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Let $t_1:M_1\overset{m_1,p_1}{\Rightarrow} N_1$ and $t_2:M_2\overset{m_2,p_2}{\Rightarrow} N_2$ be two transitions in a trace $\theta:t_1;t_1':t_2';\cdots t_n';t_2$ and let $p_1:L_1{\remb} D_1 {\lemb} R_1$ and $p_2:L_2{\remb} D_2 {\lemb} R_2$ be two corresponding rules. The morphism $M_1\pmorph M_2$ is the composition of $\spo(t_1)\circ\spo(t_1')\circ\dots\spo(t_n')$.
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\begin{description}
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\item[high res inhibition]
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Let the span $\spa:L_1\remb O\lemb L_2$ be the pullback of the cospan $L_1{\lemb}M{\remb}L_2$ in the multisum of $L_1$ and $L_2$ such that $p_1\redl{-}_{\spa} p_2$. If the diagram commutes
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Let the span $\spa:L_1\remb O\lemb L_2$ be the pullback of the cospan $L_1{\lemb}M{\remb}L_2$ in the multisum of $L_1$ and $L_2$ such that $p_2\redl{-}_{\spa} p_1$. If the diagram commutes
Let $\sim$ be a binary relation on transitions such that $t_1\sim t_1'$ iff there exists $t_2$, $t_1\Diamond_{\text{par}} t_2$ and $t_1' = t_1/t_2$.
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Let $\sim$ be a binary relation on transitions such that $t_1\sim t_1'$ iff there exists $t_2$, $t_1\Diamond_{\text{par}} t_2$ and $t_1' = t_1/t_2$. We denote $\simeq$ the transitive and reflexive closure of $\sim$.
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%% \begin{itemize}
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%% \item there exists $t_2$, $t_2;t_1$, $\neg(t_2<t_2)$, $\neg(t_2\Diamond_{\text{seq}}t_1)$ and $t_1=t_1|t_2$.
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