Define a function $\phi$ on $\mathbb{R}$ by $\phi(x) = |x|$ for $x\in [-1,1]$ and $\phi(x+2)=\phi(x)$ for all $x\in \mathbb{R}$. Show $|\phi(t) - \phi(s)|\leq |t-s|$.
Attempt: for $x\in \mathbb{R}$, $\phi(x)$ = $\bigg\{\begin{array}{cc} |-1 + \{x\}| \ \text{,if} \ [x]=1 (\mod2) \\ \{x\}\ \ , \text{if}\ \ [x] = 0(\mod 2)\end{array}$
where $\{x\}$ is the fractional part of $x$ and $[x]$ is the greatest integer of $x$.
can't proceed further