Proving that the program has no bugs is akin to proving that the program won't make you feel sad. Like ... I'm not sure we have the math.
One of the more important jobs of the software engineer is to look deep into your customer's dreams and determine how those dreams will ultimately make your customer sad unless there's some sort of intervention before you finish the implementation.
What actually would solve the customer's problem -> What the customer thinks they want -> What they communicate that they want -> What the requirements collector hears -> What the requirements collector documents -> How the implementor interprets the requirements -> What the implementor designs/plans -> What the implementor implements.
Formal proofs can help with the last 3 steps. But again that's assuming the implementor can formalize every requirement they interpreted. And that's impossible as well, there will always be implicit assumptions about the running environment, performance, scale, the behavior of dependent processes/APIs.
It helps with a small set of possible problems. If those problems are mission-critical then absolutely tackle them, but there will never be a situation where it can help with the first 5 steps of the problem, or with the implicit items in the 6th step above.
You can formally prove that it doesn't have certain kinds of bugs. And that's good! But it also is an enormous amount of work. And so, even for life-critical software, the vast majority is not formally proven, because we want more software than we can afford to formally prove.