  Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive
languages that allow the formalization of general mathematical objects and
proofs. In this context, an important goal is to reduce the time and effort
needed to prove theorems. A significant means of achieving this is by improving
proof automation. We have implemented an early prototype of proof automation
for equational reasoning in Lean by using equality saturation. To achieve this,
we need to bridge the gap between Lean's expression semantics and the
syntactically driven e-graphs in equality saturation. This involves handling
bound variables, implicit typing, as well as Lean's definitional equality,
which is more general than syntactic equality and involves notions like
$\alpha$-equivalence, $\beta$-reduction, and $\eta$-reduction. In this extended
abstract, we highlight how we attempt to bridge this gap, and which challenges
remain to be solved. Notably, while our techniques are partially unsound, the
resulting proof automation remains sound by virtue of Lean's proof checking.
