I mean to ask both: "checking whether X is true and crashing the program if not", like the assert macro, OR assert as in a weaker check that does not crash the program (such as generate a log event).

When crashing the program is acceptable and correctness preconditions can be efficiently checked, postconditions usually can be too.

What's interesting to me is the combination of two claims: formal verification is used when crashes are not acceptable, and crashing when formal assumptions are violated is therefore not acceptable. This makes sense on the surface - but the program is only proven crashproof when the formal assumptions hold. That is all formal verification proves.