Simpson's systems of second order arithmetic turn out to be five in
number; to simplify notation let's denote them A, B, C, D, E.  What
seems to be an empirical observation is that most theorems in
classical analysis "revert" to one of the five systems, meaning of
course that they are equivalent (over A = RCA$_0$) to the defining
property of the system.  

Can this empirical fact be made into a
theorem somehow?  I am thinking of something along the lines of the
classification of finite simple groups, where a consequence of the
classification is the observation that almost all groups fall into
four specific infinite families (the latter observation is of course a precise mathematical statement rather than merely an empirical observation).