Simple property of arrow notation 
Assume that $\kappa \to (\lambda)^r_s$ holds.
Prove that if $r'\le r$, $\kappa \to (\lambda)^{r'}_s$

I proved similar cases like when $s'\le s$ etc. but I have no idea about this case.
Actually I can't understand why that statment has to be true.
Any help or suggestion is welcome!

Given a coloring of the $r'$-sets, define a coloring of the $r$-sets as follows. If $x_1\lt x_2\lt\cdots\lt x_r$, give $\{x_1,\dots,x_r\}$ the same color as $\{x_{r-r'+1},\dots,x_r\}$; i.e., a set of size $r$ gets the same color as the set of its $r'$ biggest elements.
Suppose $H$ is a monochromatic set for the new coloring. If we drop the first $r-r'$ elements from $H$, we get a monochromatic set $H'$ for the original coloring, and $H'$ is as big as $H$ assuming $\lambda\ge\omega$.
