In Munkres' Analysis on Manifolds, page 57 Theorem 7.1(the Chain Rule) it states: ...For this purpose, let us introduce the function $F(\mathbf h)$ defined by setting $F(\mathbf 0)=\mathbf 0$ and \begin{equation*} F(\mathbf h)=\frac{[\Delta(\mathbf h)-Df(\mathbf a)\cdot \mathbf h]}{|\mathbf h|} for \ 0<|\mathbf h|<\delta. \end{equation*} ...Further more, one has the equation \begin{equation*} \Delta(\mathbf h)=Df(\mathbf a)\cdot \mathbf h +|\mathbf h|F(\mathbf h) \end{equation*} for $0<|\mathbf h|<\delta$, and also for $\mathbf h=0$ (trivially). The triangle inequality implies that \begin{equation*} |\Delta (\mathbf h)|\leq m|Df(\mathbf a)|\cdot|\mathbf h|+|\mathbf h|\cdot|F(\mathbf h)|. \end{equation*}
I'm confused about $|\Delta (\mathbf h)|\leq m|Df(\mathbf a)|\cdot|\mathbf h|+|\mathbf h|\cdot|F(\mathbf h)|$. Where does this "$m$" come from? I think it should be $|\Delta (\mathbf h)|\leq |Df(\mathbf a)|\cdot|\mathbf h|+|\mathbf h|\cdot|F(\mathbf h)|$.
This a question from Munkres' Analysis on Manifolds. I show you the whole context of the question below. I have trouble understanding the statement with red line.