Split from #4583
`exists_of_set` appears in Batteries as `exists_of_set'`. The
`exists_of_set` version is unused in batteries and mathlib at least and
I would argue that the primed version (i.e., the one added in this PR)
is always better anyway.
`isEmpty_iff` appears in mathlib as `isEmpty_iff_eq_nil`.
This is not the most exciting place to start, but I started here to:
* pick a function with little development in Batteries and Mathlib, so I
wouldn't have conflicts
* that is easy!
* to see how much effort it is to get fairly complete coverage
* and to set up some infrastructure to be used later, i.e.
`tests/lean/run/list_simp.lean`
This PR neither adds nor removes material, but improves the organization
of `Init/Data/List/*`.
These files are essentially completely re-ordered, to ensure that
material is developed in a consistent order between `List.Basic`,
`List.Impl`, `List.BasicAux`, and `List.Lemmas`.
Everything is organised in subsections, and I've added some module docs.
We recently discovered inconsistencies in Mathlib and Std over the
ordering of the arguments for `==`.
The most common usage puts the "more variable" term on the LHS, and the
"more constant" term on the RHS, however there are plenty of exceptions,
and they cause unnecessary pain when switching (particularly, sometimes
requiring otherwise unneeded `LawfulBEq` hypotheses).
This convention is consistent with the (obvious) preference for `x == 0`
over `0 == x` when one term is a literal.
We recently updated Std to use this convention
https://github.com/leanprover/std4/pull/430
This PR changes the two major places in Lean that use the opposite
convention, and adds a suggestion to the docstring for `BEq` about the
preferred convention.
in #4158 I was experimenting with a change to the simplifier that
affectes the order in which lemmas were tried, and of course it breaks
proofs all over the place whenever we have a non-confluent simp set.
Among the first breakages encountered, a large fraction was due to
`simp` rewriting with `List.length_pos : 0 < length l ↔ l ≠ []`.
This does not strike me a as a good simp lemma: If `l` is a manifest
constructor, the simplifier will reduce `length` and solve it anyways,
and if it isn't then an inequality usually isn’t very simp friendly. It
is also highly non-confluent with any kind of `length`-lemma we might
have.
This therefore removes it from the standard simp set.
This PR upstreams lemmas about List/Array operations already defined in
Lean from std/batteries.
Happy to take suggestions about increasing or decreasing scope.
---------
Co-authored-by: Mario Carneiro <di.gama@gmail.com>
Because of the last-added-tried-first rule for macros, all the special
purpose `decreasing_trivial` rules are tried for most recursive
definitions out there, and because they use `apply` and `assumption`
with default transparency may cause some definitoins to be unfolded over
and over again.
A quick test with one of the functions in the leansat project shows that
elaboration time goes down from 600ms to 375ms when using
```
decreasing_by all_goals decreasing_with with_reducible decreasing_trivial
```
instead of
```
decreasing_by all_goals decreasing_with decreasing_trivial
```
This change uses `with_reducible` in most of these macros.
This means that these tactics will no longer work when the
relations/definitions they look for is hidden behind a definition.
This affected in particular `Array.sizeOf_get`, which now has a
companion `sizeOf_getElem`.
In addition, there were three tactics using `apply` to apply Nat-related
lemmas
that we now expect `omega` to solve. We still need them when building
`Init` modules
that don’t have access to `omega`, but they now live in
`decreasing_trivial_pre_omega`,
meant to be only used internally.
Previously the `ac_rfl` tactic was only really usable when depending on
mathlib. With these instances, `ac_rfl` can deal with the various
operations defined in Lean.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
This removes simp attributes from `Nat.succ.injEq` and
`Nat.succ_sub_succ_eq_sub` to replace them with simprocs. This is
because any reductions involving `Nat.succ` has a high risk of leading
proof performance problems when dealing with even moderately large
numbers.
Here are a couple examples that will both report a maximum recursion
depth error currently. These examples are fixed by this PR.
```
example : (123456: Nat) = 12345667 := by
simp
example (x : Nat) (p : x = 0) : 1000 - (x + 1000) = 0 := by
simp
```
This makes changes to the `GetElem` class so that it does not lead to
unnecessary overhead in container like `RBMap`.
The changes are to:
1. Make `getElem?` and `getElem!` part of the `GetElem` class so they
can be overridden in instances.
2. Introduce a `LawfulGetElem` class that contains correctness theorems
for `getElem?` and `getElem!` using the original definitions.
3. Reorganize definitions (e.g, by moving `GetElem` out of
`Init.Prelude`) so that the `GetElem` changes are feasible.
4. Provide `LawfulGetElem` instances to complement all existing
`GetElem` instances in Lean core.
To reduce the size of the PR, this doesn't do the work of providing new
`GetElem` instances for `RBMap`, `HashMap` etc. That will be done in a
separate PR (#3688) that depends on this.
---------
Co-authored-by: Mac Malone <tydeu@hatpress.net>
This adds a number of lemmas for simplification of `Bool` and `Prop`
terms. It pulls lemmas from Mathlib and adds additional lemmas where
confluence or consistency suggested they are needed.
It has been tested against Mathlib using some automated test
infrastructure.
That testing module is not yet included in this PR, but will be included
as part of this.
Note. There are currently some comments saying the origin of the simp
rule. These will be removed prior to merging, but are added to clarify
where the rule came from during review.
---------
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
This will collect definitions from Std.Logic
---------
Co-authored-by: David Thrane Christiansen <david@davidchristiansen.dk>
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
