Let $(X,d)$ be a metric space. We say $(X,d)$ is Lipschitz injective if $\forall$ metric spaces $(Y,\rho)$ and $Z\subset Y$ and any Lipschitz map $f:Z \rightarrow X$, we have an extension of $f$ to Lipschitz map $F: Y \rightarrow X$ s.t. $F\_{|Z}=f$.

Further, if there exists $p>0$ such that, $L.C(F)\leq L.C(f)$ for all such functions, then $(X,d)$ is called $p-$ Lipschitz injective.(where L.C(f) is the Lipschitz constant of f)

The objective is to show that $(R, usual)$ is 1-Lipschitz injective.