Before this commit, `Simproc`s were defined as `Expr -> SimpM (Option Step)`, where `Step` is inductively defined as follows:
```
inductive Step where
| visit : Result → Step
| done : Result → Step
```
Here, `Result` is a structure containing the resulting expression and a proof demonstrating its equality to the input. Notably, the proof is optional; in its absence, `simp` assumes reflexivity.
A simproc can:
- Fail by returning `none`, indicating its inapplicability. In this case, the next suitable simproc is attempted, along with other simp extensions.
- Succeed and invoke further simplifications using the `.visit`
constructor. This action returns control to the beginning of the
simplification loop.
- Succeed and indicate that the result should not undergo further
simplifications. However, I find the current approach unsatisfactory, as it does not align with the methodology employed in `Transform.lean`, where we have the type:
```
inductive TransformStep where
/-- Return expression without visiting any subexpressions. -/
| done (e : Expr)
/--
Visit expression (which should be different from current expression) instead.
The new expression `e` is passed to `pre` again.
-/
| visit (e : Expr)
/--
Continue transformation with the given expression (defaults to current expression).
For `pre`, this means visiting the children of the expression.
For `post`, this is equivalent to returning `done`. -/
| continue (e? : Option Expr := none)
```
This type makes it clearer what is going on. The new `Simp.Step` type is similar but use `Result` instead of `Expr` because we need a proof.
Modifies the structure instance elaborator to
1. Fill in missing fields from sources in strict left-to-right order. In
`{a, b with}`, sometimes the elaborator
would ignore `a` even if both `a` and `b` provided the same field,
depending on what subobject fields they had.
2. Use the sources, or subobjects of the sources, to fill in entire
subobjects of the target structure as much as possible.
Currently, a field cannot be filled directly by a source itself
resulting in the term being eta expanded.
This change avoids this unnecessary and surprisingly costly extra eta
expansion.
Adds two new tests to illustrate the performance benefit (one courtesy
@semorrison). These are currently failing on master and succeed on this
branch.
There is one additional test to exercise the changes to the elaboration
of structure instances.
Changes to make mathlib build are in leanprover-community/mathlib4#9843
Closes#2451
This combines a few platform-related changes:
* Add a ternary `platformIndependent` Lean configuration option to
assert whether Lake should assume Lean code is platform-independent. If
`true`, Lake will exclude platform-independent objects like external
libraries or dynlibs created through `precompileModules` from module
traces. If `false`, Lake will add the platform to module traces. If
`none` (the default), Lake will retain the current behavior (modules are
platform-dependent if and only if it depends on native objects).
* Use `System.Platform.target` from #3207 as the platform descriptor in
Lake for the configuration file trace, the cloud release archive, and as
the platform trace in Lean modules and native artifacts (e.g., object
files, and static and shared libraries).
* Do not add the platform descriptor into custom build archive names
(i.e., a user-set `buildArchive` configuration). This allows users to
create cross-platform / platform-independent archives via a name
override should they so desire.
Closes#2754.
This replaces the no-op `unusedVariablesIgnoreFnsExt` environment
extension with an actual environment extension which can be extended
using either `@[unused_variables_ignore_fn]` or
`@[builtin_unused_variables_ignore_fn]` (although for the present all
the builtin `unused_variables_ignore_fn`s are being added using direct
calls to `builtin_initialize addBuiltinUnusedVariablesIgnoreFn`, because
this also works and a stage0 update is required before the attribute can
be used).
We would like to use this attribute to disable unused variables in
syntaxes defined in std and mathlib, like
[`proof_wanted`](https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/Unused.20variables.20and.20proof_wanted/near/408554690).
This PR adds two new delaboration settings: `pp.deepTerms : Bool`
(default: `true`) and `pp.deepTerms.threshold : Nat` (default: `20`).
Setting `pp.deepTerms` to `false` will make the delaborator terminate
early after `pp.deepTerms.threshold` layers of recursion and replace the
omitted subterm with the symbol `⋯` if the subterm is deeper than
`pp.deepTerms.threshold / 4` (i.e. it is not shallow). To display the
omitted subterm in the InfoView, `⋯` can be clicked to open a popup with
the delaborated subterm.
<details>
<summary>InfoView with pp.deepTerms set to false (click to show
image)</summary>
</details>
### Implementation
- The delaborator is adjusted to use the new configuration settings and
terminate early if the threshold is exceeded and the corresponding term
to omit is shallow.
- To be able to distinguish `⋯` from regular terms, a new constructor
`Lean.Elab.Info.ofOmissionInfo` is added to `Lean.Elab.Info` that takes
a value of a new type `Lean.Elab.OmissionInfo`.
- `ofOmissionInfo` is needed in `Lean.Widget.makePopup` for the
`Lean.Widget.InteractiveDiagnostics.infoToInteractive` RPC procedure
that is used to display popups when clicking on terms in the InfoView.
It ensures that the expansion of an omitted subterm is delaborated using
`explicit := false`, which is typically set to `true` in popups for
regular terms.
- Several `Info` widget utility functions are adjusted to support
`ofOmissionInfo`.
- The list delaborator is adjusted with special support for `⋯` so that
long lists `[x₁, ..., xₖ, ..., xₙ]` are shortened to `[x₁, ..., xₖ, ⋯]`.
this way this function does not have to peek at the `altType` to see
when there are no more arguments, which makes it a bit more explicit,
and also a bit more robust should one apply this function to the type of
an alternative with the motive already instantiated.
It seems this uncovered a variable shadow bug, where the counter `i` was
accidentially reset after removing the `i`’th entry in `ys`.
Adds support for `let_fun` to the `intro` and `intros` tactics. Also
adds support to `intro` for anonymous binder names, since the default
variable name for a `letFun` with an eta reduced body is anonymous.
Encouraged by the performance gains from making `rewrite` produce
smaller proof objects
(#3121) I am here looking for low-hanging fruit in `simp`.
Consider this typical example:
```
set_option pp.explicit true
theorem test
(a : Nat)
(b : Nat)
(c : Nat)
(heq : a = b)
(h : (c.add (c.add ((c.add b).add c))).add c = c)
: (c.add (c.add ((c.add a).add c))).add c = c
```
We get a rather nice proof term when using
```
:= by rw [heq]; assumption
```
namely
```
theorem test : ∀ (a b c : Nat),
@Eq Nat a b →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c :=
fun a b c heq h =>
@Eq.mpr (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c)
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c)
(@congrArg Nat Prop a b (fun _a => @Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c _a) c))) c) c) heq) h
```
(this is with #3121).
But with `by simp only [heq]; assumption`, it looks rather different:
```
theorem test : ∀ (a b c : Nat),
@Eq Nat a b →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c :=
fun a b c heq h =>
@Eq.mpr (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c)
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c)
(@id
(@Eq Prop (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c)
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c))
(@congrFun Nat (fun a => Prop) (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c))
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c))
(@congrArg Nat (Nat → Prop) (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c)
(Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) (@Eq Nat)
(@congrFun Nat (fun a => Nat) (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))))
(Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))))
(@congrArg Nat (Nat → Nat) (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c)))
(Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) Nat.add
(@congrArg Nat Nat (Nat.add c (Nat.add (Nat.add c a) c)) (Nat.add c (Nat.add (Nat.add c b) c)) (Nat.add c)
(@congrArg Nat Nat (Nat.add (Nat.add c a) c) (Nat.add (Nat.add c b) c) (Nat.add c)
(@congrFun Nat (fun a => Nat) (Nat.add (Nat.add c a)) (Nat.add (Nat.add c b))
(@congrArg Nat (Nat → Nat) (Nat.add c a) (Nat.add c b) Nat.add
(@congrArg Nat Nat a b (Nat.add c) heq))
c))))
c))
c))
h
```
Since simp uses only single-step `congrArg`/`congrFun` congruence lemmas
here, the proof
term grows very large, likely quadratic in this case.
Can we do better? Every nesting of `congrArg` (and it's little brother
`congrFun`) can be
turned into a single `congrArg` call.
In this PR I make making the smart app builders `Meta.mkCongrArg` and
`Meta.mkCongrFun` a bit
smarter and not only fuse with `Eq.refl`, but also with
`congrArg`/`congrFun`.
Now we get, in this simple example,
```
theorem test : ∀ (a b c : Nat),
@Eq Nat a b →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c →
@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c :=
fun a b c heq h =>
@Eq.mpr (@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c a) c))) c) c)
(@Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c b) c))) c) c)
(@congrArg Nat Prop a b (fun x => @Eq Nat (Nat.add (Nat.add c (Nat.add c (Nat.add (Nat.add c x) c))) c) c) heq) h
```
Let’s see if it works and how much we gain.
right now, the `induction` tactic accepts a custom eliminator using the
`using <ident>` syntax, but is restricted to identifiers. This
limitation becomes annoying when the elminator has explicit parameters
that are not targets, and the user (naturally) wants to be able to write
```
induction a, b, c using foo (x := …)
```
This generalizes the syntax to expressions and changes the code
accordingly.
This can be used to instantiate a multi-motive induction:
```
example (a : A) : True := by
induction a using A.rec (motive_2 := fun b => True)
case mkA b IH => exact trivial
case A => exact trivial
case mkB b IH => exact trivial
```
For this to work the term elaborator learned the `heedElabAsElim` flag,
`true` by default. But in the default setting, `A.rec (motive_2 := fun b
=> True)`
would fail to elaborate, because there is no expected type. So the
induction
tactic will elaborate in a mode where that attribute is simply ignored.
As a side effect, the “failed to infer implicit target” error message
is improved and prints the name of the implicit target that could not be
instantiated.
This PR adds support for the "call hierarchy" feature of LSP that allows
quickly navigating both inbound and outbound call sites of functions. In
this PR, "call" is taken to mean "usage", so inbound and outbound
references of all kinds of identifiers (e.g. functions or types) can be
navigated. To implement the call hierarchy feature, this PR implements
the LSP requests `textDocument/prepareCallHierarchy`,
`callHierarchy/incomingCalls` and `callHierarchy/outgoingCalls`.
<details>
<summary>Showing the call hierarchy (click to show image)</summary>
</details>
<details>
<summary>Incoming calls (click to show image)</summary>
</details>
<details>
<summary>Outgoing calls (click to show image)</summary>
</details>
It is based on #3159, which should be merged before this PR.
To route the parent declaration name through to the language server, the
`.ilean` format is adjusted, breaking backwards compatibility with
version 1 of the ILean format and yielding version 2.
This PR also makes the following more minor adjustments:
- `Lean.Server.findModuleRefs` now also combines the identifiers of
constants and FVars and prefers constant over FVars for the combined
identifier. This is necessary because e.g. declarations declared using
`where` yield both a constant (for usage outside of the function) and an
FVar (for usage inside of the function) with the same range, whereas we
would typically like all references to refer to the former. This also
fixes a bug introduced in #2462 where renaming a declaration declared
using `where` would not rename usages outside of the function, as well
as a bug in the unused variable linter where `where` declarations would
be reported as unused even if they were being used outside of the
function.
- The function converting `Lean.Server.RefInfo` to `Lean.Lsp.RefInfo`
now also computes the `Lean.DeclarationRanges` for parent declaration
names via `MetaM` and must hence be in `IO` now.
- Add a utility function `Array.groupByKey` to `HashMap.lean`.
- Stylistic refactoring of `Watchdog.lean` and `LanguageFeatures.lean`.
In the new snapshot design, we have a tree of `Task`s that represents
the asynchronously processed document structure. When transforming this
tree in response to a user edit, we want to quickly run through
reusable, already computed nodes of the tree synchronously and then
spawn new tasks for the new parts. The new flag allows us to do such
mixed sync/async tree transformations uniformly. This flag exists as
e.g.
[`ExecuteSynchronously`](https://learn.microsoft.com/en-us/dotnet/api/system.threading.tasks.taskcontinuationoptions?view=net-8.0)
in other runtimes.
I deleted internal links that seemed to have the character of "TODO". I
think that the residual TODO is of little value, given that we plan a
big revamp and revision soon anyway, but I could do it some other way as
well.
This makes changes to the definitions of Associativity, Commutativity,
Idempotence and Identity classes to be more aligned with Mathlib's
versions.
The changes are:
* Move classes are moved from `Lean` to root namespace.
* Drop `Is` prefix from names.
* Rename `IsNeutral` to `LawfulIdentity` and add Left and Right
subclasses.
* Change neutral/identity element to outParam.
* Introduce `HasIdentity` for operations not intended for proofs to
implement
The identity changes are to make this compatible with
[Mathlib](718042db9d/Mathlib/Init/Algebra/Classes.lean)
and to enable nicer fold operations in Std that can use type classes to
infer the identity/initial element on binary operations.
---------
Co-authored-by: Kyle Miller <kmill31415@gmail.com>
Makes the LLVM triple of the current platform available to Lean code
towards a solution for #2754.
Defaults to the empty string if the compiler is not clang, which can
introduce some divergence between CI and local builds but should not be
noticeable in most cases and is not really possible to avoid.
Recursive predefinitions contains “rec app” markers as mdata in the
predefinitions,
but sometimes these get in the way of termination checking, when you
have
```
[mdata (fun x => f)] arg
```
Therefore, the `preprocess` pass floats them out of applications
(originally
only for structural recursion, since #2818 also for well-founded
recursion).
But the code was incomplete: Because `Meta.transform` calls `post` on `f
x y` only
once (and not also on `f x`) one has to float out of nested applications
as well.
A consequence of this can be that in a recursive proof, `rw [foo]` does
not work
although `rw [foo _ _]` does.
Also adding the testcase where @david-christiansen and I stumbled over
this
(Maybe the two preprocess modules can be combined, now that #2973 is
landed, will try that
in a follow-up).
As suggested by @kmill, removing an unnecessary `let` (possibly only
there in the first place for copy/paste reasons) seems to fix the
included test.
This makes `~q()` matching in quote4 noticeably more useful in things
like `norm_num` (as it fixes
https://github.com/leanprover-community/quote4/issues/29)
It also makes a quote4 bug slightly more visible
(https://github.com/leanprover-community/quote4/issues/30), but the bug
there already existed anyway, and isn't caused by this patch.
Fixes#3065
Give n-ary `Expr.app` constructors such as `mkApp2`, `mkApp3`, ...,
`mkApp10` the `@[match_pattern]` attribute so that it is easier to read
and write pattern matching for applications.
This PR facilitates augmenting the context of an `InfoTree` with
*partial* contexts while elaborating a command. Using partial contexts,
this PR also adds support for tracking the parent declaration name of a
term in the `InfoTree`. The parent declaration name is needed to compute
the call hierarchy in #3082.
Specifically, the `Lean.Elab.InfoTree.context` constructor is refactored
to take a value of the new type `Lean.Elab.PartialContextInfo` instead
of a `Lean.Elab.ContextInfo`, which now refers to a full `InfoTree`
context. The `PartialContextInfo` is then merged into a `ContextInfo`
while traversing the tree using
`Lean.Elab.PartialContextInfo.mergeIntoOuter?`. The partial context
after executing `liftTermElabM` is stored in values of a new type
`Lean.Elab.CommandContextInfo`.
As a result of this, `Lean.Elab.ContextInfo.save` moves to
`Lean.Elab.CommandContextInfo.save`.
For obtaining the parent declaration for a term, a new typeclass
`MonadParentDecl` is introduced to save the parent declaration in
`Lean.Elab.withSaveParentDeclInfoContext`. `Lean.Elab.Term.withDeclName
x` now calls `withSaveParentDeclInfoContext x` to save the declaration
name.
### Migration
**The changes to the `InfoTree.context` constructor break backwards
compatibility with all downstream users that traverse the `InfoTree`
manually instead of going through the functions in `InfoUtils.lean`.**
To fix this, you can merge the outer `ContextInfo` in a traversal with
the `PartialContextInfo` of an `InfoTree.context` node using
`PartialContextInfo.mergeIntoOuter?`. See e.g.
`Lean.Elab.InfoTree.foldInfo` for an example:
```lean
partial def InfoTree.foldInfo (f : ContextInfo → Info → α → α) (init : α) : InfoTree → α :=
go none init
where go ctx? a
| context ctx t => go (ctx.mergeIntoOuter? ctx?) a t
| node i ts =>
let a := match ctx? with
| none => a
| some ctx => f ctx i a
ts.foldl (init := a) (go <| i.updateContext? ctx?)
| _ => a
```
Downstream users that manually save `InfoTree`s may need to adjust calls
to `ContextInfo.save` to use `CommandContextInfo.save` instead and
potentially wrap their `CommandContextInfo` in a
`PartialContextInfo.commandCtx` constructor when storing it in an
`InfoTree` or `ContextInfo.mk` when creating a full context.
### Motivation
As of now, `ContextInfo`s are always *full* contexts, constructed as if
they were always created in `liftTermElabM` after running the
`TermElabM` action. This is not strictly true; we already create
`ContextInfo`s in several places other than `liftTermElabM` and work
around the limitation that `ContextInfo`s are always full contexts in
certain places (e.g. `Info.updateContext?` is a crux that we need
because we can't always create partial contexts at the term-level), but
it has mostly worked out so far. Note that one must be very careful when
saving a `ContextInfo` in places other than `liftTermElabM` because the
context may not be as complete as we would like (e.g. it may lack
meta-variable assignments, potentially leading to a language server
panic).
Unfortunately, the parent declaration of a term is another example of a
context that cannot be provided in `liftTermElabM`: The parent
declaration is usually set via `withDeclName`, which itself lives in
`TermElabM`. So by the time we are trying to save the full
`ContextInfo`, the declaration name is already gone. There is no easy
fix for this like in the other cases where we would really just like to
augment the context with an extra field.
The refactor that we decided on to resolve the issue is to refactor the
`InfoTree` to take a `PartialContextInfo` instead of a `ContextInfo` and
have code that traverses the `InfoTree` merge inner contexts with outer
contexts to produce a full `ContextInfo` value.
### Bumps for downstream projects
- `lean-pr-testing-3159` branch at Std, not yet opened as a PR
- `lean-pr-testing-3159` branch at Mathlib, not yet opened as a PR
- https://github.com/leanprover/LeanInk/pull/57
- https://github.com/hargoniX/LeanInk/pull/1
- https://github.com/tydeu/lean4-alloy/pull/7
- https://github.com/leanprover-community/repl/pull/29
---------
Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
Currently we create `lean-pr-testing-NNNN` branches at Mathlib
automatically for each Lean PR.
We don't automatically create one at Std; mostly simply because Std
fails less often, so it has been okay to do this manually as needed. It
is conceptually simpler, however, if this is done uniformly.
This PR:
* does not proceed with Std/Mathlib CI unless the appropriate
`nightly-testing-YYYY-MM-DD` tag exists at Std (like it already doesn't
proceed if that tag is missing at Mathlib)
* creates `lean-pr-testing-NNNN` branches at Std
* when it creates `lean-pr-testing-NNNN` branches at Mathlib, updates
the Std dependency to use the `lean-pr-testing-NNNN` branch at Std
- [x] depends on #3199
Note that because most users do not have write access at Std, in order
to make updates to `lean-pr-testing-NNNN` branches there they will need
to make PRs. These will be merged with a very low bar, and feel free to
ping me for assistance on this. If this is annoying we will automate.
Also, frequent contributors to Lean may ask @digama0 or @joehendrix for
write access in order to easily work on these branches.
This PR requires that we have a secret here with write access at Std.
I'm arranging that [on
zulip](https://leanprover.zulipchat.com/#narrow/stream/348111-std4/topic/bot.20access/near/416686090).
I will update the documentation at
https://leanprover-community.github.io/contribute/tags_and_branches.html
to reflect these changes when they are merged.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
As discussed during the FRO meeting 2024-01-18, we are changing the
`nightly-testing-YYYY-MM-DD` branches at Std and Mathlib from branches
to tags, in:
* https://github.com/leanprover/std4/pull/545
* https://github.com/leanprover-community/mathlib4/pull/9842
This PR updates the script that creates the `lean-pr-testing-NNNN`
branches at Mathlib so it is agnostic about whether
`nightly-testing-YYYY-MM-DD` will be a branch or a tag.
---------
Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>
`Array.set!` and `Array.swap!` are fairly similar operations, both
modify an array, both take an index that it out of bounds.
But they behave different; all of these return `true`
```
#eval #[1,2].set! 2 42 == #[1,2] -- with panic
#reduce #[1,2].set! 2 42 == #[1,2] -- no panic
#eval #[1,2].swap! 0 2 == #[1,2] -- with panic
#reduce #[1,2].swap! 0 2 == default -- no panic
```
The implementations are
```
@[extern "lean_array_set"]
def Array.set! (a : Array α) (i : @& Nat) (v : α) : Array α :=
Array.setD a i v
```
but
```
@[extern "lean_array_swap"]
def swap! (a : Array α) (i j : @& Nat) : Array α :=
if h₁ : i < a.size then
if h₂ : j < a.size then swap a ⟨i, h₁⟩ ⟨j, h₂⟩
else panic! "index out of bounds"
else panic! "index out of bounds"
```
It seems to be more consistent to unify the behaviors, and define
```
@[extern "lean_array_swap"]
def swap! (a : Array α) (i j : @& Nat) : Array α :=
if h₁ : i < a.size then
if h₂ : j < a.size then swap a ⟨i, h₁⟩ ⟨j, h₂⟩
else a
else a
```
Also adds docstrings.
Fixes#3196
Consider
```
import Std.Tactic.ShowTerm
opaque a : Nat
opaque b : Nat
axiom a_eq_b : a = b
opaque P : Nat → Prop
set_option pp.explicit true
-- Using rw
example (h : P b) : P a := by show_term rw [a_eq_b]; assumption
```
Before, a typical proof term for `rewrite` looked like this:
```
-- Using the proof term that rw produces
example (h : P b) : P a :=
@Eq.mpr (P a) (P b)
(@id (@Eq Prop (P a) (P b))
(@Eq.ndrec Nat a (fun _a => @Eq Prop (P a) (P _a))
(@Eq.refl Prop (P a)) b a_eq_b))
h
```
which is rather round-about, applying `ndrec` to `refl`. It would be
more direct to write
```
example (h : P b) : P a :=
@Eq.mpr (P a) (P b)
(@id (@Eq Prop (P a) (P b))
(@congrArg Nat Prop a b (fun _a => (P _a)) a_eq_b))
h
```
which this change does.
This makes proof terms smaller, causing mild general speed up throughout
the code; if the brenchmarks don’t lie the highlights are
* olean size -2.034 %
* lint wall-clock -3.401 %
* buildtactic execution s -10.462 %
H'T to @digama0 for advice and help.
NB: One might even expect the even simpler
```
-- Using the proof term that I would have expected
example (h : P b) : P a :=
@Eq.ndrec Nat b (fun _a => P _a) h a a_eq_b.symm
```
but that would require non-local changes to the source code, so one step
at a time.
