Type-checking time at QED should not be slower than evaluating the tactics building the proof. A typical cause of being slower (and even exponentially slower) is that the type-checker does not preserve the history of reduction steps used in the proof (unfold
, simpl
, …) and try to recheck from scratch why two terms are convertible (see e.g. this typical example of long Qed
: "Qed." takes a long time). In principle, it is certainly possible to do something but I don’t know precisely how far some developers are already looking on their free time at this issue or not.