A generalized form
It simply states that any process which has a populations of interactors that replicate, and the replication is causally correlated with interactive traits.
In other terms, a group that reproduces based on characteristics of those individuals.
This process has been demonstrated to actually work, as it has been used in various environments for various methods, yielding expected results. Genetic algorithms, for example, use this process to yield algorithms that successfully fit the desired result. Other computer software has also used the process to "evolve" interactors that are better fit - for example, one program pitted two generated "creatures" against each other in an arena, with the goal to reach and control an object in the middle. Even with starting out with simple basic "creatures", the Darwinian process eventually yielded fancy, complex "creatures" much better adapted to the task than the original ones.
Note that showing the the Darwinian process works as stated doesn't mean that evolution had to occur - just that it is not impossible for it to have happened.