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Fix typo in 'arithmetic'

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Clément Pit--Claudel 2016-02-03 18:12:06 -05:00
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@ -508,7 +508,7 @@ Note that many of these are specific to the \texttt{Frap} library distributed wi
\item[\texttt{f\_equal}] When the goal is an equality between two applications of the same function, switch to proving that the function arguments are pairwise equal. \item[\texttt{f\_equal}] When the goal is an equality between two applications of the same function, switch to proving that the function arguments are pairwise equal.
\item[\texttt{induct} $x$] Where $x$ is a variable in the theorem statement, structure the proof by induction on the structure of $x$. You will get one generated subgoal per constructor in the inductive definition of $x$. (Indeed, it is required that $x$'s type was introduced with \texttt{Inductive}.) \item[\texttt{induct} $x$] Where $x$ is a variable in the theorem statement, structure the proof by induction on the structure of $x$. You will get one generated subgoal per constructor in the inductive definition of $x$. (Indeed, it is required that $x$'s type was introduced with \texttt{Inductive}.)
\item[\texttt{invert} $H$] Replace hypothesis $H$ with other facts that can be deduced from the structure of $H$'s statement. More detail to be added here soon! \item[\texttt{invert} $H$] Replace hypothesis $H$ with other facts that can be deduced from the structure of $H$'s statement. More detail to be added here soon!
\item[\texttt{linear\_arithemtic}] A complete decision procedure for linear arithmetic. Relevant formulas are essentially those built up from variables and constant natural numbers and integers using only addition and subtraction, with equality and inequality comparisons on top. (Multiplication by constants is supported, as a shorthand for repeated addition.) See Section \ref{decidable}. \item[\texttt{linear\_arithmetic}] A complete decision procedure for linear arithmetic. Relevant formulas are essentially those built up from variables and constant natural numbers and integers using only addition and subtraction, with equality and inequality comparisons on top. (Multiplication by constants is supported, as a shorthand for repeated addition.) See Section \ref{decidable}.
\item[\texttt{rewrite} $H$] Where $H$ is a hypothesis or previously proved theorem, establishing \texttt{forall x1 .. xN, e1 = e2}, find a subterm of the goal that equals \texttt{e1}, given the right choices of \texttt{xi} values, and replace that subterm with \texttt{e2}. \item[\texttt{rewrite} $H$] Where $H$ is a hypothesis or previously proved theorem, establishing \texttt{forall x1 .. xN, e1 = e2}, find a subterm of the goal that equals \texttt{e1}, given the right choices of \texttt{xi} values, and replace that subterm with \texttt{e2}.
\item[\texttt{ring}] Prove goals that are equalities over some registered ring or semiring, in the sense of algebra, where the goal follows solely from the axioms of that algebraic structure. See Section \ref{decidable}. \item[\texttt{ring}] Prove goals that are equalities over some registered ring or semiring, in the sense of algebra, where the goal follows solely from the axioms of that algebraic structure. See Section \ref{decidable}.
\item[\texttt{simplify}] Simplify throughout the goal, applying the definitions of recursive functions directly. That is, when a subterm matches one of the \texttt{match} cases in a defining \texttt{Fixpoint}, replace with the body of that case, then repeat. \item[\texttt{simplify}] Simplify throughout the goal, applying the definitions of recursive functions directly. That is, when a subterm matches one of the \texttt{match} cases in a defining \texttt{Fixpoint}, replace with the body of that case, then repeat.