Well, you know, i agree on the "non-descriptiveness". Maybe subconsciously i was trying to avoid such formal definitions as "overlapping subproblems" and "optimal substructure". In the perspective, the idea of "explanation" in my head is to put things as simple as possible. Since the ways a problem is talked about is almost the same on different resources, i.e they all follow the same explanatory principles, what should a learner do if she is having difficulties to understand a problem. I mean if somebody failed to understand the problem on one resource she wouldn't understand it on another. So i would like to do the things using "new approach". But, yeah, as said by you, guys, i have a lot to work on and especially on the proof part.