See Section "Other goodies" at
https://github.com/leanprover/lean/wiki/Refactoring-structures
This commit also improves the support for projections in the
unifier/matcher.
Now, we consider the extra case-split for projections.
Given a projection `proj`, and the constraint `proj s =?= proj t`, we need to try first `s =?= t` and if it fails, then try to reduce.
This is needed in the standard library because we now have constraints such as:
```
@has_le.le ?A ?s ?a ?b =?= @has_le.le nat nat.has_add x y
```
If we reduce the right hand side, we get the unsolvable constraint
```
@has_le.le ?A ?s ?a ?b =?= nat.le x y
```
Before this change, the constraint was `@le ?A ?s ?a ?b =?= @le nat nat.has_add x y`, and we already perform a case-split in this case.
Moreover, projections were eagerly reduced whenever possible.
The extra case-split generates a performance problem in several tests. For example `fib 8 = 34` was timing out.
I worked around this issue by performing the case-split only when the constraint contains meta-variables.
There are also minor issues. Example. `<` is notation for `has_lt.lt`, but `>` is for `gt`.
We need this improvement to be able to finish Section "Other goodies" described at
https://github.com/leanprover/lean/wiki/Refactoring-structures
Before this commit, Lean would not be able to solve constraints such as
```lean
@has_add.add nat nat.has_add a b =?= @had_add.add ?A ?inst a b
```
The problem is that projections were being reduced eagerly, and the
constraint would be reduced to
```lean
nat.add a b =?= @had_add.add ?A ?inst a b
```
The new test proj_uniy.lean contains similar unification problems.
After this commit, `(+)` is notation for (add) instead of `(fun x y, add x y)`.
This change is relevant when defining type class instances such as
```lean
instance semigroup_to_is_associative [semigroup α] : is_associative α (*) :=
⟨mul_assoc⟩
```
Motivation: see "Other goodies" section at
https://github.com/leanprover/lean/wiki/Refactoring-structures
We had to add a new transparency mode: Instances at type_context.
In this mode, instances and reducible definitions are considered
transparent.
The new mode is used in the defeq_canonizer, code generator,
and sizeof lemma generation at inductive_compiler.
We also use the new mode in the unfold tactics.
@leodemoura The forced zeta-expansion in mk_aux_definition might
cause problems if we use tactic.abstract without zeta-reduction.
However, we never use the non-zeta mode, and it already fails right now
if you accidentally use zeta-expansion in the proof we want to abstract.
