  We report on our experience formalizing differential geometry with mathlib,
the Lean mathematical library. Our account is geared towards geometers with no
knowledge of type theory, but eager to learn more about the formalization of
mathematics and maybe curious enough to give Lean a try in the future. To this
effect, we stress the possibly surprising difference between the formalization
and its pen-and-paper counterpart arising from Lean's treatment of equality.
Our three case studies are Lie groups, vector bundles and the Lie algebra of a
Lie group.
