working on quals.  set up everything to not be quotiented, and take properness explicitly.  (aside: properness is required in lots of places, but in particular, in stating what a galois connection means over the function space.  in order to do this, you must define a partial order over the function space, which is not reflexive in Coq, and you need to use a partial equivalence relation if you want to make things work.  an alternative approach is, instead of having a partial equivalence relation over coq functions, have a true equivalence relation over quotiented coq functions that know about their 'properness'.)  this change was motivated by the fact that i need another quotient in addition to the standard properness quotient, i need to quotient over monotonic functions as well (because galois connections are only generalizable to the monotonic function space).  hence, i'm throwing out all the weak equalities and equivalences and baking in reflexive relations over quotiented types.