Automatically created functions:

  ty1_tyn.bn[simp]        lifted equations for bn funs
  ty1_tyn.fv[simp]        lifted equations for fv funs
  ty1_tyn.perm[simp]      lifted permutation equations
  ty1_tyn.distinct[simp]  lifted distincts
  ty1_tyn.eq_iff
  ty1_tyn.induct
  ty1_tyn.inducts
  instance ty1 and tyn :: fs
  ty1_tyn.supp            empty when for too many bindings

Smaller things:

- lam.perm should be called permute_lam.simps (that is 
  the convention from Nominal2)

- maybe <type>_perm whould be called permute_<type>.simps;
  that would conform with the terminology in Nominal2

- we also need to lift the size function for nominal
  datatypes

- Abs.thy contains lemmas for equivariance of the alphas;
  they are not yet used anywhere

Bigger things:

- Parser adds syntax for raw datatype, but should
  add for lifted datatype.

- the alpha equivalence for

   Let as::assn t::trm   bind "bn as" in t

  creates as premise

    EX pi. as ~~bn as' /\ (bn as, t) ~~lst (bn as', t')

  but I think it should be

    as ~~bn as' /\ EX pi. (bn as, t) ~~lst (bn as', t')    

  (both are equivalent, but the second seems to be closer to
   the fv-function)

- when there are more than one shallow binder, then alpha
  equivalence creates more than one permutation. According
  to the paper, this is incorrect.

  Example in Classical.thy.

- check whether weirdo example in TestMorePerm works
  with shallow binders

- nested recursion, like types "trm list" in a constructor

- define permute_bn automatically and prove properties of it

- prove renaming-of-binders lemmas

- strong induction rules

- check support equations for more bindings per constructor

- For binding functions that call other binding functions
  the following are proved with cheat_tac: constr_rsp

- store information about defined nominal datatypes, so that
  it can be used to define new types that depend on these

- make parser aware of recursive and of different versions of abs

Less important:

- fv_rsp uses 'blast' to show goals of the type:
  a u b = c u d   ==>  a u x u b = c u x u d

When cleaning:

- remove all 'PolyML.makestring'.