation
-after each phrase.
-
-Starting with a file {\em file}{\tt.tex} containing \Coq\ phrases,
-the {\tt coq-tex} filter produces a file named {\em file}{\tt.v.tex} with
-the \Coq\ outcome.
-
-There are options to produce the \Coq\ parts in smaller font, italic,
-between horizontal rules, etc.
-See the man page of {\tt coq-tex} for more details.
-
-\medskip\noindent {\bf Remark.} This Reference Manual and the Tutorial
-have been completely produced with {\tt coq-tex}.
-
-
-\section[\Coq\ and \emacs]{\Coq\ and \emacs\label{Emacs}\index{Emacs}}
-
-\subsection{The \Coq\ Emacs mode}
-
-\Coq\ comes with a Major mode for \emacs, {\tt gallina.el}. This mode provides
-syntax highlighting
-and also a rudimentary indentation facility
-in the style of the Caml \emacs\ mode.
-
-Add the following lines to your \verb!.emacs! file:
-
-\begin{verbatim}
-  (setq auto-mode-alist (cons '("\\.v$" . coq-mode) auto-mode-alist))
-  (autoload 'coq-mode "gallina" "Major mode for editing Coq vernacular." t)
-\end{verbatim}
-
-The \Coq\ major mode is triggered by visiting a file with extension {\tt .v},
-or manually with the command \verb!M-x coq-mode!.
-It gives you the correct syntax table for
-the \Coq\ language, and also a rudimentary indentation facility:
-\begin{itemize}
-  \item pressing {\sc Tab} at the beginning of a line indents the line like
-    the line above;
-
-  \item extra {\sc Tab}s increase the indentation level
-    (by 2 spaces by default);
-
-  \item M-{\sc Tab} decreases the indentation level.
-\end{itemize}
-
-An inferior mode to run \Coq\ under Emacs, by Marco Maggesi, is also
-included in the distribution, in file \texttt{inferior-coq.el}.
-Instructions to use it are contained in this file.
-
-\subsection[{\ProofGeneral}]{{\ProofGeneral}\index{Proof General@{\ProofGeneral}}}
-
-{\ProofGeneral} is a generic interface for proof assistants based on
-Emacs. The main idea is that the \Coq\ commands you are
-editing are sent to a \Coq\ toplevel running behind Emacs and the
-answers of the system automatically inserted into other Emacs buffers.
-Thus you don't need to copy-paste the \Coq\ material from your files
-to the \Coq\ toplevel or conversely from the \Coq\ toplevel to some
-files.
-
-{\ProofGeneral} is developed and distributed independently of the
-system \Coq. It is freely available at \verb!https://proofgeneral.github.io/!.
-
-
-\section[Module specification]{Module specification\label{gallina}\ttindex{gallina}}
-
-Given a \Coq\ vernacular file, the {\tt gallina} filter extracts its
-specification (inductive types declarations, definitions, type of
-lemmas and theorems), removing the proofs parts of the file. The \Coq\
-file {\em file}{\tt.v} gives birth to the specification file
-{\em file}{\tt.g} (where the suffix {\tt.g} stands for \gallina).
-
-See the man page of {\tt gallina} for more details and options.
-
-
-\section[Man pages]{Man pages\label{ManPages}\index{Man pages}}
-
-There are man pages for the commands {\tt coqdep}, {\tt gallina} and
-{\tt coq-tex}. Man pages are installed at installation time
-(see installation instructions in file {\tt INSTALL}, step 6).
-
-%BEGIN LATEX
-\RefManCutCommand{ENDREFMAN=\thepage}
-%END LATEX
-
-%%% Local Variables:
-%%% mode: latex
-%%% TeX-master: t
-%%% End:
diff --git a/doc/refman/Reference-Manual.tex b/doc/refman/Reference-Manual.tex
deleted file mode 100644
index 7e68dd7524..0000000000
--- a/doc/refman/Reference-Manual.tex
+++ /dev/null
@@ -1,145 +0,0 @@
-%\RequirePackage{ifpdf}
-%\ifpdf
-%  \documentclass[11pt,a4paper,pdftex]{book}
-%\else
-  \documentclass[11pt,a4paper]{book}
-%\fi
-
-\usepackage[utf8]{inputenc}
-\usepackage[T1]{fontenc}
-\usepackage{textcomp}
-\usepackage{times}
-\usepackage{url}
-\usepackage{verbatim}
-\usepackage{amsmath}
-\usepackage{amssymb}
-\usepackage{alltt}
-\usepackage{hevea}
-\usepackage{ifpdf}
-\usepackage[headings]{fullpage}
-\usepackage{headers} % in this directory
-\usepackage{multicol}
-\usepackage{xspace}
-\usepackage{pmboxdraw}
-\usepackage{float}
-\usepackage{color}
-  \definecolor{dkblue}{rgb}{0,0.1,0.5}
-  \definecolor{lightblue}{rgb}{0,0.5,0.5}
-  \definecolor{dkgreen}{rgb}{0,0.4,0}
-  \definecolor{dk2green}{rgb}{0.4,0,0}
-  \definecolor{dkviolet}{rgb}{0.6,0,0.8}
-  \definecolor{dkpink}{rgb}{0.2,0,0.6}
-\usepackage{listings}
-  \def\lstlanguagefiles{coq-listing.tex}
-\usepackage{tabularx}
-\usepackage{array,longtable}
-
-\floatstyle{boxed} 
-\restylefloat{figure}
-
-% for coqide
-\ifpdf   % si on est pas en pdflatex
-  \usepackage[pdftex]{graphicx}
-\else
-  \usepackage[dvips]{graphicx}
-\fi
-
-
-%\includeonly{Setoid}
-
-\input{../common/version.tex}
-\input{../common/macros.tex}% extension .tex pour htmlgen
-\input{../common/title.tex}% extension .tex pour htmlgen
-%\input{headers}
-
-\usepackage[linktocpage,colorlinks,bookmarks=true,bookmarksnumbered=true]{hyperref}
-% The manual advises to load hyperref package last to be able to redefine
-% necessary commands.
-% The above should work for both latex and pdflatex. Even if PDF is produced
-% through DVI and PS using dvips and ps2pdf, hyperlinks should still work.
-% linktocpage option makes page numbers, not section names, to be links in
-% the table of contents.
-% colorlinks option colors the links instead of using boxes.
-
-% The command \tocnumber was added to HEVEA in version 1.06-6.
-% It instructs HEVEA to put chapter numbers into the table of
-% content entries. The table of content is produced by HACHA using
-% the options -tocbis -o toc.html. HEVEA produces a warning when
-% a command is not recognized, so versions earlier than 1.06-6 can
-% still be used.
-%HEVEA\tocnumber
-
-\begin{document}
-%BEGIN LATEX
-\sloppy\hbadness=5000
-%END LATEX
-
-%BEGIN LATEX
-\coverpage{Reference Manual}
-{The Coq Development Team}
-{This material may be distributed only subject to the terms and
-conditions set forth in the Open Publication License, v1.0 or later
-(the latest version is presently available at
-\url{http://www.opencontent.org/openpub}).
-Options A and B of the licence are {\em not} elected.}
-%END LATEX
-
-%\defaultheaders
-
-%BEGIN LATEX
-\tableofcontents
-%END LATEX
-
-\part{The language}
-%BEGIN LATEX
-\defaultheaders
-%END LATEX
-\include{RefMan-gal.v}% Gallina
-
-
-\part{The proof engine}
-\include{RefMan-oth.v}% Vernacular commands
-\include{RefMan-pro.v}% Proof handling
-\include{RefMan-ltac.v}% Writing tactics
-
-\lstset{language=SSR}
-\lstset{moredelim=[is][]{|*}{*|}}
-\lstset{moredelim=*[is][\itshape\rmfamily]{/*}{*/}}
-
-\part{User extensions}
-%%SUPPRIME \include{RefMan-tus.v}% Writing tactics
-
-\part{Practical tools}
-\include{RefMan-uti}% utilities (gallina, do_Makefile, etc)
-
-%BEGIN LATEX
-\RefManCutCommand{BEGINADDENDUM=\thepage}
-%END LATEX
-\part{Addendum to the Reference Manual}
-\include{AddRefMan-pre}%
-\include{Universes.v}% Universe polymorphes
-\include{Misc.v}
-%BEGIN LATEX
-\RefManCutCommand{ENDADDENDUM=\thepage}
-%END LATEX
-\nocite{*}
-\bibliographystyle{plain}
-\bibliography{biblio}
-\cutname{biblio.html}
-
-\printrefmanindex{default}{Global Index}{general-index.html}
-\printrefmanindex{tactic}{Tactics Index}{tactic-index.html}
-\printrefmanindex{command}{Vernacular Commands Index}{command-index.html}
-\printrefmanindex{option}{Vernacular Options Index}{option-index.html}
-\printrefmanindex{error}{Index of Error Messages}{error-index.html}
-
-%BEGIN LATEX
-\cleardoublepage
-\phantomsection
-\addcontentsline{toc}{chapter}{\listfigurename}
-\listoffigures
-%END LATEX
-
-\end{document}
-
-
diff --git a/doc/refman/Universes.tex b/doc/refman/Universes.tex
deleted file mode 100644
index c7d39c0f3e..0000000000
--- a/doc/refman/Universes.tex
+++ /dev/null
@@ -1,393 +0,0 @@
-\achapter{Polymorphic Universes}
-%HEVEA\cutname{universes.html}
-\aauthor{Matthieu Sozeau}
-
-\label{Universes-full}
-\index{Universes!presentation}
-
-\asection{General Presentation}
-
-\begin{flushleft}
-  \em The status of Universe Polymorphism is experimental.
-\end{flushleft}
-
-This section describes the universe polymorphic extension of Coq.
-Universe polymorphism makes it possible to write generic definitions making use of
-universes and reuse them at different and sometimes incompatible universe levels.
-
-A standard example of the difference between universe \emph{polymorphic} and
-\emph{monomorphic} definitions is given by the identity function:
-
-\begin{coq_example*}
-Definition identity {A : Type} (a : A) := a.
-\end{coq_example*}
-
-By default, constant declarations are monomorphic, hence the identity
-function declares a global universe (say \texttt{Top.1}) for its
-domain. Subsequently, if we try to self-apply the identity, we will get
-an error:
-
-\begin{coq_eval}
-Set Printing Universes.
-\end{coq_eval}
-\begin{coq_example}
-Fail Definition selfid := identity (@identity).
-\end{coq_example}
-
-Indeed, the global level \texttt{Top.1} would have to be strictly smaller than itself
-for this self-application to typecheck, as the type of \texttt{(@identity)} is
-\texttt{forall (A : Type@{Top.1}), A -> A} whose type is itself \texttt{Type@{Top.1+1}}.
-
-A universe polymorphic identity function binds its domain universe level
-at the definition level instead of making it global.
-
-\begin{coq_example}
-Polymorphic Definition pidentity {A : Type} (a : A) := a.
-About pidentity.
-\end{coq_example}
-
-It is then possible to reuse the constant at different levels, like so:
-
-\begin{coq_example}
-Definition selfpid := pidentity (@pidentity).
-\end{coq_example}
-
-Of course, the two instances of \texttt{pidentity} in this definition
-are different. This can be seen when \texttt{Set Printing Universes} is
-on:
-
-\begin{coq_example}
-Print selfpid.
-\end{coq_example}
-
-Now \texttt{pidentity} is used at two different levels: at the head of
-the application it is instantiated at \texttt{Top.3} while in the
-argument position it is instantiated at \texttt{Top.4}. This definition
-is only valid as long as \texttt{Top.4} is strictly smaller than
-\texttt{Top.3}, as show by the constraints. Note that this definition is
-monomorphic (not universe polymorphic), so the two universes
-(in this case \texttt{Top.3} and \texttt{Top.4}) are actually global levels.
-
-When printing \texttt{pidentity}, we can see the universes it binds in
-the annotation \texttt{@\{Top.2\}}. Additionally, when \texttt{Set
-  Printing Universes} is on we print the ``universe context'' of
-\texttt{pidentity} consisting of the bound universes and the
-constraints they must verify (for \texttt{pidentity} there are no
-constraints).
-
-Inductive types can also be declared universes polymorphic on universes
-appearing in their parameters or fields. A typical example is given by
-monoids:
-
-\begin{coq_example}
-Polymorphic Record Monoid := { mon_car :> Type; mon_unit : mon_car; 
-  mon_op : mon_car -> mon_car -> mon_car }.
-Print Monoid.
-\end{coq_example}
-
-The \texttt{Monoid}'s carrier universe is polymorphic, hence it is
-possible to instantiate it for example with \texttt{Monoid} itself.
-First we build the trivial unit monoid in \texttt{Set}:
-\begin{coq_example}
-Definition unit_monoid : Monoid := 
-  {| mon_car := unit; mon_unit := tt; mon_op x y := tt |}.
-\end{coq_example} 
-
-From this we can build a definition for the monoid of
-\texttt{Set}-monoids (where multiplication would be given by the product
-of monoids).
-
-\begin{coq_example*}
-Polymorphic Definition monoid_monoid : Monoid.
-  refine (@Build_Monoid Monoid unit_monoid (fun x y => x)).
-Defined.
-\end{coq_example*}
-\begin{coq_example}
-Print monoid_monoid.
-\end{coq_example} 
-
-As one can see from the constraints, this monoid is ``large'', it lives
-in a universe strictly higher than \texttt{Set}.
-
-\asection{\tt Polymorphic, Monomorphic}
-\comindex{Polymorphic}
-\comindex{Monomorphic}
-\optindex{Universe Polymorphism}
-
-As shown in the examples, polymorphic definitions and inductives can be
-declared using the \texttt{Polymorphic} prefix. There also exists an
-option \texttt{Set Universe Polymorphism} which will implicitly prepend
-it to any definition of the user. In that case, to make a definition
-producing global universe constraints, one can use the
-\texttt{Monomorphic} prefix. Many other commands support the
-\texttt{Polymorphic} flag, including:
-
-\begin{itemize}
-\item \texttt{Lemma}, \texttt{Axiom}, and all the other ``definition''
-  keywords support polymorphism.
-\item \texttt{Variables}, \texttt{Context}, \texttt{Universe} and
-  \texttt{Constraint} in a section support polymorphism.  This means
-  that the universe variables (and associated constraints) are
-  discharged polymorphically over definitions that use them. In other
-  words, two definitions in the section sharing a common variable will
-  both get parameterized by the universes produced by the variable
-  declaration. This is in contrast to a ``mononorphic'' variable which
-  introduces global universes and constraints, making the two
-  definitions depend on the \emph{same} global universes associated to
-  the variable.
-\item \texttt{Hint \{Resolve, Rewrite\}} will use the auto/rewrite hint
-  polymorphically, not at a single instance.
-\end{itemize}
-
-\asection{{\tt Cumulative, NonCumulative}}
-\comindex{Cumulative}
-\comindex{NonCumulative}
-\optindex{Polymorphic Inductive Cumulativity}
-
-Polymorphic inductive types, coinductive types, variants and records can be
-declared cumulative using the \texttt{Cumulative} prefix. Alternatively,
-there is an option \texttt{Set Polymorphic Inductive Cumulativity} which when set,
-makes all subsequent \emph{polymorphic} inductive definitions cumulative.  When set,
-inductive types and the like can be enforced to be
-\emph{non-cumulative} using the \texttt{NonCumulative} prefix. Consider the examples below.
-\begin{coq_example*}
-Polymorphic Cumulative Inductive list {A : Type} :=
-| nil : list
-| cons : A -> list -> list.
-\end{coq_example*}
-\begin{coq_example}
-Print list.
-\end{coq_example}
-When printing \texttt{list}, the universe context indicates the
-subtyping constraints by prefixing the level names with symbols.
-
-Because inductive subtypings are only produced by comparing inductives
-to themselves with universes changed, they amount to variance
-information: each universe is either invariant, covariant or
-irrelevant (there are no contravariant subtypings in Coq),
-respectively represented by the symbols \texttt{=}, \texttt{+} and
-\texttt{*}.
-
-Here we see that \texttt{list} binds an irrelevant universe, so any
-two instances of \texttt{list} are convertible:
-$\WTEGCONV{\mathtt{list@\{i\}} A}{\mathtt{list@\{j\}} B}$ whenever
-$\WTEGCONV{A}{B}$ and furthermore their corresponding (when fully
-applied to convertible arguments) constructors.
-
-See Chapter~\ref{Cic} for more details on convertibility and subtyping.
-The following is an example of a record with non-trivial subtyping relation:
-\begin{coq_example*}
-Polymorphic Cumulative Record packType := {pk : Type}.
-\end{coq_example*}
-\begin{coq_example}
-Print packType.
-\end{coq_example}
-\texttt{packType} binds a covariant universe, i.e.
-$\WTEGCONV{\mathtt{packType@\{i\}}}{\mathtt{packType@\{j\}}}$ whenever
-\texttt{i $\leq$ j}.
-
-Cumulative inductive types, coninductive types, variants and records
-only make sense when they are universe polymorphic. Therefore, an
-error is issued whenever the user uses the \texttt{Cumulative} or
-\texttt{NonCumulative} prefix in a monomorphic context.
-Notice that this is not the case for the option \texttt{Set Polymorphic Inductive Cumulativity}.
-That is, this option, when set, makes all subsequent \emph{polymorphic}
-inductive declarations cumulative (unless, of course the \texttt{NonCumulative} prefix is used)
-but has no effect on \emph{monomorphic} inductive declarations.
-Consider the following examples.
-\begin{coq_example}
-Monomorphic Cumulative Inductive Unit := unit.
-\end{coq_example}
-\begin{coq_example}
-Monomorphic NonCumulative Inductive Unit := unit.
-\end{coq_example}
-\begin{coq_example*}
-Set Polymorphic Inductive Cumulativity.
-Inductive Unit := unit.
-\end{coq_example*}
-\begin{coq_example}
-Print Unit.
-\end{coq_example}
-
-\subsection*{An example of a proof using cumulativity}
-
-\begin{coq_example}
-Set Universe Polymorphism.
-Set Polymorphic Inductive Cumulativity.
-
-Inductive eq@{i} {A : Type@{i}} (x : A) : A -> Type@{i} := eq_refl : eq x x.
-
-Definition funext_type@{a b e} (A : Type@{a}) (B : A -> Type@{b})
-  := forall f g : (forall a, B a),
-    (forall x, eq@{e} (f x) (g x))
-    -> eq@{e} f g.
-
-Section down.
-  Universes a b e e'.
-  Constraint e' < e.
-  Lemma funext_down {A B}
-    (H : @funext_type@{a b e} A B) : @funext_type@{a b e'} A B.
-  Proof.
-    exact H.
-  Defined.
-\end{coq_example}
-
-\subsection{\tt Cumulativity Weak Constraints}
-\optindex{Cumulativity Weak Constraints}
-
-This option, on by default, causes ``weak'' constraints to be produced
-when comparing universes in an irrelevant position. Processing weak
-constraints is delayed until minimization time. A weak constraint
-between {\tt u} and {\tt v} when neither is smaller than the other and
-one is flexible causes them to be unified. Otherwise the constraint is
-silently discarded.
-
-This heuristic is experimental and may change in future versions.
-Disabling weak constraints is more predictable but may produce
-arbitrary numbers of universes.
-
-\asection{Global and local universes}
-
-Each universe is declared in a global or local environment before it can
-be used. To ensure compatibility, every \emph{global} universe is set to
-be strictly greater than \Set~when it is introduced, while every
-\emph{local} (i.e. polymorphically quantified) universe is introduced as
-greater or equal to \Set.
-
-\asection{Conversion and unification}
-
-The semantics of conversion and unification have to be modified a little
-to account for the new universe instance arguments to polymorphic
-references. The semantics respect the fact that definitions are
-transparent, so indistinguishable from their bodies during conversion.
-
-This is accomplished by changing one rule of unification, the
-first-order approximation rule, which applies when two applicative terms
-with the same head are compared. It tries to short-cut unfolding by
-comparing the arguments directly. In case the constant is universe
-polymorphic, we allow this rule to fire only when unifying the universes
-results in instantiating a so-called flexible universe variables (not
-given by the user). Similarly for conversion, if such an equation of
-applicative terms fail due to a universe comparison not being satisfied,
-the terms are unfolded. This change implies that conversion and
-unification can have different unfolding behaviors on the same
-development with universe polymorphism switched on or off.
-
-\asection{Minimization}
-\optindex{Universe Minimization ToSet}
-
-Universe polymorphism with cumulativity tends to generate many useless
-inclusion constraints in general. Typically at each application of a
-polymorphic constant $f$, if an argument has expected type
-\verb|Type@{i}| and is given a term of type \verb|Type@{j}|, a $j \le i$
-constraint will be generated. It is however often the case that an
-equation $j = i$ would be more appropriate, when $f$'s
-universes are fresh for example. Consider the following example:
-
-\begin{coq_eval}
-Set Printing Universes.
-\end{coq_eval}
-\begin{coq_example}
-Definition id0 := @pidentity nat 0.
-Print id0.
-\end{coq_example}
-
-This definition is elaborated by minimizing the universe of id to level
-\Set~while the more general definition would keep the fresh level i
-generated at the application of id and a constraint that $\Set \le i$.
-This minimization process is applied only to fresh universe
-variables. It simply adds an equation between the variable and its lower
-bound if it is an atomic universe (i.e. not an algebraic \texttt{max()}
-universe).
-
-The option \texttt{Unset Universe Minimization ToSet} disallows
-minimization to the sort $\Set$ and only collapses floating universes
-between themselves.
-
-\asection{Explicit Universes}
-
-The syntax has been extended to allow users to explicitly bind names to
-universes and explicitly instantiate polymorphic definitions.
-
-\subsection{\tt Universe {\ident}.
-  \comindex{Universe}
-  \label{UniverseCmd}}
-
-In the monorphic case, this command declares a new global universe named
-{\ident}, which can be referred to using its qualified name as
-well. Global universe names live in a separate namespace. The command
-supports the polymorphic flag only in sections, meaning the universe
-quantification will be discharged on each section definition
-independently. One cannot mix polymorphic and monomorphic declarations
-in the same section.
-
-\subsection{\tt Constraint {\ident} {\textit{ord}} {\ident}.
-  \comindex{Constraint}
-  \label{ConstraintCmd}}
-
-This command declares a new constraint between named universes.
-The order relation can be one of $<$, $\le$ or $=$. If consistent, 
-the constraint is then enforced in the global environment. Like
-\texttt{Universe}, it can be used with the \texttt{Polymorphic} prefix
-in sections only to declare constraints discharged at section closing time.
-One cannot declare a global constraint on polymorphic universes.
-
-\begin{ErrMsgs}
-\item \errindex{Undeclared universe {\ident}}.
-\item \errindex{Universe inconsistency}
-\end{ErrMsgs}
-
-\subsection{Polymorphic definitions}
-For polymorphic definitions, the declaration of (all) universe levels
-introduced by a definition uses the following syntax:
-
-\begin{coq_example*}
-Polymorphic Definition le@{i j} (A : Type@{i}) : Type@{j} := A.
-\end{coq_example*}
-\begin{coq_example}
-Print le.
-\end{coq_example}
-
-During refinement we find that $j$ must be larger or equal than $i$, as
-we are using $A : Type@{i} <= Type@{j}$, hence the generated
-constraint. At the end of a definition or proof, we check that the only
-remaining universes are the ones declared. In the term and in general in
-proof mode, introduced universe names can be referred to in
-terms. Note that local universe names shadow global universe names.
-During a proof, one can use \texttt{Show Universes} to display
-the current context of universes.
-
-Definitions can also be instantiated explicitly, giving their full instance:
-\begin{coq_example}
-Check (pidentity@{Set}).
-Universes k l.
-Check (le@{k l}).
-\end{coq_example}
-
-User-named universes and the anonymous universe implicitly attached to
-an explicit $Type$ are considered rigid for unification and are never
-minimized. Flexible anonymous universes can be produced with an
-underscore or by omitting the annotation to a polymorphic definition.
-
-\begin{coq_example}
-  Check (fun x => x) : Type -> Type.
-  Check (fun x => x) : Type -> Type@{_}.
-
-  Check le@{k _}.
-  Check le.
-\end{coq_example}
-
-\subsection{\tt Unset Strict Universe Declaration.
-  \optindex{Strict Universe Declaration}
-  \label{StrictUniverseDeclaration}}
-
-The command \texttt{Unset Strict Universe Declaration} allows one to
-freely use identifiers for universes without declaring them first, with
-the semantics that the first use declares it. In this mode, the universe
-names are not associated with the definition or proof once it has been
-defined. This is meant mainly for debugging purposes.
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "Reference-Manual"
-%%% End: 
diff --git a/doc/refman/biblio.bib b/doc/refman/biblio.bib
deleted file mode 100644
index e69725838e..0000000000
--- a/doc/refman/biblio.bib
+++ /dev/null
@@ -1,1397 +0,0 @@
-@String{jfp   = "Journal of Functional Programming"}
-@String{lncs  = "Lecture Notes in Computer Science"}
-@String{lnai  = "Lecture Notes in Artificial Intelligence"}
-@String{SV    = "{Sprin-ger-Verlag}"}
-
-@InProceedings{Aud91,
-  author      = {Ph. Audebaud},
-  booktitle   = {Proceedings of the sixth Conf. on Logic in Computer Science.},
-  publisher   = {IEEE},
-  title       = {Partial {Objects} in the {Calculus of Constructions}},
-  year        = {1991}
-}
-
-@PhDThesis{Aud92,
-  author      = {Ph. Audebaud},
-  school      = {{Universit\'e} Bordeaux I},
-  title       = {Extension du Calcul des Constructions par Points fixes},
-  year        = {1992}
-}
-
-@InProceedings{Audebaud92b,
-  author      = {Ph. Audebaud},
-  booktitle   = {{Proceedings of the 1992 Workshop on Types for Proofs and Programs}},
-  editor      = {{B. Nordstr\"om and K. Petersson and G. Plotkin}},
-  note        = {Also Research Report LIP-ENS-Lyon},
-  pages       = {21--34},
-  title       = {{CC+ : an extension of the Calculus of Constructions with fixpoints}},
-  year        = {1992}
-}
-
-@InProceedings{Augustsson85,
-  author      = {L. Augustsson},
-  title       = {{Compiling Pattern Matching}},
-  booktitle   = {Conference Functional Programming and
-Computer Architecture},
-  year        = {1985}
-}
-
-@Article{BaCo85,
-  author      = {J.L. Bates and R.L. Constable},
-  journal     = {ACM transactions on Programming Languages and Systems},
-  title       = {Proofs as {Programs}},
-  volume      = {7},
-  year        = {1985}
-}
-
-@Book{Bar81,
-  author      = {H.P. Barendregt},
-  publisher   = {North-Holland},
-  title       = {The Lambda Calculus its Syntax and Semantics},
-  year        = {1981}
-}
-
-@TechReport{Bar91,
-  author      = {H. Barendregt},
-  institution = {Catholic University Nijmegen},
-  note        = {In Handbook of Logic in Computer Science, Vol II},
-  number      = {91-19},
-  title       = {Lambda {Calculi with Types}},
-  year        = {1991}
-}
-
-@Article{BeKe92,
-  author      = {G. Bellin and J. Ketonen},
-  journal     = {Theoretical Computer Science},
-  pages       = {115--142},
-  title       = {A decision procedure revisited : Notes on direct logic, linear logic and its implementation},
-  volume      = {95},
-  year        = {1992}
-}
-
-@Book{Bee85,
-  author      = {M.J. Beeson},
-  publisher   = SV,
-  title       = {Foundations of Constructive Mathematics, Metamathematical Studies},
-  year        = {1985}
-}
-
-@Book{Bis67,
-  author      = {E. Bishop},
-  publisher   = {McGraw-Hill},
-  title       = {Foundations of Constructive Analysis},
-  year        = {1967}
-}
-
-@Book{BoMo79,
-  author      = {R.S. Boyer and J.S. Moore},
-  key         = {BoMo79},
-  publisher   = {Academic Press},
-  series      = {ACM Monograph},
-  title       = {A computational logic},
-  year        = {1979}
-}
-
-@MastersThesis{Bou92,
-  author      = {S. Boutin},
-  month       = sep,
-  school      = {{Universit\'e Paris 7}},
-  title       = {Certification d'un compilateur {ML en Coq}},
-  year        = {1992}
-}
-
-@InProceedings{Bou97,
-  title       = {Using reflection to build efficient and certified decision procedure
-s},
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-  publisher   = {Prentice-Hall},
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-@PhDThesis{Coq85,
-  author      = {Th. Coquand},
-  month       = jan,
-  school      = {Universit\'e Paris~7},
-  title       = {Une Th\'eorie des Constructions},
-  year        = {1985}
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-  publisher   = {IEEE Computer Society Press},
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-  year        = {1986}
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-@InProceedings{Coq90,
-  author      = {Th. Coquand},
-  booktitle   = {Logic and Computer Science},
-  editor      = {P. Oddifredi},
-  note        = {INRIA Research Report 1088, also in~\cite{CoC89}},
-  publisher   = {Academic Press},
-  title       = {{Metamathematical Investigations of a Calculus of Constructions}},
-  year        = {1990}
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-@InProceedings{Coq91,
-  author      = {Th. Coquand},
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-  month       = {August},
-  year        = {1991}
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-@InProceedings{Coq92,
-  author      = {Th. Coquand},
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-  year        = {1992},
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-  volume      = {806},
-  year        = {1993},
-  pages       = {62-78}
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-@inproceedings{Corbineau08types,
-  author      = {P. Corbineau},
-  title       = {A Declarative Language for the Coq Proof Assistant},
-  editor      = {M. Miculan and I. Scagnetto and F. Honsell},
-  booktitle   = {TYPES '07, Cividale del Friuli, Revised Selected Papers},
-  publisher   = {Springer},
-  series      = LNCS,
-  volume      = {4941},
-  year        = {2007},
-  pages       = {69-84},
-  ee          = {http://dx.doi.org/10.1007/978-3-540-68103-8_5},
-}
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-@PhDThesis{Cor97,
-  author      = {C. Cornes},
-  month       = nov,
-  school      = {{Universit\'e Paris 7}},
-  title       = {Conception d'un langage de haut niveau de représentation de preuves},
-  type        = {Th\`ese de Doctorat},
-  year        = {1997}
-}
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-@MastersThesis{Cou94a,
-  author      = {J. Courant},
-  month       = sep,
-  school      = {DEA d'Informatique, ENS Lyon},
-  title       = {Explicitation de preuves par r\'ecurrence implicite},
-  year        = {1994}
-}
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-  author      = {Haskell B. Curry and Robert Feys and William Craig},
-  title       = {Combinatory Logic},
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-  year        = 1958,
-  note        = {{\S{9E}}},
-}
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-@InProceedings{Del99,
-  author      = {Delahaye, D.},
-  title       = {Information Retrieval in a Coq Proof Library using
-                 Type Isomorphisms},
-  booktitle   = {Proceedings of TYPES '99, L\"okeberg},
-  publisher   = SV,
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-  year        = {1999},
-  url         =
-    "\\{\sf ftp://ftp.inria.fr/INRIA/Projects/coq/David.Delahaye/papers/}"#
-    "{\sf TYPES99-SIsos.ps.gz}"
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-    "{\sf LPAR2000-ltac.ps.gz}"
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-    "\\{\sf ftp://ftp.inria.fr/INRIA/Projects/coq/David.Delahaye/papers/}"#
-    "{\sf JFLA2000-Field.ps.gz}"
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-  number      = {12},
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-  volume      = {I, 312},
-  year        = {1991}
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-  author      = {G. Dowek},
-  month       = dec,
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-  year        = {1991}
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-  author      = {G. Dowek},
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-  number      = 2,
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-  year        = {1994}
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-  year        = {1994}
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-  author      = {J.-C. Filli\^atre},
-  title       = {Preuve de programmes imp\'eratifs en th\'eorie des types},
-  type        = {Thèse de Doctorat},
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-  url         = {\url{http://www.lri.fr/~filliatr/ftp/publis/find.ps.gz}}
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-  author      = {J.-C. Filli\^atre and N. Magaud},
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-                 Emerging Trends},
-  year        = 1999,
-  url         = {\url{http://www.lri.fr/~filliatr/ftp/publis/Filliatre-Magaud.ps.gz}}
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-  author      = {E. Gim\'enez and P. Cast\'eran},
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-  year        = {1995}
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-  year        = {1970}
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-  school      = {Universit\'e Paris~7},
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-  year        = {1972}
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-  author      = {J.-Y. Girard and Y. Lafont and P. Taylor},
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-  year        = {1994}
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-  author      = {Martin Hofmann and Thomas Streicher},
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-  author      = {W.A. Howard},
-  booktitle   = {to H.B. Curry : Essays on Combinatory Logic, Lambda Calculus and Formalism.},
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-  year        = {1992}
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-@Article{Rushby98,
-  title       = {Subtypes for Specifications: Predicate Subtyping in
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-  number      = {2345},
-  title       = {{Axiomatization of a lambda-calculus with explicit-substitutions in the Coq System}},
-  year        = {1994}
-}
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-@MastersThesis{Ter92,
-  author      = {D. Terrasse},
-  month       = sep,
-  school      = {IARFA},
-  title       = {{Traduction de TYPOL en COQ. Application \`a Mini ML}},
-  year        = {1992}
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-  institution = {INRIA Sophia},
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-  type        = {Research Report},
-  year        = {1992}
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-  title       = {Une th\'eorie des constructions inductives},
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-@Article{dowek93,
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-  number      = {3},
-  pages       = {287--315},
-  month       = {June},
-  year        = {1993}
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-@InProceedings{manoury94,
-  author      = {P. Manoury},
-  title       = {{A User's Friendly Syntax to Define
-Recursive Functions as Typed $\lambda-$Terms}},
-  booktitle   = {{Types for Proofs and Programs, TYPES'94}},
-  series      = {LNCS},
-  volume      = {996},
-  month       = jun,
-  year        = {1994}
-}
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-@TechReport{maranget94,
-  author      = {L. Maranget},
-  institution = {INRIA},
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-  title       = {{Two Techniques for Compiling Lazy Pattern Matching}},
-  year        = {1994}
-}
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-@InProceedings{puel-suarez90,
-  author      = {L.Puel and A. Su\'arez},
-  booktitle   = {{Conference Lisp and Functional Programming}},
-  series      = {ACM},
-  publisher   = SV,
-  title       = {{Compiling Pattern Matching by Term
-Decomposition}},
-  year        = {1990}
-}
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-@MastersThesis{saidi94,
-  author      = {H. Saidi},
-  month       = sep,
-  school      = {DEA d'Informatique Fondamentale, Universit\'e Paris 7},
-  title       = {R\'esolution d'\'equations dans le syst\`eme T
- de G\"odel},
-  year        = {1994}
-}
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-@inproceedings{sozeau06,
-  author = {Matthieu Sozeau},
-  title = {Subset Coercions in {C}oq},
-  year = {2007},
-  booktitle = {TYPES'06},
-  pages = {237-252},
-  volume = {4502},
-  publisher = "Springer",
-  series =    {LNCS}
-}
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-@inproceedings{sozeau08,
-	Author = {Matthieu Sozeau and Nicolas Oury},
-	booktitle = {TPHOLs'08},
-	Pdf = {http://www.lri.fr/~sozeau/research/publications/drafts/classes.pdf},
-	Title = {{F}irst-{C}lass {T}ype {C}lasses},
-	Year = {2008},
-}
-
-@Misc{streicher93semantical,
-  author      = {T. Streicher},
-  title       = {Semantical Investigations into Intensional Type Theory},
-  note        = {Habilitationsschrift, LMU Munchen.},
-  year        = {1993}
-}
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-@Misc{Pcoq,
-  author      = {Lemme Team},
-  title       = {Pcoq a graphical user-interface for {Coq}},
-  note        = {\url{http://www-sop.inria.fr/lemme/pcoq/}}
-}
-
-@Misc{ProofGeneral,
-  author      = {David Aspinall},
-  title       = {Proof General},
-  note        = {\url{https://proofgeneral.github.io/}}
-}
-
-@Book{CoqArt,
-  title       = {Interactive Theorem Proving and Program Development.
-                 Coq'Art: The Calculus of Inductive Constructions},
-  author      = {Yves Bertot and Pierre Castéran},
-  publisher   = {Springer Verlag},
-  series      = {Texts in Theoretical Computer Science. An EATCS series}, 
-  year        = 2004
-}
-
-@InCollection{wadler87,
-  author      = {P. Wadler},
-  title       = {Efficient  Compilation of Pattern Matching},
-  booktitle   = {The Implementation of Functional Programming
-Languages},
-  editor      = {S.L. Peyton Jones},
-  publisher   = {Prentice-Hall},
-  year        = {1987}
-}
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-@inproceedings{DBLP:conf/types/CornesT95,
-  author    = {Cristina Cornes and
-               Delphine Terrasse},
-  title     = {Automating Inversion of Inductive Predicates in Coq},
-  booktitle = {TYPES},
-  year      = {1995},
-  pages     = {85-104},
-  crossref  = {DBLP:conf/types/1995},
-  bibsource = {DBLP, http://dblp.uni-trier.de}
-}
-@proceedings{DBLP:conf/types/1995,
-  editor    = {Stefano Berardi and
-               Mario Coppo},
-  title     = {Types for Proofs and Programs, International Workshop TYPES'95,
-               Torino, Italy, June 5-8, 1995, Selected Papers},
-  booktitle = {TYPES},
-  publisher = {Springer},
-  series    = {Lecture Notes in Computer Science},
-  volume    = {1158},
-  year      = {1996},
-  isbn      = {3-540-61780-9},
-  bibsource = {DBLP, http://dblp.uni-trier.de}
-}
-
-@inproceedings{DBLP:conf/types/McBride00,
-  author    = {Conor McBride},
-  title     = {Elimination with a Motive},
-  booktitle = {TYPES},
-  year      = {2000},
-  pages     = {197-216},
-  ee        = {http://link.springer.de/link/service/series/0558/bibs/2277/22770197.htm},
-  crossref  = {DBLP:conf/types/2000},
-  bibsource = {DBLP, http://dblp.uni-trier.de}
-}
-
-@proceedings{DBLP:conf/types/2000,
-  editor    = {Paul Callaghan and
-               Zhaohui Luo and
-               James McKinna and
-               Robert Pollack},
-  title     = {Types for Proofs and Programs, International Workshop, TYPES
-               2000, Durham, UK, December 8-12, 2000, Selected Papers},
-  booktitle = {TYPES},
-  publisher = {Springer},
-  series    = {Lecture Notes in Computer Science},
-  volume    = {2277},
-  year      = {2002},
-  isbn      = {3-540-43287-6},
-  bibsource = {DBLP, http://dblp.uni-trier.de}
-}
-
-@INPROCEEDINGS{sugar,
-    author = {Alessandro Giovini and Teo Mora and Gianfranco Niesi and Lorenzo Robbiano and Carlo Traverso},
-    title = {"One sugar cube, please" or Selection strategies in the Buchberger algorithm},
-    booktitle = { Proceedings of the ISSAC'91, ACM Press},
-    year = {1991},
-    pages = {5--4},
-    publisher = {}
-}
-
-@article{LeeWerner11,
-  author    = {Gyesik Lee and
-               Benjamin Werner},
-  title     = {Proof-irrelevant model of {CC} with predicative induction
-               and judgmental equality},
-  journal   = {Logical Methods in Computer Science},
-  volume    = {7},
-  number    = {4},
-  year      = {2011},
-  ee        = {http://dx.doi.org/10.2168/LMCS-7(4:5)2011},
-  bibsource = {DBLP, http://dblp.uni-trier.de}
-}
-
-@Comment{cross-references, must be at end}
-
-@Book{Bastad92,
-  editor      = {B. Nordstr\"om and K. Petersson and G. Plotkin},
-  publisher   = {Available by ftp at site ftp.inria.fr},
-  title       = {Proceedings of the 1992 Workshop on Types for Proofs and Programs},
-  year        = {1992}
-}
-
-@Book{Nijmegen93,
-  editor      = {H. Barendregt and T. Nipkow},
-  publisher   = SV,
-  series      = LNCS,
-  title       = {Types for Proofs and Programs},
-  volume      = {806},
-  year        = {1994}
-}
-
-@article{ TheOmegaPaper,
-    author = "W. Pugh",
-    title = "The Omega test: a fast and practical integer programming algorithm for dependence analysis",
-    journal = "Communication of the ACM",
-    pages = "102--114",
-    year = "1992",
-}
-
-@inproceedings{CSwcu,
-    hal_id = {hal-00816703},
-    url = {http://hal.inria.fr/hal-00816703},
-    title = {{Canonical Structures for the working Coq user}},
-    author = {Mahboubi, Assia and Tassi, Enrico},
-    booktitle = {{ITP 2013, 4th Conference on Interactive Theorem Proving}},
-    publisher = {Springer},
-    pages = {19-34},
-    address = {Rennes, France},
-    volume = {7998},
-    editor = {Sandrine Blazy and Christine Paulin and David Pichardie },
-    series = {LNCS },
-    doi = {10.1007/978-3-642-39634-2\_5 },
-    year = {2013},
-}
-
-@article{CSlessadhoc,
- author = {Gonthier, Georges and Ziliani, Beta and Nanevski, Aleksandar and Dreyer, Derek},
- title = {How to Make Ad Hoc Proof Automation Less Ad Hoc},
- journal = {SIGPLAN Not.},
- issue_date = {September 2011},
- volume = {46},
- number = {9},
- month = sep,
- year = {2011},
- issn = {0362-1340},
- pages = {163--175},
- numpages = {13},
- url = {http://doi.acm.org/10.1145/2034574.2034798},
- doi = {10.1145/2034574.2034798},
- acmid = {2034798},
- publisher = {ACM},
- address = {New York, NY, USA},
- keywords = {canonical structures, coq, custom proof automation, hoare type theory, interactive theorem proving, tactics, type classes},
-}
-
-@inproceedings{CompiledStrongReduction,
-  author    = {Benjamin Gr{\'{e}}goire and
-               Xavier Leroy},
-  editor    = {Mitchell Wand and
-               Simon L. Peyton Jones},
-  title     = {A compiled implementation of strong reduction},
-  booktitle = {Proceedings of the Seventh {ACM} {SIGPLAN} International Conference
-               on Functional Programming {(ICFP} '02), Pittsburgh, Pennsylvania,
-               USA, October 4-6, 2002.},
-  pages     = {235--246},
-  publisher = {{ACM}},
-  year      = {2002},
-  url       = {http://doi.acm.org/10.1145/581478.581501},
-  doi       = {10.1145/581478.581501},
-  timestamp = {Tue, 11 Jun 2013 13:49:16 +0200},
-  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/icfp/GregoireL02},
-  bibsource = {dblp computer science bibliography, http://dblp.org}
-}
-
-@inproceedings{FullReduction,
-  author    = {Mathieu Boespflug and
-               Maxime D{\'{e}}n{\`{e}}s and
-               Benjamin Gr{\'{e}}goire},
-  editor    = {Jean{-}Pierre Jouannaud and
-               Zhong Shao},
-  title     = {Full Reduction at Full Throttle},
-  booktitle = {Certified Programs and Proofs - First International Conference, {CPP}
-               2011, Kenting, Taiwan, December 7-9, 2011. Proceedings},
-  series    = {Lecture Notes in Computer Science},
-  volume    = {7086},
-  pages     = {362--377},
-  publisher = {Springer},
-  year      = {2011},
-  url       = {http://dx.doi.org/10.1007/978-3-642-25379-9_26},
-  doi       = {10.1007/978-3-642-25379-9_26},
-  timestamp = {Thu, 17 Nov 2011 13:33:48 +0100},
-  biburl    = {http://dblp.uni-trier.de/rec/bib/conf/cpp/BoespflugDG11},
-  bibsource = {dblp computer science bibliography, http://dblp.org}
-}
diff --git a/doc/refman/coq-listing.tex b/doc/refman/coq-listing.tex
deleted file mode 100644
index c69c3b1b81..0000000000
--- a/doc/refman/coq-listing.tex
+++ /dev/null
@@ -1,152 +0,0 @@
-%=======================================================================
-% Listings LaTeX package style for Gallina + SSReflect (Assia Mahboubi 2007)
-
-\lstdefinelanguage{SSR} {
-
-% Anything betweeen $ becomes LaTeX math mode
-mathescape=true,
-% Comments may or not include Latex commands
-texcl=false,
-
-
-% Vernacular commands
-morekeywords=[1]{
-From, Section, Module, End, Require, Import, Export, Defensive, Function,
-Variable, Variables, Parameter, Parameters, Axiom, Hypothesis, Hypotheses,
-Notation, Local, Tactic, Reserved, Scope, Open, Close, Bind, Delimit,
-Definition, Let, Ltac, Fixpoint, CoFixpoint, Add, Morphism, Relation,
-Implicit, Arguments, Set, Unset, Contextual, Strict, Prenex, Implicits,
-Inductive, CoInductive, Record, Structure, Canonical, Coercion,
-Theorem, Lemma, Corollary, Proposition, Fact, Remark, Example,
-Proof, Goal, Save, Qed, Defined, Hint, Resolve, Rewrite, View,
-Search, Show, Print, Printing, All, Graph, Projections, inside,
-outside, Locate, Maximal},
-
-% Gallina
-morekeywords=[2]{forall, exists, exists2, fun, fix, cofix, struct,
-      match, with, end, as, in, return, let, if, is, then, else,
-      for, of, nosimpl},
-
-% Sorts
-morekeywords=[3]{Type, Prop},
-
-% Various tactics, some are std Coq subsumed by ssr, for the manual purpose
-morekeywords=[4]{
-         pose, set, move, case, elim, apply, clear,
-            hnf, intro, intros, generalize, rename, pattern, after,
-	    destruct, induction, using, refine, inversion, injection,
-         rewrite, congr, unlock, compute, ring, field,
-            replace, fold, unfold, change, cutrewrite, simpl,
-         have, gen, generally, suff, wlog, suffices, without, loss, nat_norm,
-            assert, cut, trivial, revert, bool_congr, nat_congr, abstract,
-	 symmetry, transitivity, auto, split, left, right, autorewrite},
-
-% Terminators
-morekeywords=[5]{
-         by, done, exact, reflexivity, tauto, romega, omega,
-         assumption, solve, contradiction, discriminate},
-
-
-% Control
-morekeywords=[6]{do, last, first, try, idtac, repeat},
-
-% Various symbols
-% For the ssr manual we turn off the prettyprint of formulas
-% literate=
-%	{->}{{$\rightarrow\,$}}2
-% 	{->}{{\tt ->}}3
-%	{<-}{{$\leftarrow\,$}}2
-% 	{<-}{{\tt <-}}2
-% 	{>->}{{$\mapsto$}}3
-% 	{<=}{{$\leq$}}1
-% 	{>=}{{$\geq$}}1
-% 	{<>}{{$\neq$}}1
-% 	{/\\}{{$\wedge$}}2
-% 	{\\/}{{$\vee$}}2
-% 	{<->}{{$\leftrightarrow\;$}}3
-% 	{<=>}{{$\Leftrightarrow\;$}}3
-% 	{:nat}{{$~\in\mathbb{N}$}}3
-%	{fforall\ }{{$\forall_f\,$}}1
-%	{forall\ }{{$\forall\,$}}1
-%	{exists\ }{{$\exists\,$}}1
-% 	{negb}{{$\neg$}}1
-% 	{spp}{{:*:\,}}1
-% 	{~}{{$\sim$}}1
-% 	{\\in}{{$\in\;$}}1
-% 	{/\\}{$\land\,$}1
-% 	{:*:}{{$*$}}2
-%	{=>}{{$\,\Rightarrow\ $}}1
-% 	{=>}{{\tt =>}}2
-% 	{:=}{{{\tt:=}\,\,}}2
-% 	{==}{{$\equiv$}\,}2
-% 	{!=}{{$\neq$}\,}2
-% 	{^-1}{{$^{-1}$}}1
-% 	{elt'}{elt'}1
-%       {=}{{\tt=}\,\,}2
-%       {+}{{\tt+}\,\,}2,
-literate=
-	{isn't }{{{\ttfamily\color{dkgreen} isn't }}}1,
-
-% Comments delimiters, we do turn this off for the manual
-%comment=[s]{(*}{*)},
-
-% Spaces are not displayed as a special character
-showstringspaces=false,
-
-% String delimiters
-morestring=[b]",
-morestring=[d]",
-
-% Size of tabulations
-tabsize=3,
-
-% Enables ASCII chars 128 to 255
-extendedchars=true,
-
-% Case sensitivity
-sensitive=true,
-
-% Automatic breaking of long lines
-breaklines=true,
-
-% Default style fors listings
-basicstyle=\ttfamily,
-
-% Position of captions is bottom
-captionpos=b,
-
-% Full flexible columns
-columns=[l]fullflexible,
-
-% Style for (listings') identifiers
-identifierstyle={\ttfamily\color{black}},
-% Note : highlighting of Coq identifiers is done through a new
-% delimiter definition through an lstset at the begining of the
-% document. Don't know how to do better.
-
-% Style for declaration keywords
-keywordstyle=[1]{\ttfamily\color{dkviolet}},
-
-% Style for gallina keywords
-keywordstyle=[2]{\ttfamily\color{dkgreen}},
-
-% Style for sorts keywords
-keywordstyle=[3]{\ttfamily\color{lightblue}},
-
-% Style for tactics keywords
-keywordstyle=[4]{\ttfamily\color{dkblue}},
-
-% Style for terminators keywords
-keywordstyle=[5]{\ttfamily\color{red}},
-
-
-%Style for iterators
-keywordstyle=[6]{\ttfamily\color{dkpink}},
-
-% Style for strings
-stringstyle=\ttfamily,
-
-% Style for comments
-commentstyle=\rmfamily,
-
-}
diff --git a/doc/refman/coqdoc.tex b/doc/refman/coqdoc.tex
deleted file mode 100644
index 26dbd59e76..0000000000
--- a/doc/refman/coqdoc.tex
+++ /dev/null
@@ -1,573 +0,0 @@
-
-%\newcommand{\Coq}{\textsf{Coq}}
-\newcommand{\javadoc}{\textsf{javadoc}}
-\newcommand{\ocamldoc}{\textsf{ocamldoc}}
-\newcommand{\coqdoc}{\textsf{coqdoc}}
-\newcommand{\texmacs}{\TeX{}macs}
-\newcommand{\monurl}[1]{#1}
-%HEVEA\renewcommand{\monurl}[1]{\ahref{#1}{#1}}
-%\newcommand{\lnot}{not} % Hevea handles these symbols nicely
-%\newcommand{\lor}{or}
-%\newcommand{\land}{\&}
-%%% Beware : in a \texttt, -- is displayed as a unique - hence
-%%% the following macro:
-\newcommand{\mm}{\symbol{45}\symbol{45}}
-
-
-\coqdoc\ is a documentation tool for the proof assistant
-\Coq, similar to \javadoc\ or \ocamldoc. 
-The task of \coqdoc\ is
-\begin{enumerate}
-\item to produce a nice \LaTeX\ and/or HTML document from the \Coq\ 
-  sources, readable for a human and not only for the proof assistant;
-\item to help the user navigating in his own (or third-party) sources.
-\end{enumerate}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\subsection{Principles}
-
-Documentation is inserted into \Coq\ files as \emph{special comments}.  
-Thus your files will compile as usual, whether you use \coqdoc\ or not.
-\coqdoc\ presupposes that the given \Coq\ files are well-formed (at
-least lexically).  Documentation starts with
-\texttt{(**}, followed by a space, and ends with the pending \texttt{*)}. 
-The documentation format is inspired
-  by Todd~A.~Coram's \emph{Almost Free Text (AFT)} tool: it is mainly
-ASCII text with some syntax-light controls, described below.
-\coqdoc\ is robust: it shouldn't fail, whatever the input is. But
-remember: ``garbage in, garbage out''.
-
-\paragraph{\Coq\ material inside documentation.}
-\Coq\ material is quoted between the
-delimiters \texttt{[} and \texttt{]}. Square brackets may be nested,
-the inner ones being understood as being part of the quoted code (thus
-you can quote a term like \texttt{fun x => u} by writing
-\texttt{[fun x => u]}). Inside quotations, the code is pretty-printed in
-the same way as it is in code parts.
-
-Pre-formatted vernacular is enclosed by \texttt{[[} and
-\texttt{]]}. The former must be followed by a newline and the latter
-must follow a newline.
-
-\paragraph{Pretty-printing.}
-\coqdoc\ uses different faces for identifiers and keywords.  
-The pretty-printing of \Coq\ tokens (identifiers or symbols) can be
-controlled using one of the following commands:
-\begin{alltt}
-(** printing \emph{token} %...\LaTeX...% #...HTML...# *)
-\end{alltt}
-or
-\begin{alltt}
-(** printing \emph{token} $...\LaTeX\ math...$ #...HTML...# *)
-\end{alltt}
-It gives the \LaTeX\ and HTML texts to be produced for the given \Coq\
-token. One of the \LaTeX\ or HTML text may be omitted, causing the
-default pretty-printing to be used for this token.
-
-The printing for one token can be removed with
-\begin{alltt}
-(** remove printing \emph{token} *)
-\end{alltt}
-
-Initially, the pretty-printing table contains the following mapping:
-\begin{center}
-  \begin{tabular}{ll@{\qquad\qquad}ll@{\qquad\qquad}ll@{\qquad\qquad}}
-    \verb!->!            & $\rightarrow$   &
-    \verb!<-!            & $\leftarrow$    &
-    \verb|*|             & $\times$        \\
-    \verb|<=|            & $\le$           &
-    \verb|>=|            & $\ge$           &
-    \verb|=>|            & $\Rightarrow$   \\
-    \verb|<>|            & $\not=$         &
-    \verb|<->|           & $\leftrightarrow$ &
-    \verb!|-!            & $\vdash$        \\
-    \verb|\/|            & $\lor$          &
-    \verb|/\|            & $\land$         &
-    \verb|~|             & $\lnot$ 
-  \end{tabular}
-\end{center}
-Any of these can be overwritten or suppressed using the
-\texttt{printing} commands.
-
-Important note: the recognition of tokens is done by a (ocaml)lex
-automaton and thus applies the longest-match rule. For instance,
-\verb!->~! is recognized as a single token, where \Coq\ sees two
-tokens. It is the responsibility of the user to insert space between
-tokens \emph{or} to give pretty-printing rules for the possible
-combinations, e.g. 
-\begin{verbatim}
-(** printing ->~ %\ensuremath{\rightarrow\lnot}% *)
-\end{verbatim}
-
-
-\paragraph{Sections.}
-Sections are introduced by 1 to 4 leading stars (i.e. at the beginning of the
-line) followed by a space. One star is a section, two stars a sub-section, etc.
-The section title is given on the remaining of the line.
-Example:
-\begin{verbatim}
-    (** * Well-founded relations
-  
-        In this section, we introduce...  *)
-\end{verbatim}
-
-
-%TODO \paragraph{Fonts.}
-
-
-\paragraph{Lists.}
-List items are introduced by a leading dash.  \coqdoc\ uses whitespace
-to determine the depth of a new list item and which text belongs in
-which list items.  A list ends when a line of text starts at or before
-the level of indenting of the list's dash.  A list item's dash must
-always be the first non-space character on its line (so, in
-particular, a list can not begin on the first line of a comment -
-start it on the second line instead).
-
-Example:
-\begin{verbatim}
-     We go by induction on [n]:
-     - If [n] is 0...
-     - If [n] is [S n'] we require...
-
-       two paragraphs of reasoning, and two subcases:
-
-       - In the first case...
-       - In the second case...
-
-     So the theorem holds.
-\end{verbatim}
-
-\paragraph{Rules.}
-More than 4 leading dashes produce a horizontal rule.
-
-\paragraph{Emphasis.}
-Text can be italicized by placing it in underscores.  A non-identifier
-character must precede the leading underscore and follow the trailing
-underscore, so that uses of underscores in names aren't mistaken for
-emphasis.  Usually, these are spaces or punctuation.
-
-\begin{verbatim}
-    This sentence contains some _emphasized text_.
-\end{verbatim}
-
-\paragraph{Escaping to \LaTeX\ and HTML.}
-Pure \LaTeX\ or HTML material can be inserted using the following
-escape sequences:
-\begin{itemize}
-\item \verb+$...LaTeX stuff...$+ inserts some \LaTeX\ material in math mode.
-  Simply discarded in HTML output.
-
-\item \verb+%...LaTeX stuff...%+ inserts some \LaTeX\ material.
-  Simply discarded in HTML output.
-
-\item \verb+#...HTML stuff...#+ inserts some HTML material. Simply
-  discarded in \LaTeX\ output.
-\end{itemize}
-
-Note: to simply output the characters \verb+$+, \verb+%+ and \verb+#+
-and escaping their escaping role, these characters must be doubled.
-
-\paragraph{Verbatim.} 
-Verbatim material is introduced by a leading \verb+<<+ and closed by
-\verb+>>+ at the beginning of a line. Example:
-\begin{verbatim}
-Here is the corresponding caml code:
-<<
-  let rec fact n = 
-    if n <= 1 then 1 else n * fact (n-1)
->>
-\end{verbatim}
-
-
-\paragraph{Hyperlinks.}
-Hyperlinks can be inserted into the HTML output, so that any
-identifier is linked to the place of its definition.
-
-\texttt{coqc \emph{file}.v} automatically dumps localization information
-in \texttt{\emph{file}.glob} or appends it to a file specified using option
-\texttt{\mm{}dump-glob \emph{file}}. Take care of erasing this global file, if
-any, when starting the whole compilation process.
-
-Then invoke \texttt{coqdoc} or \texttt{coqdoc \mm{}glob-from \emph{file}} to tell
-\coqdoc\ to look for name resolutions into the file \texttt{\emph{file}}
-(it will look in \texttt{\emph{file}.glob} by default).
-
-Identifiers from the \Coq\ standard library are linked to the \Coq\
-web site at \url{http://coq.inria.fr/library/}. This behavior can be
-changed using command line options \texttt{\mm{}no-externals} and
-\texttt{\mm{}coqlib}; see below.
-
-
-\paragraph{Hiding / Showing parts of the source.}
-Some parts of the source can be hidden using command line options
-\texttt{-g} and \texttt{-l} (see below), or using such comments:
-\begin{alltt}
-(* begin hide *)
-\emph{some Coq material}
-(* end hide *)
-\end{alltt}
-Conversely, some parts of the source which would be hidden can be
-shown using such comments: 
-\begin{alltt}
-(* begin show *)
-\emph{some Coq material}
-(* end show *)
-\end{alltt}
-The latter cannot be used around some inner parts of a proof, but can
-be used around a whole proof.
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\subsection{Usage}
-
-\coqdoc\ is invoked on a shell command line as follows:
-\begin{displaymath}
-  \texttt{coqdoc }<\textit{options and files}>
-\end{displaymath}
-Any command line argument which is not an option is considered to be a
-file (even if it starts with a \verb!-!). \Coq\ files are identified
-by the suffixes \verb!.v! and \verb!.g! and \LaTeX\ files by the
-suffix \verb!.tex!. 
-
-\begin{description}
-\item[HTML output] ~\par
-  This is the default output.
-  One HTML file is created for each \Coq\ file given on the command line,
-  together with a file \texttt{index.html} (unless option
-  \texttt{-no-index} is passed). The HTML pages use a style sheet
-  named \texttt{style.css}. Such a file is distributed with \coqdoc.
-
-\item[\LaTeX\ output] ~\par
-  A single \LaTeX\ file is created, on standard output. It can be
-  redirected to a file with option \texttt{-o}. 
-  The order of files on the command line is kept in the final
-  document. \LaTeX\ files given on the command line are copied `as is'
-  in the final document .
-  DVI and PostScript can be produced directly with the options
-  \texttt{-dvi} and \texttt{-ps} respectively.
-
-\item[\texmacs\ output] ~\par
-  To translate the input files to \texmacs\ format, to be used by
-  the \texmacs\ Coq interface.
-  %broken link:
-  %(see \url{http://www-sop.inria.fr/lemme/Philippe.Audebaud/tmcoq/}).
-\end{description}
-
-
-\subsubsection*{Command line options}
-
-
-\paragraph{Overall options}
-
-\begin{description}
-
-\item[\texttt{\mm{}html}] ~\par
-  
-  Select a HTML output.
-
-\item[\texttt{\mm{}latex}] ~\par
-  
-  Select a \LaTeX\ output.
-
-\item[\texttt{\mm{}dvi}] ~\par
-  
-  Select a DVI output.
-
-\item[\texttt{\mm{}ps}] ~\par
-  
-  Select a PostScript output.
-
-\item[\texttt{\mm{}texmacs}] ~\par
-  
-  Select a \texmacs\ output.
-
-\item[\texttt{\mm{}stdout}] ~\par
-
-  Write output to stdout.
-
-\item[\texttt{-o }\textit{file}, \texttt{\mm{}output }\textit{file}] ~\par
-  
-  Redirect the output into the file `\textit{file}' (meaningless with
-  \texttt{-html}).
-
-\item[\texttt{-d }\textit{dir}, \texttt{\mm{}directory }\textit{dir}] ~\par
-
-  Output files into directory `\textit{dir}' instead of current
-  directory (option \texttt{-d} does not change the filename specified
-  with option \texttt{-o}, if any).
-
-\item[\texttt{\mm{}body-only}] ~\par
-
-  Suppress the header and trailer of the final document. Thus, you can
-  insert the resulting document into a larger one.
-
-\item[\texttt{-p} \textit{string}, \texttt{\mm{}preamble} \textit{string}]~\par
-
-  Insert some material in the \LaTeX\ preamble, right before
-  \verb!\begin{document}! (meaningless with \texttt{-html}).
-
-\item[\texttt{\mm{}vernac-file }\textit{file},
-      \texttt{\mm{}tex-file }\textit{file}] ~\par
-      
-      Considers the file `\textit{file}' respectively as a \verb!.v!
-      (or \verb!.g!) file or a \verb!.tex! file.
-
-\item[\texttt{\mm{}files-from }\textit{file}] ~\par
-
-  Read file names to process in file `\textit{file}' as if they were
-  given on the command line. Useful for program sources split up into
-  several directories.
-  
-\item[\texttt{-q}, \texttt{\mm{}quiet}] ~\par
-
-  Be quiet. Do not print anything except errors.
-
-\item[\texttt{-h}, \texttt{\mm{}help}] ~\par
-
-  Give a short summary of the options and exit.
-
-\item[\texttt{-v}, \texttt{\mm{}version}] ~\par
-
-  Print the version and exit.
-
-\end{description}
-
-\paragraph{Index options}
-
-Default behavior is to build an index, for the HTML output only, into
-\texttt{index.html}.
-
-\begin{description}
-
-\item[\texttt{\mm{}no-index}] ~\par
-  
-  Do not output the index.
-
-\item[\texttt{\mm{}multi-index}] ~\par
-  
-  Generate one page for each category and each letter in the index,
-  together with a top page \texttt{index.html}.
-
-\item[\texttt{\mm{}index }\textit{string}] ~\par
-
-  Make the filename of the index \textit{string} instead of ``index''.
-  Useful since ``index.html'' is special.
-
-\end{description}
-
-\paragraph{Table of contents option}
-
-\begin{description}
-
-\item[\texttt{-toc}, \texttt{\mm{}table-of-contents}] ~\par
-
-  Insert a table of contents.
-  For a \LaTeX\ output, it inserts a \verb!\tableofcontents! at the
-  beginning of the document. For a HTML output, it builds a table of
-  contents into \texttt{toc.html}.
-
-\item[\texttt{\mm{}toc-depth }\textit{int}] ~\par
-
-  Only include headers up to depth \textit{int} in the table of
-  contents.
-
-\end{description}
-
-\paragraph{Hyperlinks options}
-\begin{description}
-
-\item[\texttt{\mm{}glob-from }\textit{file}] ~\par
-  
-  Make references using \Coq\ globalizations from file \textit{file}. 
-  (Such globalizations are obtained with \Coq\ option \texttt{-dump-glob}).
-
-\item[\texttt{\mm{}no-externals}] ~\par
-  
-  Do not insert links to the \Coq\ standard library.
-
-\item[\texttt{\mm{}external }\textit{url}~\textit{coqdir}] ~\par
-  
-  Use given URL for linking references whose name starts with prefix
-  \textit{coqdir}.
-
-\item[\texttt{\mm{}coqlib }\textit{url}] ~\par
-
-  Set base URL for the \Coq\ standard library (default is 
-  \url{http://coq.inria.fr/library/}). This is equivalent to
-  \texttt{\mm{}external }\textit{url}~\texttt{Coq}.
-
-\item[\texttt{-R }\textit{dir }\textit{coqdir}] ~\par
-
-  Map physical directory \textit{dir} to \Coq\ logical directory
-  \textit{coqdir} (similarly to \Coq\ option \texttt{-R}).
-
-  Note: option \texttt{-R} only has effect on the files
-  \emph{following} it on the command line, so you will probably need
-  to put this option first.
-
-\end{description}
-
-\paragraph{Title options}
-\begin{description}
-\item[\texttt{-s }, \texttt{\mm{}short}] ~\par
-  
-  Do not insert titles for the files. The default behavior is to
-  insert a title like ``Library Foo'' for each file.
-
-\item[\texttt{\mm{}lib-name }\textit{string}] ~\par
-
-  Print ``\textit{string} Foo'' instead of ``Library Foo'' in titles.
-  For example ``Chapter'' and ``Module'' are reasonable choices.
-
-\item[\texttt{\mm{}no-lib-name}] ~\par
-
-  Print just ``Foo'' instead of ``Library Foo'' in titles.
-
-\item[\texttt{\mm{}lib-subtitles}] ~\par
-
-  Look for library subtitles.  When enabled, the beginning of each
-  file is checked for a comment of the form:
-\begin{alltt}
-(** * ModuleName : text *)
-\end{alltt}
-  where \texttt{ModuleName} must be the name of the file.  If it is
-  present, the \texttt{text} is used as a subtitle for the module in
-  appropriate places.
-
-\item[\texttt{-t }\textit{string}, 
-      \texttt{\mm{}title }\textit{string}] ~\par
-  
-  Set the document title.      
-
-\end{description}
-
-\paragraph{Contents options}
-\begin{description}
-
-\item[\texttt{-g}, \texttt{\mm{}gallina}] ~\par
-
-  Do not print proofs.
-
-\item[\texttt{-l}, \texttt{\mm{}light}] ~\par
-  
-  Light mode. Suppress proofs (as with \texttt{-g}) and the following commands:
-  \begin{itemize}
-  \item {}[\texttt{Recursive}] \texttt{Tactic Definition}
-  \item \texttt{Hint / Hints} 
-  \item \texttt{Require}
-  \item \texttt{Transparent / Opaque}
-  \item \texttt{Implicit Argument / Implicits}
-  \item \texttt{Section / Variable / Hypothesis / End}
-  \end{itemize}
-
-\end{description}
-The behavior of options \texttt{-g} and \texttt{-l} can be locally
-overridden using the \texttt{(* begin show *)} \dots\ \texttt{(* end
-  show *)} environment (see above).
-
-There are a few options to drive the parsing of comments:
-\begin{description}
-\item[\texttt{\mm{}parse-comments}] ~\par
-
-  Parses regular comments delimited by \texttt{(*} and \texttt{*)} as 
-  well. They are typeset inline.
-
-\item[\texttt{\mm{}plain-comments}] ~\par
-
-  Do not interpret comments, simply copy them as plain-text.
-
-\item[\texttt{\mm{}interpolate}] ~\par
-
-  Use the globalization information to typeset identifiers appearing in
-  \Coq{} escapings inside comments.
-\end{description}
-
-
-\paragraph{Language options}
-
-Default behavior is to assume ASCII 7 bits input files.
-
-\begin{description}
-
-\item[\texttt{-latin1}, \texttt{\mm{}latin1}] ~\par
-
-  Select ISO-8859-1 input files. It is equivalent to
-  \texttt{\mm{}inputenc latin1 \mm{}charset iso-8859-1}.
-
-\item[\texttt{-utf8}, \texttt{\mm{}utf8}] ~\par
-
-  Set \texttt{\mm{}inputenc utf8x} for \LaTeX\ output and
-  \texttt{\mm{}charset utf-8} for HTML output. Also use Unicode
-  replacements for a couple of standard plain ASCII notations such
-  as $\rightarrow$ for \texttt{->} and $\forall$ for
-  \texttt{forall}. \LaTeX\ UTF-8 support can be found at
-  \url{http://www.ctan.org/pkg/unicode}.
-
-  For the interpretation of Unicode characters by \LaTeX, extra
-  packages which {\coqdoc} does not provide by default might be
-  required, such as \texttt{textgreek} for some Greek letters or
-  \texttt{stmaryrd} for some mathematical symbols. If a Unicode
-  character is missing an interpretation in the \texttt{utf8x} input
-  encoding, add
-  \verb=\DeclareUnicodeCharacter{=\textit{code}\verb=}{=\textit{latex-interpretation}\verb=}=. Packages
-  and declarations can be added with option \texttt{-p}.
-
-\item[\texttt{\mm{}inputenc} \textit{string}] ~\par
-
-  Give a \LaTeX\ input encoding, as an option to \LaTeX\ package
-  \texttt{inputenc}. 
-
-\item[\texttt{\mm{}charset} \textit{string}] ~\par
-
-  Specify the HTML character set, to be inserted in the HTML header.
-
-\end{description}
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\subsection[The coqdoc \LaTeX{} style file]{The coqdoc \LaTeX{} style file\label{section:coqdoc.sty}}
-
-In case you choose to produce a document without the default \LaTeX{}
-preamble (by using option \verb|--no-preamble|), then you must insert
-into your own preamble the command
-\begin{quote}
-  \verb|\usepackage{coqdoc}|
-\end{quote}
-
-The package optionally takes the argument \verb|[color]| to typeset
-identifiers with colors (this requires the \verb|xcolor| package).
-
-Then you may alter the rendering of the document by
-redefining some macros:
-\begin{description}
-
-\item[\texttt{coqdockw}, \texttt{coqdocid}, \ldots] ~ 
-  
-  The one-argument macros for typesetting keywords and identifiers.
-  Defaults are sans-serif for keywords and italic for identifiers.
-
-  For example, if you would like a slanted font for keywords, you
-  may insert  
-\begin{verbatim}
-     \renewcommand{\coqdockw}[1]{\textsl{#1}}
-\end{verbatim}
-  anywhere between \verb|\usepackage{coqdoc}| and
-  \verb|\begin{document}|. 
-
-\item[\texttt{coqdocmodule}] ~ 
-  
-  One-argument macro for typesetting the title of a \verb|.v| file.
-  Default is
-\begin{verbatim}
-\newcommand{\coqdocmodule}[1]{\section*{Module #1}}
-\end{verbatim}
-  and you may redefine it using \verb|\renewcommand|.
-
-\end{description}
-
-
diff --git a/doc/refman/coqide-queries.png b/doc/refman/coqide-queries.png
deleted file mode 100644
index 7a46ac4e68..0000000000
--- a/doc/refman/coqide-queries.png
+++ /dev/null
diff --git a/doc/refman/coqide.png b/doc/refman/coqide.png
deleted file mode 100644
index e300401c9f..0000000000
--- a/doc/refman/coqide.png
+++ /dev/null
diff --git a/doc/refman/headers.hva b/doc/refman/headers.hva
deleted file mode 100644
index 9714a29beb..0000000000
--- a/doc/refman/headers.hva
+++ /dev/null
@@ -1,44 +0,0 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% File headers.hva
-% Hevea version of headers.sty
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Commands for indexes
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\usepackage{index}
-\makeindex
-
-
-\newindex{tactic}{tacidx}{tacind}{Tactics Index}
-\newindex{command}{comidx}{comind}{Vernacular Commands Index}
-\newindex{option}{optidx}{optind}{Vernacular Options Index}
-\newindex{error}{erridx}{errind}{Index of Error Messages}
-\renewindex{default}{idx}{ind}{Global Index}
-
-\newcommand{\printrefmanindex}[3]{%
-\addcontentsline{toc}{chapter}{#2}%
-\printindex[#1]%
-\cutname{#3}%
-}
-
-\newcommand{\tacindex}[1]{%
-\index{#1@\texttt{#1}}\index[tactic]{#1@\texttt{#1}}}
-\newcommand{\comindex}[1]{%
-\index{#1@\texttt{#1}}\index[command]{#1@\texttt{#1}}}
-\newcommand{\optindex}[1]{%
-\index{#1@\texttt{#1}}\index[option]{#1@\texttt{#1}}}
-\newcommand{\errindex}[1]{\texttt{#1}\index[error]{#1}}
-\newcommand{\errindexbis}[2]{\texttt{#1}\index[error]{#2}}
-\newcommand{\ttindex}[1]{\index{#1@\texttt{#1}}}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% For the Addendum table of contents
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newcommand{\aauthor}[1]{{\LARGE \bf #1} \bigskip}  % 3 \bigskip's that were here originally
-						    % may be good for LaTeX but too much for HTML    
-\newcommand{\atableofcontents}{}
-\newcommand{\achapter}[1]{\chapter{#1}}
-\newcommand{\asection}{\section}
-\newcommand{\asubsection}{\subsection}
-\newcommand{\asubsubsection}{\subsubsection}
diff --git a/doc/refman/headers.sty b/doc/refman/headers.sty
deleted file mode 100644
index fb39f687d7..0000000000
--- a/doc/refman/headers.sty
+++ /dev/null
@@ -1,88 +0,0 @@
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% File headers.sty
-% Commands for pretty headers, multiple indexes, and the appendix.
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\usepackage{fancyhdr}
-
-\setlength{\headheight}{14pt}
-
-\pagestyle{fancyplain}
-
-\newcommand{\coqfooter}{\tiny Coq Reference Manual, V\coqversion{}, \today}
-
-\cfoot{}
-\lfoot[{\coqfooter}]{}
-\rfoot[]{{\coqfooter}}
-
-\newcommand{\setheaders}[1]{\rhead[\fancyplain{}{\textbf{#1}}]{\fancyplain{}{\thepage}}\lhead[\fancyplain{}{\thepage}]{\fancyplain{}{\textbf{#1}}}}
-\newcommand{\defaultheaders}{\rhead[\fancyplain{}{\leftmark}]{\fancyplain{}{\thepage}}\lhead[\fancyplain{}{\thepage}]{\fancyplain{}{\rightmark}}}
-
-\renewcommand{\chaptermark}[1]{\markboth{{\bf \thechapter~#1}}{}}
-\renewcommand{\sectionmark}[1]{\markright{\thesection~#1}}
-\renewcommand{\contentsname}{%
-\protect\setheaders{Table of contents}Table of contents}
-\renewcommand{\bibname}{\protect\setheaders{Bibliography}%
-\protect\RefManCutCommand{BEGINBIBLIO=\thepage}%
-\protect\addcontentsline{toc}{chapter}{Bibliography}Bibliography}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Commands for indexes
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\usepackage{index}
-\makeindex
-
-\newindex{tactic}{tacidx}{tacind}{Tactics Index}
-\newindex{command}{comidx}{comind}{Vernacular Commands Index}
-\newindex{option}{optidx}{optind}{Vernacular Options Index}
-\newindex{error}{erridx}{errind}{Index of Error Messages}
-\renewindex{default}{idx}{ind}{Global Index}
-
-\newcommand{\printrefmanindex}[3]{%
-\cleardoublepage%
-\phantomsection%
-\setheaders{#2}%
-\addcontentsline{toc}{chapter}{#2}%
-\printindex[#1]%
-\cutname{#3}%
-}
-
-\newcommand{\tacindex}[1]{%
-\index{#1@\texttt{#1}}\index[tactic]{#1@\texttt{#1}}}
-\newcommand{\comindex}[1]{%
-\index{#1@\texttt{#1}}\index[command]{#1@\texttt{#1}}}
-\newcommand{\optindex}[1]{%
-\index{#1@\texttt{#1}}\index[option]{#1@\texttt{#1}}}
-\newcommand{\errindex}[1]{\texttt{#1}\index[error]{#1}}
-\newcommand{\errindexbis}[2]{\texttt{#1}\index[error]{#2}}
-\newcommand{\ttindex}[1]{\index{#1@\texttt{#1}}}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% For the Addendum table of contents
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\newcommand{\aauthor}[1]{{\LARGE \bf #1} \bigskip \bigskip \bigskip}
-\newcommand{\atableofcontents}{\section*{Contents}\@starttoc{atoc}}
-\newcommand{\achapter}[1]{
-  \chapter{#1}\addcontentsline{atoc}{chapter}{#1}}
-\newcommand{\asection}[1]{
-  \section{#1}\addcontentsline{atoc}{section}{#1}}
-\newcommand{\asubsection}[1]{
-  \subsection{#1}\addcontentsline{atoc}{subsection}{#1}}
-\newcommand{\asubsubsection}[1]{
-  \subsubsection{#1}\addcontentsline{atoc}{subsubsection}{#1}}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% Reference-Manual.sh is generated to cut the Postscript
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\@starttoc{sh}
-\newwrite\RefManCut@out%
-\immediate\openout\RefManCut@out\jobname.sh
-\newcommand{\RefManCutCommand}[1]{%
-\immediate\write\RefManCut@out{#1}}
-\newcommand{\RefManCutClose}{%
-\immediate\closeout\RefManCut@out}
-
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: "Reference-Manual"
-%%% End: 
diff --git a/doc/refman/index.html b/doc/refman/index.html
deleted file mode 100644
index b937350e6e..0000000000
--- a/doc/refman/index.html
+++ /dev/null
@@ -1,14 +0,0 @@
-<HTML>
-
-<HEAD>
-
-<TITLE>The Coq Proof Assistant Reference Manual</TITLE>
-
-</HEAD>
-
-<FRAMESET ROWS=90%,*>
-  <FRAME SRC="cover.html" NAME="UP">
-  <FRAME SRC="menu.html">
-</FRAMESET>
-
-</HTML>
diff --git a/doc/refman/menu.html b/doc/refman/menu.html
deleted file mode 100644
index 7312ad344c..0000000000
--- a/doc/refman/menu.html
+++ /dev/null
@@ -1,32 +0,0 @@
-<HTML>
-
-<BODY>
-
-<CENTER>
-
-<TABLE BORDER="0" CELLPADDING=10>
-<TR>
-<TD><CENTER><A HREF="cover.html" TARGET="UP"><FONT SIZE=2>Cover page</FONT></A></CENTER></TD>
-<TD><CENTER><A HREF="toc.html" TARGET="UP"><FONT SIZE=2>Table of contents</FONT></A></CENTER></TD>
-<TD><CENTER><A HREF="biblio.html" TARGET="UP"><FONT SIZE=2>
-Bibliography</FONT></A></CENTER></TD>
-<TD><CENTER><A HREF="general-index.html" TARGET="UP"><FONT SIZE=2>
-Global Index
-</FONT></A></CENTER></TD>
-<TD><CENTER><A HREF="tactic-index.html" TARGET="UP"><FONT SIZE=2>
-Tactics Index
-</FONT></A></CENTER></TD>
-<TD><CENTER><A HREF="command-index.html" TARGET="UP"><FONT SIZE=2>
-Vernacular Commands Index
-</FONT></A></CENTER></TD>
-<TD><CENTER><A HREF="option-index.html" TARGET="UP"><FONT SIZE=2>
-Vernacular Options Index
-</FONT></A></CENTER></TD>
-<TD><CENTER><A HREF="error-index.html" TARGET="UP"><FONT SIZE=2>
-Index of Error Messages
-</FONT></A></CENTER></TD>
-</TABLE>
-
-</CENTER>
-
-</BODY></HTML>