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\title{Substitutions for $\lambda$-free higher-order terms}
\author{Vincent Trélat}

\begin{document}

\maketitle

\begin{abstract}
  \looseness=-1
  This theory provides a formalization of substitutions on $\lambda$-free higher-order terms,
  establishing a structured framework with the expected algebraic properties.
  It introduces a type construction for the rigorous definition and manipulation of substitutions.
  The main theorem of this theory proves the existence of fixed-point substitutions under acyclicity,
  a theorem that is too often regarded as trivial in the literature~\cite{BarbosaFR17,TourretFOB20}.
\end{abstract}

\tableofcontents
\pagebreak

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