> Lean can prove that "2 + 2 = 5" is not an unprovable truth
> By simply proving that NOT(2 + 2 = 5) is true (inhabited, technically, for category folks)
.
This is a pretty good distillation of proof theory's unique selling point. It's easy to replace the expression inside the quotes with any first-order sentence and get provability data with just an arbitrary pile of other constructions, since you can get computers to iterate over them. But where is the article showing that Lean is a good implementation of formal proof assistant in comparison to the other options, like Coq or HoTT?
> Lean can prove that "2 + 2 = 5" is not an unprovable truth
> By simply proving that NOT(2 + 2 = 5) is true (inhabited, technically, for category folks)
.
This is a pretty good distillation of proof theory's unique selling point. It's easy to replace the expression inside the quotes with any first-order sentence and get provability data with just an arbitrary pile of other constructions, since you can get computers to iterate over them. But where is the article showing that Lean is a good implementation of formal proof assistant in comparison to the other options, like Coq or HoTT?