\section{Soundness Proof} \label{sec:soundness-proof} This section contains proof of soundness of the VEIN framework, which is organized in mathematical definitions (\textbf{\Cref{sec:mathematical-definitions}}), proof of the translation layer (\textbf{\Cref{sec:soundness-of-translation}}), proof of the interaction rules (\textbf{\Cref{sec:soundness-of-interaction-rules}}) and the final induction proof (\textbf{\Cref{sec:soundness-of-reduction}}). \input{chapters/core/soundness-proof/01-mathematical-definitions} \input{chapters/core/soundness-proof/02-soundness-of-translation} \input{chapters/core/soundness-proof/03-soundness-of-interaction-rules} \input{chapters/core/soundness-proof/04-soundness-of-reduction}