The proof is that humans do it all the time and that you do it inside your head as well. People need to stop with this absurd level of rampant skepticism that makes them doubt their own basic functions.
the concept is too nebulous to "prove" but the fact im operating a machine (relatively) skillfully to write to you shows we are in fact able to generalise. This wasn't planned, we came up with this. Same with cars etc. We're quite good at the whole "tool use" thing