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authorherbelin2009-05-20 14:07:14 +0000
committerherbelin2009-05-20 14:07:14 +0000
commit8a6e3f648fa3171e3583e7c93c8967ac853a0d60 (patch)
tree835f86f9c226e91b3f0be73342faa08fd1d4d755 /doc
parent18d4283e4129f6f347970c76d209817f1f66f232 (diff)
- Fixing declarative mode in presence of high use of Change_evars nodes
(bug 2092 and decl_mode.v in test suite). - Added a debugging printer for pftreestate. - Fixing American spelling in RefMan-decl.tex. - Optimizing application of tactic validation by removing consistency test in descend. - Fixing printing ambiguity for Hint Rewrite ->/<- in extratactics.ml4. git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12134 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'doc')
-rw-r--r--doc/refman/RefMan-decl.tex33
1 files changed, 16 insertions, 17 deletions
diff --git a/doc/refman/RefMan-decl.tex b/doc/refman/RefMan-decl.tex
index b5684f929a..ba8a5ac635 100644
--- a/doc/refman/RefMan-decl.tex
+++ b/doc/refman/RefMan-decl.tex
@@ -35,7 +35,7 @@ proofs. Well-formed proofs are actually proof script where only the
reasoning is incomplete. All the other aspects of the proof are
correct:
\begin{itemize}
-\item All objects refered to exist where they are used
+\item All objects referred to exist where they are used
\item Conclusion steps actually prove something related to the
conclusion of the theorem (the {\tt thesis}.
\item Hypothesis introduction steps are done when the goal is an
@@ -50,7 +50,7 @@ correct:
This section explain what differences the casual Coq user will
experience using the \DPL .
\begin{enumerate}
-\item The focussing mechanism is constrained so that only one goal at
+\item The focusing mechanism is constrained so that only one goal at
a time is visible.
\item Giving a statement that Coq cannot prove does not produce an
error, only a warning: this allows to go on with the proof and fill
@@ -133,7 +133,7 @@ Conventions:\begin{itemize}
\subsection{Temporary names}
-In proof commands where an optional name is asked for, ommiting the
+In proof commands where an optional name is asked for, omitting the
name will trigger the creation of a fresh temporary name (e.g. for a
hypothesis). Temporary names always start with an undescore '\_'
character (e.g. {\tt \_hyp0}). Temporary names have a lifespan of one
@@ -143,8 +143,7 @@ command: they get erased after the next command. They can however be safely in t
\subsection{Starting and Ending a mathematical proof}
-
- The standard way to use the \DPL is to first state a {\texttt{Lemma/Theorem/Definition}} and then use the {\texttt{proof}} command to switch the current subgoal to mathematical mode. After the proof is completed, the {\texttt{end proof}} command will close the mathematical proof. If any subgoal remains to be proven, they will be displayed using the usual Coq display.
+ The standard way to use the \DPL is to first state a {\texttt{Lemma/Theorem/Definition}} and then use the {\texttt{proof}} command to switch the current subgoal to mathematical mode. After the proof is completed, the {\texttt{end proof}} command will close the mathematical proof. If any subgoal remains to be proved, they will be displayed using the usual Coq display.
\begin{coq_example}
Theorem this_is_trivial: True.
@@ -178,7 +177,7 @@ Abort.
As with all other block structures, the {\texttt{end proof}} command
assumes that your proof is complete. If not, executing it will be
-equivalent to admitting that tehe statement is proven: A warning will
+equivalent to admitting that the statement is proved: A warning will
be issued and you will not be able to run the {\texttt{Qed}}
command. Instead, you can run {\texttt{Admitted}} if you wish to start
another theorem and come back
@@ -348,7 +347,7 @@ conclusion step & {\tt thus} & {\tt hence} &
{\tt focus on} & {\tt thus $\sim$=/=$\sim$}\\
\hline
\end{tabular}
-\caption{Correspondance between basic forward steps and conclusion steps}
+\caption{Correspondence between basic forward steps and conclusion steps}
\end{figure}
Let us begin with simple examples :
@@ -462,7 +461,7 @@ hence (P 2).
Abort.
\end{coq_eval}
-Here a more involved exmaple where the choice of {\tt P 2} propagates
+Here a more involved example where the choice of {\tt P 2} propagates
the choice of {\tt 2} to another part of the formula.
\begin{coq_eval}
@@ -534,10 +533,10 @@ Abort.
\subsection{Introduction steps}
-When the {\tt thesis} consists of a hypothestical formula (implication
+When the {\tt thesis} consists of a hypothetical formula (implication
or universal quantification (e.g. \verb+A -> B+) , it is possible to
-assume the hypotetical part {\tt A} and then prove {\tt B}. In the
-\DPL{}, this comes in two syntactic flavours that are semantically
+assume the hypothetical part {\tt A} and then prove {\tt B}. In the
+\DPL{}, this comes in two syntactic flavors that are semantically
equivalent : {\tt let} and {\tt assume}. Their syntax is designed so that {\tt let} works better for universal quantifiers and {\tt assume} for implications.
\begin{coq_eval}
@@ -554,7 +553,7 @@ assume HP:(P x).
Abort.
\end{coq_eval}
-In the {\tt let} variant, the type of the assumed objet is optional
+In the {\tt let} variant, the type of the assumed object is optional
provided it can be deduced from the command. The objects introduced by
let can be followed by assumptions using {\tt such that}.
@@ -572,7 +571,7 @@ let x be such that HP:(P x). (* here x's type is inferred from (P x) *)
Abort.
\end{coq_eval}
-In the {\tt assume } variant, the type of the assumed objet is mandatory but the name is optional :
+In the {\tt assume } variant, the type of the assumed object is mandatory but the name is optional :
\begin{coq_eval}
Theorem T: forall (P:nat -> Prop), forall x, P x -> P x -> P x.
@@ -606,8 +605,8 @@ Abort.
\subsection{Tuple elimination steps}
In the \CIC, many objects dealt with in simple proofs are tuples :
-pairs , records, existentially quantified formulae. These are so
-comman that the \DPL{} provides a mechanism to extract members of
+pairs , records, existentially quantified formulas. These are so
+common that the \DPL{} provides a mechanism to extract members of
those tuples, and also objects in tuples within tuples within
tuples...
@@ -735,7 +734,7 @@ End Coq.
If the object on which a case analysis occurs in the statement to be
proved, the command {\tt suppose it is }\emph{pattern} is better
suited than {\tt suppose}. \emph{pattern} may contain nested patterns
-with {\tt as} clauses. A detailled description of patterns is to be
+with {\tt as} clauses. A detailed description of patterns is to be
found in figure \ref{term-syntax-aux}. here is an example.
\begin{coq_eval}
@@ -793,7 +792,7 @@ language justifications are made of two components:
Justification objects : {\texttt{by}} followed by a comma-{}separated
list of objects that will be used by a selected tactic to prove the
statement. This defaults to the empty list (the statement should then
-be tautological). The * wildcard provides the usual tactics behaviour:
+be tautological). The * wildcard provides the usual tactics behavior:
use all statements in local context. However, this wildcard should be
avoided since it reduces the robustness of the script.