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