$\forall$$T$:Type, $P$:($T$$\rightarrow$Prop), $R_{1}$, $R_{2}$:($T$$\rightarrow$$T$$\rightarrow$Prop).
\\[0ex]when $P$, $R_{1}$ =$>$ $R_{2}$ $\Rightarrow$ $R_{1}$ preserves $P$ $\Rightarrow$ when $P$, $R_{1}$$^{\mbox{\scriptsize $\ast$}}$ =$>$ $R_{2}$$^{\mbox{\scriptsize $\ast$}}$