% Macros
% ======

% This is a collection of commonly used synonyms for notions hard-coded into
% Naproche. It is intended to be imported to other ForTheL files to provide
% these synonyms for them, rather that being considered as a stand-alone file.


\begin{forthel}
  % Equality
  % --------

  Let $x$ and $y$ agree stand for $x = y$.
  Let $x$ agrees with $y$ stand for $x = y$.
  Let $x$ and $y$ are distinct stand for $x \neq y$.

  % Elementhood relation
  % --------------------

  Let a member of $X$ stand for an element of $X$.
  Let $x$ belongs to $X$ stand for $x$ is an element of $X$.
  Let $X$ contains $x$ stand for $x$ is an element of $X$.
  Let $x$ is contained in $X$ stand for $x$ is an element of $X$.
  Let $x$ lies in $X$ stand for $x$ is an element of $X$.
  Let $x$ is in $X$ stand for $x$ is an element of $X$.

  % Domain
  % ------

  Let the domain of $f$ stand for $\dom(f)$.
  Let $f$ is defined on $X$ stand for $\dom(f) = X$.

  % Map application
  % ---------------

  Let the value of $f$ at $x$ stand for $f(x)$.
  Let $f(x,y)$ stand for $f((x,y))$.
\end{forthel}
