Analogues of Grün's lemma and Baer's theorem for skew left braces

We prove in this paper some analogues of the well-known group-theoretical Grün's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theorem, stating that if the quotient by the $n$th centre of a group is finite, then so is the $(n+1)$th term of the lower cent