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