Unfortunately it is difficult to "prove" this definitively currently, until someone comes up with a "complexity polynomial metric over time" for code, except to talk to old programmers like myself (44) who have done this for a long while and gotten disillusioned due to all the time spent repairing OO complexity/tech debt bugs, and have become entranced by functional langs and the way they avoid inheritance, use immutable values and are super careful with state, all of which contributes to better long term code life
Fortunately I'm not the only old OO guy proclaiming this, I have John Carmack on my side:
http://www.gamasutra.com/view/news/169296/Indepth_Functional...
"My pragmatic summary: A large fraction of the flaws in software development are due to programmers not fully understanding all the possible states their code may execute in. In a multithreaded environment, the lack of understanding and the resulting problems are greatly amplified, almost to the point of panic if you are paying attention. Programming in a functional style makes the state presented to your code explicit, which makes it much easier to reason about, and, in a completely pure system, makes thread race conditions impossible."
"No matter what language you work in, programming in a functional style provides benefits. You should do it whenever it is convenient, and you should think hard about the decision when it isn't convenient."