\paragraph{Semantic equivalence}
\inlinedefinition Two statements $s_1$ and $s_2$ are \bi{semantically equivalent}, denoted $s_1 \simeq s_2$, if and only if
\[
    \forall \sigma, \sigma' . (\vdash \langle s_1, \sigma \rangle \rightarrow \sigma' \Longleftrightarrow \; \vdash \langle s_2, \sigma \rangle \rightarrow \sigma')
\]
