Maybe you'll find this example to be a bit more useful: https://blog.adacore.com/i-cant-believe-that-i-can-prove-tha...

The idea is that you define a number of pre- and post- condition predicates for a function that you want proved (in what's effectively the header file of your Ada program). Like with tests, these checks that show that the output is correct are often shorter than the function body, as in this sorting example.

Then you implement your function body and the prover attempts to verify that your post-conditions hold given the pre-conditions. Along the way it tries to check other stuff like overflows, whether the pre- and post- conditions of the routines called inside are satisfied, etc. So you can use the prover to try to ensure in compile-time that any properties that you care about in your program are satisfied that you may otherwise catch in run-time via assertions.