This instance leads to exponential failing searches.

These trees are useful to show that other types are countable.

This patch was created using

  find -name *.v | xargs -L 1 awk -i inplace '{from = 0} /^From/{ from = 1; ever_from = 1} { if (from == 0 && seen == 0 && ever_from == 1) { print "Set Default Proof Using \"Type*\"."; seen = 1 } }1 '

and some minor manual editing

simplify_equality        => simplify_eq
simplify_equality'       => simplify_eq/=
simplify_map_equality    => simplify_map_eq
simplify_map_equality'   => simplify_map_eq/=
simplify_option_equality => simplify_option_eq
simplify_list_equality   => simplify_list_eq
f_equal'                 => f_equal/=

The /= suffixes (meaning: do simpl) are inspired by ssreflect.

Also, make our redefinition of done more robust under different
orders of Importing modules.

Also do some minor clean up.

Also, use a different encoding of lists.

The port makes the following notable changes:

* The carrier types of separation algebras and integer environments are no
  longer in Set. Now they have a type at a fixed type level above Set. This
  both works better in 8.5 and makes the formalization more general.
  I have tried putting them at polymorphic type levels, but that increased the
  compilation time by an order of magnitude.
* I am using a custom f_equal tactic written in Ltac to circumvent bug #4069.
  That bug has been fixed, so this custom tactic can be removed when the next
  beta of 8.5 is out.

Major changes:
* Make void a base type, and include a proper void base value. This is necessary
  because expressions (free, functions without return value) can yield a void.
  We now also allow void casts conforming to the C standard.
* Various missing lemmas about typing, weakening, decidability, ...
* The operations "free" and "alloc" now operate on l-values instead of r-values.
  This removes some duplication.
* Improve notations of expressions and statements. Change the presence of the
  operators conforming to the C standard.

Small changes:
* Use the classes "Typed" and "TypeCheck" for validity of indexes in memory.
  This gives more uniform notations.
* New tactic "typed_inversion" performs inversion on an inductive predicate
  of type "Typed" and folds the premises.
* Remove a horrible hack in the definitions of the classes "FMap", "MBind",
  "OMap", "Alter" that was used to let "simpl" behave better. Instead, we have
  defined a tactic "csimpl" that folds the results after performing an
  ordinary "simpl".
* Fast operation to remove duplicates from lists using hashsets.
* Make various type constructors (mainly finite map implementations) universe
  polymorphic by packing them into an inductive. This way, the whole C syntax
  can live in type, avoiding the need for (slow) universe checks.