In the article [_A free group functor for stable homotopy theory_](http://www.sciencedirect.com/science/article/pii/0040938374900366), Barratt and Eccles define for each $X\in\mathsf{sSet}_{\ast}$, the free simplicial monoid $\Gamma^{+}X$. 

Proposition 6.2 states 

>if $X$ is a $(n-1)$-connected pointed Kan complex, then $H_{i}(\Gamma^{+}X,X)=0$ for $i<2n$

My doubt starts when it is defined the quotient $\mathscr{D}=\Gamma^{+}_{p}X/\Gamma^{+}_{p-1}X$ and the following is asserted: 
>if $X$ is a $(n-1)$-connected, $\mathscr{D}_{p}X$ is clearly $(np-1)$-connected. 

Actually, it is not clear for me. Could anybody help me to conclude this last assertion? thanks in advance.