I addressed two problems. First, the theorem names and notation were all in
the namespace complete_lattice. The problem was that if you opened that
namespace, names (like "sup" and "inf") and notation clashed with global notation
for lattices.
The other problem was that if you defined a lattice using Sup, the Sup you got
was not the Sup you want; it was the Sup-construction from the Inf-construction
from the Sup.
Everything seems good now.
Convert two instances of has_zero and has_one to local instance,
and change one "[instance]" to a "[trans_instance]". This (by
accident) fixed a problem Rob had a couple of weeks ago.
more about pointed truncated types, including pointed sets.
also increase the priority of some basic instances that nat/num/pos_num/trunc_index have 0, 1 and + (in both libraries)
also move the notation + for sum into the namespace sum, to (sometimes) avoid overloading with add
After this commit we need some more advanced theorems in init/wf, notably function extenstionality.
For this reason I had to refactor the init folder a little bit.
To keep the init folders in both libraries similar, I did the same refactorization in the standard library, even though that was not required for the standard library
@avigad, @fpvandoorn, @rlewis1988, @dselsam
I changed how transitive instances are named.
The motivation is to avoid a naming collision problem found by Daniel.
Before this commit, we were getting an error on the following file
tests/lean/run/collision_bug.lean.
Now, transitive instances contain the prefix "_trans_".
It makes it clear this is an internal definition and it should not be used
by users.
This change also demonstrates (again) how the `rewrite` tactic is
fragile. The problem is that the matching procedure used by it has
very little support for solving matching constraints that involving type
class instances. Eventually, we will need to reimplement `rewrite`
using the new unification procedure used in blast.
In the meantime, the workaround is to use `krewrite` (as usual).
At real.comm_ring, `add` is `@add real real_has_add`.
This is bad for any tactic (e.g., blast) that only unfolds reducible definitions.
`add` is not reducible. So, the tactic will not be able to establish
that `@add real real_has_add` is definitionally equal to `real.add`.
