Replaces `@[eliminator]` with two attributes `@[induction_eliminator]`
and `@[cases_eliminator]` for defining custom eliminators for the
`induction` and `cases` tactics, respectively.
Adds `Nat.recAux` and `Nat.casesAuxOn`, which are eliminators that are
defeq to `Nat.rec` and `Nat.casesOn`, but these use `0` and `n + 1`
rather than `Nat.zero` and `Nat.succ n`.
For example, using `induction` to prove that the factorial function is
positive now has the following goal states (thanks also to #3616 for the
goal state after unfolding).
```lean
example : 0 < fact x := by
induction x with
| zero => decide
| succ x ih =>
/-
x : Nat
ih : 0 < fact x
⊢ 0 < fact (x + 1)
-/
unfold fact
/-
...
⊢ 0 < (x + 1) * fact x
-/
simpa using ih
```
Thanks to @adamtopaz for initial work on splitting the `@[eliminator]`
attribute.
This PR adds per-package server options to resolve#2455. It is based on
the previous work in #2456, but takes a different approach: options are
loaded for the specific file in the file worker when `print-paths` is
called, instead of loading them in the watchdog with a separate Lake
command. This change addresses review comments made in #2456.
In doing so, it introduces two new Lake config fields:
- `leanOptions`: `-D` flag options that are passed to both the language
server and `lean` when building.
- `moreServerOptions`: `-D` flag options that are passed to the language
server.
Since `print-paths` must also accept a file path to compute the options
for that file, this PR is changing the API for `print-paths`. As there
have been numerous complaints about the name `print-paths`, I also
decided to change it to `setup-file` in this PR, since it would break
compatibility with the old Lake API anyways.
This PR deprecates the Lakefile field `moreServerArgs` in favor of
`moreGlobalServerArgs`, as suggested in the review for #2456.
Fixes#2455
---------
Co-authored-by: digama0 <mcarneir@andrew.cmu.edu>
