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`.
Before this commit, an user could define their own prelude and change
the types of quot, quot.mk, quot.lift or quot.ind.
By doing that, they could prove false.
This commit prevents this kind of abuse.
It also modifies the definition of `quot` and avoids the `setoid`
dependency.
The previous `quot` type is now called `quotient`, and it is defined
using the new `quot` type provided by the kernel.
See discussion at #1330
