There are shades between full formal verification of literally everything and then "trust the elders". You can know a little bit about a lot and use that as a sort of statistical verification because you're basically running a monte carlo sim to find holes in the logic, if you find no holes then you can reasonably assume that the rest is true and that's not based on trust.
It's a bit like having a 500-dimensional jigsaw puzzle, once you show that most of the pieces fit together the other ones have nowhere to go any more except to fit.
There are shades between full formal verification of literally everything and then "trust the elders". You can know a little bit about a lot and use that as a sort of statistical verification because you're basically running a monte carlo sim to find holes in the logic, if you find no holes then you can reasonably assume that the rest is true and that's not based on trust.
It's a bit like having a 500-dimensional jigsaw puzzle, once you show that most of the pieces fit together the other ones have nowhere to go any more except to fit.