Formal methods aren't as widespread in safety critical industries as you might hope or believe. Model-based testing is still considered cutting edge, never mind formal verification.

Formal verification is only as good as your model, anyway. Problem comes from outside your model? Formal verification won't save you.

My father-in-law works on control systems for airplanes and I get the impression that it's based much more on testing in flight simulators than on any amount of proofs.

The level he works at might be higher level though. It sounds like control systems for airplanes are fairly modular.

If it is possible to use proof that is lovely; but it isn't necessary. Things have been engineered to very high levels of reliability with only the most tangential reliance on proofs.

Software is highly unusual in that proofs can even be deployed. Most highly safe processes can't even use proofs. How do you prove that a dam won't fail? It is impossible.

Sure because the alternative is death

Me shit posting is not a life or death situation so a bug here or there is fine

The bolts don't, and yet they don't (usually) fail.