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\title{An Isabelle/HOL formalisation of Green's Theorem}
\author{Mohammad Abdulaziz and Lawrence C.\ Paulson}
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\begin{abstract}
  We formalise a statement of Green’s theorem---the first formalisation to
  our knowledge---in Isabelle/HOL. The theorem statement that we formalise
  is enough for most applications, especially in physics and
  engineering. Our formalisation is made possible by a novel proof that
  avoids the ubiquitous line integral cancellation argument. This
  eliminates the need to formalise orientations and region boundaries
  explicitly with respect to the outwards-pointing normal vector.
  Instead we appeal to a homological argument about equivalences between
  paths.
\end{abstract}

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\section{Acknowledgements}
Paulson was supported by the ERC Advanced Grant ALEXANDRIA (Project 742178) funded by the European Research Council
at the University of Cambridge, UK.

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