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However, the first equation is derivable from the second and third However, the first equation is derivable from the second and third
equations. I first learned this from Paul{-}Andr{\'{e}} Melli{\`{e}}s equations. I first learned this from Paul{-}Andr{\'{e}} Melli{\`{e}}s
during Shonan Seminar No.103 \emph{Semantics of Effects, Resources, during Shonan Seminar No.103 \emph{Semantics of Effects, Resources,
and Applications}. I have been unable to find a proof of this fact and Applications}. I have been unable to find a proof of this fact in
in the literature, though, \citeauthor{Mellies14} does have published the literature, though, \citeauthor{Mellies14} does have a published
paper, which only states the three necessary paper, which states only the three necessary
equations~\cite{Mellies14}. equations~\cite{Mellies14}.
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Therefore I include a proof of this fact here (thanks to Sam Lindley Therefore I include a proof of this fact here (thanks to Sam Lindley