Also make names more consistent.

This fixes the following issue by JH Jourdan:

  The fact of including uPred_[...] in the module uPred (in base_logic.v),
  implies that typeclasses instances are declared twice. Once in module
  uPred and once in module uPred_[...]. This has the unfortunate
  consequence that it has to backtrack to both instances each time the
  first one fails, making failure of type class search for e.g.
  PersistentP potentially exponential.

  Goal ((□ ∀ (x1 x2 x3 x4 x5: nat), True -∗ True) -∗ True : iProp Σ).
    Time iIntros "#H".
    Undo.
    Remove Hints uPred_derived.forall_persistent : typeclass_instances.
    Time iIntros "#H".

Thanks to Jason Gross @ Coq club for suggesting this fix.

Also:

- Remove the wp_strip_later hack.
- Let wp_lam, wp_rec, wp_... initiate the proof mode.

I also renamed `iProof` into `iStartProof`, as it is supposed to be
something internal, and not a substitute of Coq's `Proof` command (as
originally intended).

Fix a typo in constructions.tex

x_1 should be a_1

See merge request !35

Really, *all* of our files contain proof rules

Use agree instead of dec_agree

This demonstrates that a list-based agreement could work, and form an OFE. I didn't bother to prove all the functor laws.

Man, this reasoning with about the lists is annoying^^.

What I don't like about this is that un-injection (`agree_car`) is only non-expansive for valid elements. I want to try using a different equivalence relation, maybe I can find one where this works.

Cc @jjourdan @robbertkrebbers

See merge request !22

Thanks to Robbert for fixing gen_heap

State invariants in WP and the dead of heap_ctx.

This merge request changes the WP construction so that it takes _state interpretation_ as its parameter (part of the `irisG` type class), instead of building in the authoritative ownership of the entire state. When instantiating WP with a concrete language, one can choose the state interpretation. For example, for `heap_lang` we directly use `auth (gmap loc (frac * dec_agree val))`, and avoid the indirection through an invariant managing ownership of the entire state.

As a result, we no longer have to carry around `heap_ctx`.

See merge request !25