Is is true that $(1-\lambda)^p\leq1-\lambda^p$ for all $\lambda\in [0,1]$ and $p\in (0,1)$? For all $\lambda\in\Bbb{R}$, $0\leq\lambda\leq1$ and $0<p<1$, $p\in\Bbb{R}$ is the following true?  $$(1-\lambda)^p\leq1-\lambda^p$$

$$(1-\lambda)^p > 1-\lambda$$ and $$\lambda^p > \lambda$$
so their sum is bigger than $1$
