Generic mathematical macros

maths.sty

\RequirePackage{xparse}
\RequirePackage{mathtools}
\RequirePackage{jmsdelim}

%% Defining equality and equivalence
\NewDocumentCommand{\defeq}{}{\stackrel{\mathclap{\mbox{\tiny def}}}{=}}
\newcommand{\defequiv}{\stackrel{\mathclap{\mbox{\tiny def}}}{\equiv}}

%% Some bracket shorthands
\NewDocumentCommand{\prn}{m}{\DelimPrn{#1}}
\NewDocumentCommand{\brc}{m}{\DelimBrc{#1}}
\NewDocumentCommand{\brk}{m}{\DelimBrk{#1}}
\NewDocumentCommand{\gls}{m}{\DelimGl{#1}}
\NewDocumentCommand{\sem}{m}{\DelimBbrk{#1}}

%% Sets
\NewDocumentCommand{\FinSub}{}{\subseteq_\text{fin}}
\NewDocumentCommand{\SetComp}{mm}{\DelimBetweenSurround{\lbrace}{\vert}{\rbrace}{#1}{#2}}
\NewDocumentCommand{\Powerset}{so}{
  \mathcal{P}\IfNoValueTF{#2}{}{
    \IfBooleanTF{#1}{\DelimPrn{#2}}{#2}
  }
}

%% Functions
\NewDocumentCommand{\FunctionSet}{smm}{
  \IfBooleanTF{#1}{\DelimPrn{#2 \to #3}}{#2 \to #3}
}
\NewDocumentCommand{\Surj}{}{\twoheadrightarrow}
\NewDocumentCommand{\Image}{sm}{
  \IfBooleanTF{#1}{\mathop{\text{im}}\DelimPrn{#2}}{\mathop{\text{im}} #2}
}
\NewDocumentCommand{\DepFun}{mmm}{\DelimPrn{#1 : #2} \to #3}

%% Lists
\NewDocumentCommand{\List}{sm}{\SuperscriptS{#1}{#2}{\ast}}
\NewDocumentCommand{\FinInfList}{sm}{\SuperscriptS{#1}{#2}{\infty}}
\NewDocumentCommand{\ListBrk}{m}{\DelimBrk{#1}}
\NewDocumentCommand{\ListComp}{mm}{\DelimBetweenSurround{[}{\vert}{]}{#1}{#2}}
\NewDocumentCommand{\EmptyList}{}{[\,]}
\NewDocumentCommand{\ConsList}{mm}{#1{:}#2}
\NewDocumentCommand{\ConcatOp}{}{\mathrel{+\!\!+}}