  We investigate the lower bound of the consistency strength of $\mathsf{CZF}$
with Full Separation $\mathsf{Sep}$ and a Reinhardt set, a constructive
analogue of Reinhardt cardinals. We show that $\mathsf{CZF+Sep}$ with a
Reinhardt set interprets $\mathsf{ZF^-}$ with a cofinal elementary embedding
$j\colon V\prec V$. We also see that $\mathsf{CZF+Sep}$ with a Reinhardt set
interprets $\mathsf{ZF^-}$ with a model of $\mathsf{ZF+WA_0}$, the Wholeness
axiom for bounded formulas.
