$\forall$$A_{1}$, $A_{2}$:Type, $B_{1}$:($A_{1}$$\rightarrow$Type), $B_{2}$:($A_{2}$$\rightarrow$Type).
\\[0ex]strong{-}subtype($A_{1}$;$A_{2}$) $\Rightarrow$ ($\forall$$a$:$A_{1}$. $B_{1}$($a$) $\subseteq\rho$ $B_{2}$($a$)) $\Rightarrow$ $a$:$A_{1}$ fp$\rightarrow$ $B_{1}$($a$) $\subseteq\rho$ $a$:$A_{2}$ fp$\rightarrow$ $B_{2}$($a$)