$\forall$$T$:Type, $L$:$T$ List, $R$:($\mathbb{N}$$_{\mbox{\scriptsize $<\parallel$$L$$\parallel$}}$$\rightarrow\mathbb{N}$$_{\mbox{\scriptsize $<\parallel$$L$$\parallel$}}$$\rightarrow$Prop), $P_{1}$, $P_{2}$, $P_{3}$:($\mathbb{N}$$_{\mbox{\scriptsize $<\parallel$$L$$\parallel$}}$$\rightarrow$Prop).
\\[0ex](Trans $1$,$2$:$\mathbb{N}$$_{\mbox{\scriptsize $<\parallel$$L$$\parallel$}}$. $R$($1$,$2$))
\\[0ex]$\Rightarrow$ causal\_order($L$;$R$;$P_{1}$;$P_{2}$)
\\[0ex]$\Rightarrow$ causal\_order($L$;$R$;$P_{1}$;$P_{3}$)
\\[0ex]$\Rightarrow$ causal\_order($L$;$R$;$P_{1}$;$\lambda$$i$.$P_{2}$($i$) $\vee$ $P_{3}$($i$))