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Author SHA1 Message Date
Kim Morrison
1b65301859 feat: some missing Array grind annotations 2025-11-06 05:50:36 +01:00
Sebastian Ullrich
ea2b745e57 chore: new module system adjustments for the Mathlib port (#11093) 2025-11-05 22:17:53 +00:00
Kim Morrison
28a3cf9a6c chore: grind attributes for Prod (#11085) 2025-11-05 20:52:28 +00:00
Joachim Breitner
343887e480 perf: use hasIndepIndices (#11095)
This PR makes use of `hasIndepIndices`. That function was unused since
commit 54f6517ca3, but it seems it should
be used.
2025-11-05 18:41:23 +00:00
Joachim Breitner
d8a67095d6 chore: make workspaceSymbol benchmarks modules (#11094)
This PR makes workspaceSymbol benchmarks `module`s, so that they are
less sensitive to additions of private symbols in the standard library.
2025-11-05 18:40:39 +00:00
Joachim Breitner
0cb79868f4 feat: sparse casesOn constructions (#11072)
This PR adds “sparse casesOn” constructions. They are similar to
`.casesOn`, but have arms only for some constructors and a catch-all
(providing `t.ctorIdx ≠ 42` assumptions). The compiler has native
support for these constructors and now (because of the similarity) also
the per-constructor elimination principles.
2025-11-05 15:49:11 +00:00
Leonardo de Moura
ccecac5a56 chore: use abbrev in denote functions (#11092)
This PR ensures that `grind ac` denotation functions used in proof by
reflection are marked as `abbrev`.
2025-11-05 13:51:36 +00:00
Marc Huisinga
8b43fc54b2 doc: clarify server protocol violations around initialize (#11091) 2025-11-05 09:53:39 +00:00
Leonardo de Moura
e7f4f98071 fix: stackoverflow during proof construction in grind (#11084)
This PR fixes a stack overflow that occurs when constructing a proof
term in `grind`.

Closes #11081
2025-11-05 02:35:05 +00:00
Leonardo de Moura
52e37e0d55 refactor: denote functions in grind (#11071)
This PR ensures that the `denote` functions used to implement
proof-by-reflection terms in `grind` are abbreviations. This change
eliminates the need for the `withAbstractAtoms` gadget.
2025-11-04 23:34:17 +00:00
Leonardo de Moura
a4e073f565 fix: panic during equality propagation in grind ring (#11080)
This PR fixes a panic during equality propagation in the `grind ring`
module. If the maximum number of steps has been reached, the polynomials
may not be fully simplified.

Closes #11073
2025-11-04 23:20:38 +00:00
Sebastian Ullrich
18131de438 fix: evalConst meta check and auxiliary IR decls (#11079)
Uncovered in Mathlib through new boxed decls from `BaseIO` changes
2025-11-04 21:29:49 +00:00
Leonardo de Moura
e430626d8a fix: anchor values in grind? (#11077)
This PR fixes the anchor values produced by `grind?`
2025-11-04 13:03:18 +00:00
Kim Morrison
e76bbef79b feat: simp? +suggestions handles ambiguity (#11075)
This PR updates `simp? +suggestions` so that if a name is ambiguous
(because of namespaces) all alternatives are used, rather than erroring.
2025-11-04 05:26:51 +00:00
Kim Morrison
04d72fe346 chore: basic dev instructions for Claude (#11074)
This PR adds a `.claude/claude.md`, with basic development instructions
for Claude Code to operate in this repository.
2025-11-04 04:07:53 +00:00
Sebastian Ullrich
e4fb780f8a perf: remove unused argument to ExternEntry.opaque (#11066)
This used to create quite a few unique objects in public .olean
2025-11-03 17:26:32 +00:00
Wojciech Różowski
00e29075f3 feat: add union on DTreeMap/TreeMap/TreeSet (#10896)
This PR adds union operations on DTreeMap/TreeMap/TreeSet and their raw
variants and provides lemmas about union operations.

---------

Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
2025-11-03 13:47:44 +00:00
Kim Morrison
ec775907e4 chore: update stage0 2025-11-03 23:26:40 +11:00
Kim Morrison
8d603d34dc feat: make set_library_suggestions persistent 2025-11-03 23:26:40 +11:00
Mac Malone
528c0dd2e4 feat: lake: require dependencies by semver range (#10959)
This PR enables Lake users to require Reservoir dependencies by a
semantic version range. On a `lake update`, Lake will fetch the
package's version information from Reservoir and select the newest
version of the package that satisfies the range.

### Using Version Ranges

Version ranges can be specified through the `version` field of a TOML
`require` or the `@` clause of a Lean `require`. They are only
meaningful on Reservoir dependencies.

**lakefile.lean**
```lean-4
require "Seasawher" / "mdgen" @ "2.*"
```

**lakefile.toml**
```toml
[[require]]
name = "mdgen"
scope = "Seasawher"
version = "2.*"
```

The syntax for these versions ranges is a mix of
[Rust's](https://doc.rust-lang.org/stable/cargo/reference/specifying-dependencies.html?highlight=caret#version-requirement-syntax)
and
[Node's](https://github.com/npm/node-semver/tree/v7.7.3?tab=readme-ov-file#ranges)
with some Lean-friendly deviations.

### Comparators

The basic unit of semantic version ranges are version comparators. They
take a base version and a comparison operator and match versions which
compare positively with their base. Lake supports the following
comparison operators.

* `<`, `<=` / `≤`, `>`, `>=` / `≥`, `=`, `!=` / `≠`

Unlike Rust and Node, Lake supports Unicode alternatives for the
operators. It also adds the not-equal operator (`!=` / `≠`) to make
excluding broken versions easier.

Comparators can be combined into clauses via conjunction or disjunction:

* **AND clauses**: Rust-style `≥1.2.3, <1.8.0` or Node-style `1.2.3
<1.8.0`
* **OR clauses**: Node-style `1.2.7 || >=1.2.9, <2.0.0`

When the base version of a comparator has a `-` suffix (e.g.,
`>1.2.3-alpha.3`) it will match versions of the same core (`1.2.3`) with
suffixes that lexicographically compare (e.g., `1.2.3-alpha.7` or
`1.2.3-beta.2`) but will not match suffixed versions of different cores
(e.g., `3.4.5-rc5`). An empty `-` suffix can be used to disable this
behavior. For example, `<2.0.0-` will match `1.2.3-beta.2` and
`2.0.0-alpha.1`.

### Range Macros

In addition to the basic comparators, Lake also supports standard
shorthand for specifying more complex ranges. Namely, it supports the
caret (`^`) and tilde (`~`) operator along with wildcard ranges.

**Caret Ranges**
* `^1` => `≥1.0.0, <2.0.0-`
* `^1.2` => `≥1.2.0, <2.0.0-`
* `^1.2.3` => `≥1.2.3, <2.0.0-`
* `^1.2.3-beta.2` => `≥1.2.3-beta.2, <2.0.0-`
* `^0.2` => `≥0.0.0, <0.3.0-`
* `^0.2.3` => `≥0.2.3, <0.3.0-`
* `^0.0.3` => `≥0.0.3, <0.0.4-`
* `^0` => `≥0.0.0, <1.0.0-`
* `^0.0` => `≥0.0.0, <0.1.0-`

**Tilde Ranges**
* `~1` => `≥1.0.0, <2.0.0-`
* `~1.2` => `≥1.2.0, <1.3.0-`
* `~1.2.3` => `≥1.2.3, <1.3.0-`
* `~1.2.3-beta.2` => `≥1.2.3-beta.2, <1.3.0-`
* `^0` => `≥0.0.0, <1.0.0-`
* `^0.2.3` => `≥0.2.3, <0.3.0-`
* `^0.0.3` => `≥0.0.3, <0.0.4-`
* `~0` => `≥0.0.0, <1.0.0-`
* `~0.0` => `≥0.0.0, <0.1.0-`
* `~0.0.0` => `≥0.0.0, <0.1.0-`

**Wildcard Ranges**
* `*` => `≥0.0.0`
* `1.x` => `≥1.0.0, <2.0.0-`
* `1.*.x` => `≥1.0.0, <2.0.0-`
* `1.2.*` => `≥1.2.0, <1.3.0-`

These ranges closely follow Rust's and Node's syntax. Like Node but
unlike Rust, wildcard ranges support `x` and `X` as alternative syntax
for wildcards.
2025-11-03 04:18:24 +00:00
Kim Morrison
b8bd91d92b feat: simp? +suggestions (#11032)
This PR implements `simp? +suggestions`, which uses the configured
library suggestion engine to add relevant theorems to the `simp` call.
`simp +suggestions` without the `?` prints a message requiring adding
the `?`.
2025-11-03 03:26:16 +00:00
Lean stage0 autoupdater
e05b0e097c chore: update stage0 2025-11-03 02:54:49 +00:00
Mac Malone
d23dcc88ea fix: lake: pin mathlib in new/init to toolchain (#11063)
This PR changes the `math` and `math-lax` templates for `lake new` and
`lake init` to use the version of Mathlib corresponding to the current
Lean toolchain. Thus, `lake +x.y.z new <pkg> math` will use the Mathlib
for Lean `x.y.z`. On the other hand, `lake update` on such packages will
no longer update Mathlib automatically. Users will need to change the
Mathlib revision in the configuration file before updating.

This change was inspired by a
[discussion](https://leanprover.zulipchat.com/#narrow/channel/270676-lean4/topic/Build.20error.20on.20.60lake.20.2Bleanprover.2Flean4.3Av4.2E22.2E0.20new.20foo.20math.60/near/546236449)
on the community Zulip.
2025-11-03 02:16:29 +00:00
Mac Malone
1aca181fe2 fix: lake: use -O0 for debug builds (#11062)
This PR changes Lake's debug build type to use `-O0` instead of `-Og`
when compiling C code. `-Og` was found to be insufficient for debugging
compiled Lean code -- relevant code was stilled optimized out.
2025-11-03 02:16:26 +00:00
Leonardo de Moura
2c45d55683 fix: deep recursion type checking grind proof (#11061)
This PR fixes a deep recursion issue in the kernel when type-checking a
proof term produced by `grind`.

Closes #11059
2025-11-02 19:43:48 +00:00
Rob23oba
f4c71f6ec8 fix: simplify Nat.ble (#11058)
This PR changes `Nat.ble` by joining the two `Nat.ble Nat.zero _` cases
into one, allowing `decide (0 <= x) = true` and `decide (0 < succ x) =
true` to be solvable by `rfl`.
2025-11-02 12:39:49 +00:00
Henrik Böving
823173a761 fix: make ST.Ref.ptrEq behave as stated in the docs (#11056)
This PR fixes `ST.Ref.ptrEq` to act as described in the docs. This fixes
two bugs:
1. The recent `IO.RealWorld` elimination PR overlooked this function
(afaik this is the only one),
   causing its return value to be generally wrong.
2. The implementation of `ptrEq` would previously always consider two
different cells with pointer
equivalent value to be pointer equal. However, the function is supposed
to check whether two
   `Ref` are the same cell, not whether the contained elements are.
2025-11-02 10:42:33 +00:00
Leonardo de Moura
3e86729ee0 feat: grind? using finish? infrastructure (#11057)
This PR implements `grind?` using the new `grind => finish?`
infrastructure.
2025-11-02 05:00:50 +00:00
Leonardo de Moura
2da124d469 chore: remove grind offset (#11051)
This PR removes the `grind offset` module because it is (now) subsumed
by `grind order`.
2025-11-01 19:08:18 +00:00
Leonardo de Moura
1d00dee392 fix: grind order equality propagation for Nat (#11050)
This PR fixes equality propagation for `Nat` in `grind order`.
2025-11-01 18:35:34 +00:00
Leonardo de Moura
e5a6901161 feat: Nat equality propagation in grind order (#11049)
This PR implements equality propagation for `Nat` in `grind order`.
`grind order` supports offset equalities for rings, but it has an
adapter for `Nat`. Example:
```lean
example (a b : Nat) (f : Nat → Int) : a ≤ b + 1 → b + 1 ≤ a → f (1 + a) = f (1 + b + 1) := by
  grind -offset -mbtc -lia -linarith (splits := 0)
```
2025-11-01 15:37:17 +00:00
Markus Himmel
cf871a892c chore: use String.ofList instead of String.mk in elaborator+kernel (#11048)
This PR is a follow-up to #11017, preparing for the eventual removal of
the `String.mk` function.
2025-11-01 14:44:16 +00:00
Markus Himmel
d24ece1396 feat: String.toList_map (#11021)
This PR adds more theory about `Splits` for strings and deduces the
first user-facing `String` lemma, `String.toList_map`.
2025-11-01 13:54:39 +00:00
Leonardo de Moura
faed852c2f feat: equality propagation in grind order (#11047)
This PR implements (nested term) equality propagation in `grind order`.
That is, it propagates implied equalities from `grind order` back to the
`grind` core. Examples:
```lean
open Lean Grind Std

example [LE α] [IsPartialOrder α] (a b : α) (f : α → Nat) : a ≤ b → b ≤ c → c ≤ a → f a = f b := by
  grind (splits := 0)

example [CommRing α] [LE α] [LT α] [LawfulOrderLT α] [IsPartialOrder α] [OrderedRing α]
    (a b : α) (f : α → Int) : a ≤ b + 1 → b ≤ a - 1 → f a = f (2 + b - 1) := by
  grind -mbtc -lia -linarith (splits := 0)

example (a b : Int) (f : Int → Int) : a ≤ b + 1 → b ≤ a - 1 → f a = f (2 + b - 1) := by
  grind -mbtc -lia -linarith (splits := 0)
```
2025-11-01 13:45:54 +00:00
Sebastian Ullrich
4939f447a3 test: avoid testing colliding private inductives (#11041)
`prelude-injectivity.lean` was testing inj thm generation for all
inductives in core, including private ones, which could lead to name
clashes that should not be able to occur in actual files. Put it under
the module system to not load private decls in the first place.
2025-11-01 11:47:52 +00:00
Henrik Böving
3d307925b7 refactor: make constant folding more robust for future bugs (#11044)
This PR enforces users of the constant folder API to provide proofs of
their algebraic properties,
thus hopefully avoiding bugs such as #11042 and #11043 in the future.
2025-11-01 11:07:20 +00:00
Rob23oba
1fa67d0d47 fix: overeager Nat.sub constant folding (#11043)
This PR fixes a case of overeager constant folding on Nat where the
compiler would mistakenly assume `0 - x = x` (see also #11042 for the
same bug on UInts).
2025-11-01 10:14:20 +00:00
Henrik Böving
51ef1dcc5e fix: overeager uint constant folding (#11042)
This PR fixes a case of overeager constant folding on UInts where the
compiler would mistakenly
assume `0 - x = x`.
2025-11-01 02:42:43 +00:00
Leonardo de Moura
282b583f1d fix: panic during the processing of generalized patterns in grind (#11040)
This PR fixes a panic that occurred during the processing of generalized
E-matching patterns in `grind`.

Closes #10983
2025-10-31 16:58:11 +00:00
Leonardo de Moura
4a111501eb fix: grind invalid universe level regression (#11039)
This PR fixes the `grind` invalid universe level regression reported in
#11036

Closes #11036
2025-10-31 15:44:34 +00:00
Leonardo de Moura
16d0005991 feat: finish? produces finish only suggestion (#11034)
This PR adds a new suggestion to `finish?`. It now generates the `grind`
tactic script as before, and a `finish only` tactic. Example:
```lean
/--
info: Try these:
  [apply] ⏎
    instantiate only [findIdx, insert, = mem_indices_of_mem]
    instantiate only [= getElem?_neg, = getElem?_pos]
    cases #1bba
    · instantiate only [findIdx]
    · instantiate only
      instantiate only [= HashMap.mem_insert, = HashMap.getElem_insert]
  [apply] finish only [findIdx, insert, = mem_indices_of_mem, = getElem?_neg, = getElem?_pos, = HashMap.mem_insert,
    = HashMap.getElem_insert, #1bba]
-/
example (m : IndexMap α β) (a : α) (b : β) :
    (m.insert a b).findIdx a = if h : a ∈ m then m.findIdx a else m.size := by
  grind => finish?
```
2025-10-31 14:47:24 +00:00
Markus Himmel
377f149862 refactor: use String.ofList and String.toList for String <-> List Char conversion (#11017)
This PR establishes `String.ofList` and `String.toList` as the preferred
method for converting between strings and lists of characters and
deprecates the alternatives `String.mk`, `List.asString` and
`String.data`.
2025-10-31 14:41:23 +00:00
Markus Himmel
c41cb64ca7 chore: adjust pr-title check to enforce capitalization (#11033)
This PR updates the `pr-title` CI check to enforce that the commit
message does not start with a capital letter followed by a non-capital
letter.

This should ensure that messages do not start with a capitalized word,
but allow messages that start with an acronym.
2025-10-31 07:23:25 +00:00
Kim Morrison
1ce05b2a17 feat: library suggestion engine for local theorems (#11030)
This PR adds a library suggestion engine for local theorems. To be
useful, I still need to write more combinators to re-rank and combine
suggestions from multiple engines.

This is stacked on top of #11029.
2025-10-31 04:48:53 +00:00
Kim Morrison
0db89d65b2 chore: use 'library suggestions' rather than 'premise selection' (#11029)
This PR changes the terminology used from "premise selection" to
"library suggestions". This will be more understandable to users (we
don't assume anyone is familiar with the premise selection literature),
and avoids a conflict with the existing use of "premise" in Lean
terminology (e.g. "major premise" in induction, as well as generally the
synonym for "hypothesis"/"argument").
2025-10-31 04:07:49 +00:00
Kim Morrison
00d41d64e5 feat: remove +premises from grind? output (#11028)
This PR ensures that `grind? +premises` removes `+premises` from the
"Try this" suggestion.
2025-10-31 03:00:33 +00:00
Leonardo de Moura
40e1e097c1 fix: grind order nontermination and propagation issues (#11026)
This PR fixes a nontermination and missing propagation bug in `grind
order`. It also register relevant case-splits for arithmetic.

Closes #11001
2025-10-30 23:12:51 +00:00
Joachim Breitner
d7e4f32d75 feat: Bool.ctorIdx (#11024)
This PR lets `Bool` have `.ctorIdx` like any other inductive.
2025-10-30 21:17:43 +00:00
Joachim Breitner
c7f57d6a0b fix: avoid unnecessary branching in match compilation (#10763)
This PR improves match compilation: Branch on variables in the order
suggested by the first remaining alternative, and do not branch when the
first remaining alternative does not require it. This fixes
https://github.com/leanprover/lean4/issues/10749. With `set_option
backwards.match.rowMajor false` the old behavior can be turned on.

(For now this is an experiment to get familiar with the code and the
whole
problem domain. It is likely overly naive.)
2025-10-30 20:05:13 +00:00
Wrenna Robson
275f9077b6 fix: Rename theorems that use sorted instead of pairwise (#10743)
This PR renames theorems that use `sorted` in their name to instead use
`pairwise`.


Closes #10742.

---------

Co-authored-by: Markus Himmel <markus@lean-fro.org>
2025-10-30 16:07:35 +00:00
Henrik Böving
8b28467655 perf: better detection of repeated branching on same value (#11020)
This PR improves the detection of situations where we branch multiple
times on the same value in the
code generator. Previously this would only consider repeated branching
on function arguments, now on
arbitrary values.


Closes: #11018
2025-10-30 16:02:45 +00:00
Markus Himmel
c0ad969b14 fix: docstring of ByteArray.IsValidUTF8.intro (#11022)
This PR fixes an incomplete docstring.
2025-10-30 15:57:01 +00:00
AxelBoldt
e73e0901f8 doc: improve variable names and specify types in SMul doc (#10989)
When documenting smul : M → α → α, it is unintuitive and confusing to
use variables a:M and b:α. It is better to use m:M and a:α. I also
specified the types of all involved terms in the documentation text.
2025-10-30 15:56:42 +00:00
Henrik Böving
cc046e0c18 perf: improve join point finding (#10999)
This PR improves join point finding in the compiler through two means:
1. We now handle situations where a function `f` can only become a join
point when a function `g`
   becomes a join point as well correctly.
2. We introduce a second join point finding pass after specialisation
and before the following
simplification pass, as the specialiser might have introduced new join
point opportunities for
   the simplifier to exploit.

Notably in the code from #10995 we now correctly detect the missing join
point which required both
of these changes to be made.

Closes: #10995
2025-10-30 15:05:11 +00:00
Wrenna Robson
e11ef3ee4e fix: Remove redundant instance requirement (#10941)
This PR removes a redundant instance requirement from
`Std.instIrreflLtOfIsPreorderOfLawfulOrderLT`.
2025-10-30 13:21:26 +00:00
Kim Morrison
b2b385b456 chore: update stage0 2025-10-30 18:43:59 +11:00
Kim Morrison
7a8c2daf96 feat: sine qua non premise selection 2025-10-30 18:43:59 +11:00
Lean stage0 autoupdater
33e92677ba chore: update stage0 2025-10-30 07:41:23 +00:00
Markus Himmel
5af12df54b chore: add String.ofList redefine String.toList (#11016)
This PR ensures that `String.toList` and `String.ofList` exist and have
the right `extern` annotations.
2025-10-30 07:07:12 +00:00
Kim Morrison
705084d9ba chore: deprecate more duplications (#11004)
This PR deprecates various duplicated definitions, detected in
[#mathlib4 > duplicate declarations @
💬](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/duplicate.20declarations/near/547434277)
2025-10-30 05:58:29 +00:00
Joachim Breitner
e2f5938e74 refactor: some Meta.Match.Match refactorings (#11011)
This PR extracts some refactorings from #10763, including dropping dead
code and not failing in `inaccessibleAsCtor`, which leadas to (slightly)
better error messages, and also on the grounds that the failing
alternative may actually be unreachable.
2025-10-29 23:24:57 +00:00
Leonardo de Moura
d3c9056d2b feat: support grind parameters in finish and finish? (#11012)
This PR ensures the `grind` tactics `finish` and `finish?` can take
parameters.
2025-10-29 20:51:48 +00:00
Joachim Breitner
2f0f0a3018 chore: pr release: git commit --allow-empty (#11013)
This PR uses `--allow-empty` so that the PR release script does not fail
when it's being retried after an intermittent failure.
2025-10-29 21:48:11 +01:00
Henrik Böving
1587d02dfb fix: more stable eager lambda lifting heuristic (#11010)
This PR makes the eager lambda lifting heuristic more predictable by
blocking it from lifting from
any kind of inlineable function, not just `@[inline]`. It also adapts
the doc-string to describe
what is actually going on.
2025-10-29 13:58:23 +00:00
Henrik Böving
a51822ead2 perf: inline Decidable instances (#11008)
This PR inlines several Decidable instances for performance reasons.

Unlike the previous #10934 it does not attempt to also simplify the
Decidable instance system as
that has proven to have non trivial performance impact.

Co-authored-by: Rob23oba <152706811+Rob23oba@users.noreply.github.com>
2025-10-29 10:59:54 +00:00
Henrik Böving
2cfd980528 fix: revert the waitAny refactoring (#11000)
This PR fixes a memleak caused by the Lean based `IO.waitAny`
implementation by reverting it.

This the faulty Lean implementation:
```lean
def IO.waitAny (tasks : @& List (Task α)) (h : tasks.length > 0 := by exact Nat.zero_lt_succ _) :
    BaseIO α := do
  have : Nonempty α := ⟨tasks[0].get⟩
  let promise : IO.Promise α ← IO.Promise.new
  tasks.forM <| fun t => BaseIO.chainTask (sync := true) t promise.resolve
  return promise.result!.get
```
In a situation where we call this function repeatedly in a loop with a
pair of tasks `[t1, t2]`
where `t2` is a long lived task that we pass every time and `t1` is
fresh a short lived task, `t2` will
accumlate more and more children from `BaseIO.chainTask` that fill
memory over time. The old C++
implementation did not have this issue so we are reverting.
2025-10-29 08:27:16 +00:00
Henrik Böving
2497cf0b40 fix: Revert "perf: inline decidable instances" (#11007)
This PR reverts leanprover/lean4#10934
2025-10-29 08:06:51 +00:00
Markus Himmel
167429501b refactor: redefine String.replace (#10986)
This PR defines `String.Slice.replace` and redefines `String.replace` to
use the `Slice` version.

The new implementation is generic in the pattern, so it supports things
like `"education".replace isVowel "☃!" = "☃!d☃!c☃!t☃!☃!n"`. Since it
uses the `ForwardSearcher` infrastructure, `String` patterns are
searched using KMP, unlike the previous implementation which had
quadratic runtime. As a side effect, the behavior when replacing an
empty string now matches that of most other programming languages,
namely `"abc".replace "" "k" = "kakbkck"`.
2025-10-29 07:48:33 +00:00
Sebastian Graf
d427423917 chore: remove duplicate lemmas in Std.Do.SPred (#11006)
This PR removes the duplicate lemmas
`Std.Do.SPred.{and_pure,or_pure,imp_pure,entails_pure_intro}`.
2025-10-29 07:26:24 +00:00
Markus Himmel
106b0fa661 fix: KMP implementation (#10998)
This PR fixes the KMP implementation, which did incorrect bookkeeping of
the backtracking process, leading to incorrect starting ranges of
matches.

The new implementation does not require `partial` anywhere.
2025-10-29 06:04:45 +00:00
Kim Morrison
335e34df19 chore: add deprecations for duplicated theorems (#10967) 2025-10-29 05:26:16 +00:00
Leonardo de Moura
d436619c6d feat: add anchor support for restricting search space in grind only (#11003)
This PR adds support for specifying anchors to restrict the search space
in `grind` when using `grind only`. Anchors can limit which case splits
are performed and which local lemmas are instantiated.
2025-10-29 01:16:10 +00:00
Marc Huisinga
19533ab1d4 feat: revamp server logging (#10787)
This PR revamps the server logging mechanism to allow filtering the log
output by LSP method.
2025-10-28 16:26:59 +00:00
Leonardo de Moura
28310a77ad feat: config options at finish (#10997)
This PR adds support for configuration options at `finish` and
`finish?`.
2025-10-28 15:41:26 +00:00
Lean stage0 autoupdater
8ff5b8ec2c chore: update stage0 2025-10-28 13:47:28 +00:00
Leonardo de Moura
99ff606d58 chore: rename cutsat => lia (#10991)
This PR renames `cutsat` in configuration options and trace messages to
`lia`.
2025-10-28 12:25:48 +00:00
Kim Morrison
8862d23453 chore: cleanup in Dyadic API (#10994) 2025-10-28 06:41:46 +00:00
Kim Morrison
d8335bd661 feat: add @[grind ext] attributes for extensional maps (#10993)
This PR allows `grind` to work extensionally on extensional maps/sets.
2025-10-28 05:20:45 +00:00
Kim Morrison
1981c62604 feat: make grind +premises more robust to bad suggestions (#10992)
This PR ensures that `grind +premises` silently drops warnings and
errors about bad suggestions.
2025-10-28 03:22:42 +00:00
Leonardo de Moura
bb3dd13f72 feat: set_config for setting grind configuration options (#10990)
This PR adds the `set_config` tactic for setting `grind` configuration
options. It uses the same syntax used for setting configuration options
in the `grind` main tactic.
2025-10-28 02:25:01 +00:00
Joachim Breitner
808d123e6f doc: typo in grindDef docstring (#10988)
This PR fixes a typo in the `grindDef` docstring.
2025-10-27 15:59:06 +00:00
Joachim Breitner
14d76cc062 fix: decreasing_by: preserve variable names of match alts (#10980)
This PR tries to preserve names of pattern variables in match
alternatives in `decreasing_by`, by telescoping into the concrete
alternative rather than the type of the matcher's alt. Fixes #10976.
2025-10-27 14:00:36 +00:00
Markus Himmel
d2f76ade61 fix: search for empty string (#10985)
This PR ensures that searching for an empty string returns the expected
pattern of alternating size-zero matches and size-one rejects.

In particular, splitting by an empty string returns an array formed of
the empty string, all of the string's characters as singleton strings,
followed by another empty string. This matches the [Rust
behavior](https://doc.rust-lang.org/std/primitive.str.html#method.split),
for example.
2025-10-27 13:05:33 +00:00
Rob23oba
12750d25b5 perf: inline decidable instances (#10934)
This PR adds inline annotations to several `Decidable` instances.
Additionally, it removes the `Decidable` instance for `p → q` which is
made redundant by `forall_prop_decidable`.
2025-10-27 12:05:01 +00:00
Henrik Böving
334fa475b4 fix: use general allocator for closures (#10982)
This PR changes the closure allocator to use the general allocator
instead of the small object one.
This is because users may create closures with a gigantic amount of
closed variables which in turn
boost the size of the closure beyond the small object threshold.

This issue was uncovered by #10979. Detecting that the small object
threshold is at fault requires
building mimalloc in debug mode at which point it yields:
```
mimalloc: assertion failed: at "/home/henrik/lean4/build/debug/mimalloc/src/mimalloc/src/alloc.c":132, mi_heap_malloc_small_zero
  assertion: "size <= MI_SMALL_SIZE_MAX"
```
The generated code at fault here looks as follows:
```c
LEAN_EXPORT lean_object* l_initExec___at___00res_spec__0(lean_object* x_1) {
_start:
{
lean_object* x_2; lean_object* x_3; lean_object* x_4; lean_object* x_5; lean_object* x_6; lean_object* x_7; lean_object* x_8; lean_object* x_9; lean_object* x_10; lean_object* x_11; lean_object* x_12; lean_object* x_13; lean_object* x_14;
x_2 = lean_alloc_closure((void*)(l_initializer_ext___at___00initExec___at___00res_spec__0_spec__0___lam__0___boxed), 3, 0);
x_3 = l_initExec___redArg___closed__0;
x_4 = l_initExec___redArg___closed__1;
x_5 = l_instMonadLiftNonDetT___closed__0;
x_6 = l_initExec___redArg___closed__2;
x_7 = l_initExec___at___00res_spec__0___closed__0;
lean_inc_ref(x_2);
x_8 = lean_alloc_closure((void*)(l_initExec___at___00res_spec__0___lam__29___boxed), 213, 212);
lean_closure_set(x_8, 0, x_3);
lean_closure_set(x_8, 1, x_2);
lean_closure_set(x_8, 2, x_4);
lean_closure_set(x_8, 3, x_3);
lean_closure_set(x_8, 4, x_4);
lean_closure_set(x_8, 5, x_3);
lean_closure_set(x_8, 6, x_4);
lean_closure_set(x_8, 7, x_3);
lean_closure_set(x_8, 8, x_4);
lean_closure_set(x_8, 9, x_3);
lean_closure_set(x_8, 10, x_4);
lean_closure_set(x_8, 11, x_3);
lean_closure_set(x_8, 12, x_4);
lean_closure_set(x_8, 13, x_3);
lean_closure_set(x_8, 14, x_4);
lean_closure_set(x_8, 15, x_5);
lean_closure_set(x_8, 16, x_6);
lean_closure_set(x_8, 17, x_5);
lean_closure_set(x_8, 18, x_5);
lean_closure_set(x_8, 19, x_5);
lean_closure_set(x_8, 20, x_5);
lean_closure_set(x_8, 21, x_5);
lean_closure_set(x_8, 22, x_5);
...
```
With the crash happening in `lean_alloc_closure` where we
unconditionally invoke the small allocator
which cannot cope with closures this large. Hopefully changing this to
the general purpose allocator
doesn't have too much of an impact on performance.

Closes: #10979
2025-10-27 10:16:59 +00:00
Markus Himmel
8fe260de55 feat: termination arguments for String.ValidPos and String.Slice.Pos (#10933)
This PR adds the basic infrastructure to perform termination proofs
about `String.ValidPos` and `String.Slice.Pos`.

We choose approach where the intended way to do termination arguments is
to argue about the position itself rather than some projection of it
like `remainingBytes`.

The types `String.ValidPos` and `String.Slice.Pos` are equipped with a
`WellFoundedRelation` instance given by the greater-than relation. This
means that if a function takes a position `p` and performs a recursive
call on `q`, then the decreasing obligation will be `p < q`. This works
well in the common case where `q` is `p.next h`, in which case the goal
`p < p.next h` is solved by the simplifier.

For stepping through a string backwards, we introduce a type synonym
with a `WellFoundedRelation` instance given by the less-than relation.
This means that if a function takes a position `p` and performs a
recursive call on `q` and specifies `termination_by p.down`, then the
decreasing obligation will be `q < p`. This works well in the case where
`q` is `p.prev h`, in which case the goal `p.prev h < p` is solved by
the simplifier.

For termination arguments invoving multiple strings, the lower-level
primitive `p.remainingBytes` (landing in `Nat`) is also available.

In a future PR, we will additionally provide the necessary typeclasses
instances to register `String.ValidPos` and `String.Slice.Pos` with
`grind` to make complex termination arguments more convenient in user
code.
2025-10-27 10:05:44 +00:00
Henrik Böving
7e1be20317 perf: widen more in ElimDeadBranches (#10856)
This PR performs more widening in ElimDeadBranches in an attempt to
improve performance in situations with a lot of local precision.

While this is not enough to make the compilation instant it pushes
compilation time from 12s to 3s for the example in #10857 and barely
introduces regressions so it seems like a good first step in this
direction.

Closes: #10857
2025-10-27 09:12:16 +00:00
Leonardo de Moura
3a42ee0c30 feat: grind tactic mode improvements (#10978)
This PR implements the following `grind` improvements:
1. `set_option` can now be used to set `grind` configuration options in
the interactive mode.
2. Fixes a bug in the repeated theorem instantiation detection.
3. Adds the macro `use [...]` as a shorthand for `instantiate only
[...]`.
2025-10-27 04:47:02 +00:00
Kim Morrison
30ecacd625 feat: add LawfulOfScientific class (#10971)
This PR adds a `LawfulOfScientific` class, providing compatibility with
a `Lean.Grind.Field` structure.
2025-10-27 04:18:55 +00:00
Kim Morrison
a0e742be5e chore: >6 month old deprecations (#10969) 2025-10-26 22:48:41 +00:00
Leonardo de Moura
50e2fdaa74 feat: add cdot combinator in grind tactic mode (#10975)
This PR adds the combinator ` · t_1 ... t_n` to the `grind` interactive
mode. The `finish?` tactic now generates scripts using this combinator
to conform to Mathlib coding standards. The new format is also more
compact. Example:
```lean
/--
info: Try this:
  [apply] ⏎
    instantiate only [= mem_indices_of_mem, insert, = getElem_def]
    instantiate only [= getElem?_neg, = getElem?_pos]
    cases #f590
    · cases #ffdf
      · instantiate only
        instantiate only [= Array.getElem_set]
      · instantiate only
        instantiate only [size, = HashMap.mem_insert, = HashMap.getElem_insert, = Array.getElem_push]
    · instantiate only [= mem_indices_of_mem, = getElem_def]
      instantiate only [usr getElem_indices_lt]
      instantiate only [size]
      cases #ffdf
      · instantiate only [=_ WF]
        instantiate only [= getElem?_neg, = getElem?_pos, = Array.getElem_set]
        instantiate only [WF']
      · instantiate only
        instantiate only [= HashMap.mem_insert, = HashMap.getElem_insert, = Array.getElem_push]
-/
#guard_msgs in
example (m : IndexMap α β) (a a' : α) (b : β) (h : a' ∈ m.insert a b) :
    (m.insert a b)[a'] = if h' : a' == a then b else m[a'] := by
  grind => finish?
```
2025-10-26 21:27:00 +00:00
Sebastian Ullrich
77ddfd49e6 chore: further shake improvements (#10947) 2025-10-26 11:27:19 +00:00
Kim Morrison
4887eeb77c chore: remove >6 month old deprecations (#10968) 2025-10-26 10:01:30 +00:00
Kim Morrison
9cf2877945 fix: mis-stated lemmas about empty raw maps (#10966)
This PR fixes some mis-stated lemmas which should have been about the
`.Raw` variants of maps.
2025-10-26 07:51:39 +00:00
Leonardo de Moura
97d63db52c fix: mbtc for nonlinear terms in grind cutsat (#10965)
This PR ensures that model-based theory combination in `grind cutsat`
considers nonlinear terms. Nonlinear multiplications such as `x * y` are
treated as uninterpreted symbols in `cutsat`.

Closes #10885
2025-10-26 04:35:34 +00:00
Leonardo de Moura
f8b0beeba9 fix: propagator for a^(n+m) in grind (#10964)
This PR adds a propagator for `a^(n+m)` and removes its normalizer. This
change was motivated by issue #10661

Closes #10661
2025-10-26 03:52:28 +00:00
Leonardo de Moura
93c5bd0fdd chore: use realizeGlobalConstNoOverloadWithInfo (#10963)
closes #10427
closes #10426
2025-10-26 02:45:46 +00:00
Leonardo de Moura
feb864712f fix: spurious warning message in grind (#10962)
This PR fixes a spurious warning message in `grind`.

Closes #10670
2025-10-26 02:40:12 +00:00
Leonardo de Moura
2f3211028b feat: support for Rat scientific literals (#10961)
This PR adds support for scientific literals for `Rat` in `grind`.
`grind` does not yet add support for this kind of literal in arbitrary
fields.

closes #10489
2025-10-26 02:05:26 +00:00
Leonardo de Moura
cdaa827b2a fix: grind linarith counterexample (#10960)
This PR fixes a bug in the `grind linarith` model/counterexample
construction.

Closes #10500
2025-10-26 00:27:47 +00:00
Kim Morrison
a9d6bc60d0 chore: update stage0 2025-10-26 10:29:47 +11:00
Kim Morrison
9166c71e08 feat: don't count symbols in instances and proofs 2025-10-26 10:29:47 +11:00
Kim Morrison
43b2d41e81 chore: add test file 2025-10-26 10:29:47 +11:00
Kim Morrison
e8620255a0 feat: symbol frequency environment extension 2025-10-26 10:29:47 +11:00
Leonardo de Moura
48f0eb206c test: rationals in grind linarith (#10958) 2025-10-25 21:48:43 +00:00
Leonardo de Moura
962e7d5a30 test: for #10317 (#10957)
This PR adds tests for issue that has been fixed by previous commits.

closes #10317
2025-10-25 21:42:56 +00:00
Leonardo de Moura
aa59c01742 fix: equality propagation in grind order (#10956)
This PR fixes a bug in the equality propagation procedure in
`grind.order`. Specifically, it affects the procedure that asserts
equalities in the `grind` core state that are implied by (ring)
inequalities in the `grind.order` module.

closes #10622
2025-10-25 20:12:04 +00:00
Leonardo de Moura
cd60d9c14a fix: grind order regression (#10955)
This PR fixes a regression in the `grind order` module introduced by

Closes #10953
2025-10-25 16:12:28 +00:00
Eric Wieser
b3ef7c9f25 chore: add an assertion about mkValueTypeClosure (#10954)
This is a guard against #10705; if a kernel error is raised when the
return value of this function is eventually checked, it is often
silenced downstream, making it hard to spot the failure.
If we panic here via `assert!`, then the diagnostic cannot be missed.
2025-10-25 12:59:17 +00:00
Lean stage0 autoupdater
be2c2bcf9b chore: update stage0 2025-10-25 11:32:01 +00:00
Leonardo de Moura
d5ca0c7032 fix: bug in cutsat model construction (#10951)
This PR fixes a bug in the `cutsat` incremental model construction. The
model was not being reset when new (unsatisfied) equalities were
asserted.
2025-10-25 04:16:32 +00:00
Leonardo de Moura
3c2ab0fefa feat: model-based theory combination tactic and action (#10950)
This PR adds the `mbtc` tactic to the `grind` interactive mode. It
implements model-based theory combination. It also ensures `finish?` is
capable of generating it.
2025-10-25 03:35:19 +00:00
Leonardo de Moura
1643fd7532 fix: finish? checks whether solver propagation steps are needed (#10949)
This PR ensures that solver propagation steps are necessary in the
generated tactic script to close the goal.

It produces more compact proof scripts, but this is not just an
optimization, if we include an unnecessary step, we may fail to replay
the generated script when `cases` steps are pruned using
non-chronological backtracking (NCB). For example, when executing
`finish?`, we may have performed a `cases #<anchor>` step that enabled
`ring` to propagate a new fact. If this fact is not used in the final
proof, and the corresponding `cases #<anchor>` step is pruned by NCB,
the `ring` step will fail during replay.
2025-10-25 02:27:44 +00:00
Leonardo de Moura
53442d48f5 feat: finish? produces partial tactic scripts with sorry (#10948)
This PR ensures that `finish?` produces partial tactic scripts
containing `sorry`s.
We may add an option to disable this feature in the future.
It is enabled by default because it provides a useful way to debug
`grind` failures.
2025-10-24 23:47:30 +00:00
Joachim Breitner
96bace56fa fix: run enableRealizationsForConst on sizeOf decls (#10944)
This PR runs enableRealizationsForConst on sizeOf declarations. Fixes
#10573.
2025-10-24 16:15:38 +00:00
Sebastian Ullrich
b0127e01e3 chore: final module system fixes and refinements for initial Mathlib porting (#10869) 2025-10-24 15:53:49 +00:00
Joachim Breitner
e71d0abc7d test: test case for #10775 (#10943) 2025-10-24 14:54:36 +00:00
Joachim Breitner
a6d50a61b3 fix: Meta.Closure: topologically sort abstracted vars (#10926)
This PR topologically sorts abstracted vars in
`Meta.Closure.mkValueTypeClosure` if MVars are being abstracted.
Fixes #10705

---------

Co-authored-by: Eric Wieser <efw@google.com>
2025-10-24 12:07:16 +00:00
Sebastian Ullrich
dec007693a chore: fix C++ warning (#10922) 2025-10-24 11:09:08 +00:00
Henrik Böving
1145498521 fix: regression from ST redefinition (#10940)
This PR fixes a regression introduced by the `ST` redefinition by making
the definition of `ST` as
reducible as previously. The key issue here is that in the previous
state it would reduce to a
function at which point the monad lifting mechanisms don't kick in in
the same fashion anymore.
2025-10-24 08:50:56 +00:00
Leonardo de Moura
2f07b70870 fix: default parameter value in constructor footgun at cases tactic (#10939)
This PR fixes another instance of the “default parameter value in
constructor” footgun, which was affecting the `cases` tactic in the
`grind` interactive mode.
2025-10-24 00:56:15 +00:00
Leonardo de Moura
09b36c332a fix: missing processNewFacts at solver tactics (#10938)
This PR ensures solver `grind` tactics (e.g., `ac`, `ring`, `lia`, etc)
process pending facts after making progress.
2025-10-24 00:08:06 +00:00
Leonardo de Moura
955fff52c5 fix: missing reset ematch.num at cases (#10937)
This PR fixes a missing counter reset at the `cases` tactic in `grind`
interactive mode.
2025-10-23 23:58:36 +00:00
Leonardo de Moura
6d665f3e91 fix: bugs at grind => finish? (#10936)
This PR fixes issues in `grind => finish?` that were preventing
generated `grind` tactic scripts from being successfully replayed.
2025-10-23 22:35:20 +00:00
Joachim Breitner
74fd46894f fix: deprecation warning location with field notation (#10826)
This PR fixes the location of the “deprecated constant” and similar
error messages on field notation (`e.f`, `(e).f`, `e |>. f`). Fixes
#10821.
2025-10-23 20:55:25 +00:00
Joachim Breitner
ffaadcc990 doc: warning for wf_preprocess (#10897)
This PR adds a warning to `wf_preproces` that these lemmas can be used
to introduce hidden partiality.

---------

Co-authored-by: Rob23oba <152706811+Rob23oba@users.noreply.github.com>
2025-10-23 20:54:40 +00:00
Joachim Breitner
54175f3b99 fix: decreasing_by: remove mdata (#10931)
This PR strips the `Expr.mdata` that `WF.Fix` uses to associate goal
with recursive calls from the goal presented to the tactics.
Fixes #10895.
2025-10-23 20:54:32 +00:00
Markus Himmel
59573646c2 chore: more minor String improvements (#10930)
This PR moves some more material out of `Init.Data.String.Basic` and
fixes the incorrect name
`String.Pos.Raw.IsValidForSlice.le_utf8ByteSize`.
2025-10-23 13:57:23 +00:00
Markus Himmel
ba7798b389 chore: more reorganization of strings (#10928)
This PR splits more material out of `Init.Data.String.Basic`.
2025-10-23 11:56:11 +00:00
Henrik Böving
f1203f3d0d perf: used hashmaps for symbol lookup in the interpreter (#10927)
This PR uses hashmaps for the symbol lookups in the IR interpreter
instead of the existing rbmaps.
Thus reducing the constant overhead per function call.

---------

Co-authored-by: Sebastian Ullrich <sebasti@nullri.ch>
2025-10-23 11:45:20 +00:00
Henrik Böving
881a131ad3 chore: re-enable tests (#10923) 2025-10-23 08:38:57 +00:00
Lean stage0 autoupdater
fb3e2c15fd chore: update stage0 2025-10-23 08:03:18 +00:00
Rob23oba
fad0e69cc7 fix: make name mangling unambiguous (#10727)
This PR fixes name mangling to be unambiguous / injective by adding `00`
for disambiguation where necessary. Additionally, the inverse function,
`Lean.Name.unmangle` has been added which can be used to unmangle a
mangled identifier. This unmangler has been added to demonstrate the
injectivity but also to allow unmangling identifiers e.g. for debugging
purposes.

Closes #10724
2025-10-23 07:18:07 +00:00
Kim Morrison
cf22c367a1 feat: grind +premises (#10920)
This PR adds support for `grind +premises`, calling the currently
configured premise selection algorithm and including the results as
parameters to `grind`. (Recall that there is not currently a default
premise selector provided by Lean4: you need a downstream premise
selector to make use of this.)
2025-10-23 06:42:48 +00:00
Mac Malone
291d238ec4 test: symbol clash on private import of same def (#10915)
This PR adds a test for depending on two packages which privately import
modules that define the same Lean definition. It verifies the current
behavior of a symbol clash. This behavior will be fixed later this
quarter.
2025-10-23 03:42:52 +00:00
Kim Morrison
69e1eae480 feat: grind +lax ignores bad parameters (#10890)
This PR adds a `+lax` configuration option for `grind`, causing it to
ignore parameters referring to non-existent theorems, or to theorems for
which we can't generate a pattern. This allows throwing large sets of
theorems (e.g. from a premise selection enginre) into `grind` to see
what happens.
2025-10-23 03:19:31 +00:00
Leonardo de Moura
b1d4c9b9d5 feat: grind "silent" have (#10919)
This PR implements the `have <ident>? : <prop>` tactic for the `grind`
interactive mode. The proposition is proved using the default `grind`
search strategy. This tactic is also useful for inspecting or querying
the current `grind` state.
2025-10-23 02:36:49 +00:00
Leonardo de Moura
d748b0c8c9 feat: instantiate tactic parameter optimizer (#10916)
This PR implements parameter optimization for the generated
`instantiate` tactics produced by `finish?`.
We use a simple parameter optimizer that takes two sets as input: the
lower and upper bounds.
The lower bound consists of the theorems actually used in the proof
term, while the upper bound includes all the theorems instantiated in a
particular theorem instantiation step.
The lower bound is often sufficient to replay the proof, but in some
cases, additional theorems must be included because a theorem
instantiation may contribute to the proof by providing terms and many
not be present in the final proof term.
2025-10-23 01:22:33 +00:00
Kim Morrison
90af66d64b chore: minor changes to MePo (#10917)
This PR makes minor changes to the MePo premise selection algorithm.

I'm increasingly believing that MePo will not work well in Lean; I've
tried a few things without success. Alistair Geesing's thesis from 2023
had similar conclusions.

My intention is to reach the point we can properly benchmark premise
selection algorithms before doing any more work here.
2025-10-23 01:15:38 +00:00
Markus Himmel
3ce7d4ef5c chore: minor optimizations on the critical path (#10900)
This PR optimizes two `String` proofs and makes sure that
`MkIffOfInductiveProp` does not import `Lean.Elab.Tactic`, which
previously pushed it to the very end of the import graph.
2025-10-22 19:32:26 +00:00
Leonardo de Moura
63c06725bb feat: preserve instantiation order at finish? (#10899)
This PR ensures the generated `instantiate` tactic instantiates the
theorems using the same order used by `finish?`
2025-10-22 17:44:26 +00:00
Markus Himmel
b5dc11e8d3 chore: move some material out of Init.Data.String.Basic (#10893)
This PR splits some low-hanging fruit out of `Init.Data.String.Basic`:
basic material about `String.Pos.Raw`, `String.Substrig`, and
`String.Iterator`.

More splitting required and the remaining material is quite unorganized,
but it's a start.
2025-10-22 16:31:08 +00:00
Eric Wieser
08bc333705 perf: mark move constructors and assignment operators as noexcept (#10784)
Detected by
https://clang.llvm.org/extra/clang-tidy/checks/performance/noexcept-move-constructor.html.
This ensures constructions like `std::vector<object_ref>` call these
operators instead of the copy ones, and do not do extra refcounting.

Note that `optional` and `atomic` need something more complex using
`noexcept()`, as they are templated.
2025-10-22 14:21:51 +00:00
Henrik Böving
52b1b342ab feat: zero cost BaseIO (#10625)
This PR implements zero cost `BaseIO` by erasing the `IO.RealWorld`
parameter from argument lists and structures. This is a **major breaking
change for FFI**.

Concretely:
- `BaseIO` is defined in terms of `ST IO.RealWorld`
- `EIO` (and thus `IO`) is defined in terms of `EST IO.RealWorld`
- The opaque `Void` type is introduced and the trivial structure
optimization updated to account for it. Furthermore, arguments of type
`Void s` are removed from the argument lists of the C functions.
- `ST` is redefined as `Void s -> ST.Out s a` where `ST.Out` is a pair
of `Void s` and `a`

This together has the following major effects on our generated code:
- Functions that return `BaseIO`/`ST`/`EIO`/`IO`/`EST` now do not take
the dummy world parameter anymore. To account for this FFI code needs to
delete the dummy world parameter from the argument lists.
- Functions that return `BaseIO`/`ST` now return their wrapped value
directly. In particular `BaseIO UInt32` now returns a `uint32_t` instead
of a `lean_object*`. To account for this FFI code might have to change
the return type and does not need to call `lean_io_result_mk_ok` anymore
but can instead just `return` values right away (same with extracting
values from `BaseIO` computations.
- Functions that return `EIO`/`IO`/`EST` now only return the equivalent
of an `Except` node which reduces the allocation size. The
`lean_io_result_mk_ok`/`lean_io_result_mk_error` functions were updated
to account for this already so no change is required.

Besides improving performance by dropping allocation (sizes) we can now
also do fun new things such as:
```lean
@[extern "malloc"]
opaque malloc (size : USize) : BaseIO USize
```
2025-10-22 10:55:12 +02:00
Hikaru Hasegawa
6ee8511ae3 doc: fix example parenthesis in natAbs docstring (#10870)
This PR fixes an incorrect parenthesis in the `natAbs` docstring in
`src/Init/Data/Int/Basic.lean`.
2025-10-22 08:23:09 +00:00
Markus Himmel
6a1cc7d6b8 chore: minor String improvements (#10891)
This PR renames the cast functions on `String.ValidPos` for `set` and
`modify` to adhere to the established naming convention.

It also fixes two typos and very slighly tweaks the import graph,
shortening the critical path by a negligible amount.
2025-10-22 06:35:51 +00:00
Kim Morrison
2fb4d4bac2 chore: updates to release automation (#10888) 2025-10-22 03:17:28 +00:00
Leonardo de Moura
9b794befe0 feat: use new TermInfo.isDisplayableTerm when hovering grind anchors (#10887)
This PR uses the new `TermInfo.isDisplayableTerm` when hovering over
`cases` tactic anchors in the `grind` interactive mode.
2025-10-22 02:52:18 +00:00
Kim Morrison
38240612bc chore: add Rat.max_def lemma (#10886)
Closes #10842.
2025-10-22 00:38:52 +00:00
Mac Malone
3768c07654 fix: lake: cache revision path (#10883)
This PR fixes a bug with Lake's cache where revisions were stored at the
incorrect path. Revisions were stored at `<rev>/<pkg>.jsonl` rather than
the correct `<pkg>/<rev>.jsonl`.
2025-10-21 23:59:44 +00:00
Kim Morrison
466b0f824c chore: begin development cycle for v4.26 (#10884) 2025-10-21 23:22:58 +00:00
Kim Morrison
11eabdb000 chore: release_steps runs lake exe cache get when needed (#10882) 2025-10-21 22:49:38 +00:00
Leonardo de Moura
bd05f87d01 fix: grind proof instability (#10881)
This PR fixes a proof instability source in `grind`.

We say a proof is *unstable* if minor changes in the `.lean` file
containing the proof **affect** it.
2025-10-21 22:08:15 +00:00
Leonardo de Moura
56f3ca6fc7 fix: propagation in grind order (#10877)
This PR fixes theory propagation issue in `grind order`.
2025-10-21 16:38:39 +00:00
Sofia Rodrigues
94cb32bc46 fix: ipv4 address encoding from libuv to lean (#10854)
This PR fixes the IPv4 address encoding from libuv to lean
2025-10-21 14:17:22 +00:00
Leonardo de Moura
2f90b1dadd fix: elaborate grind state filter (#10874)
This PR uses the correct context for elaborating the `grind` state
filter.
2025-10-21 12:31:21 +00:00
Sebastian Graf
2991c66c81 chore: add missing spec lemmas for OptionT (#10867) 2025-10-21 12:01:35 +00:00
Eric Wieser
3f82b307aa fix: rule of 3 for xtimit (#10818)
This PR adds a missing move assignment operator, and deletes the copy
assignment operator.

C++ types should not implement move constructors without also
implementing move assignment. This also ensures that `m_fn` is correctly
emptied after a move, which is not guaranteed by the standard.

This change is also needed to allow `lean::optional` to be eventually
replaced by `std::optional`.
2025-10-21 12:01:23 +00:00
Sebastian Graf
bce47c6e0d fix: improve performance of mvcgen by optimizing try (mpure_intro; trivial) (#10872)
This PR improves the performance of `mvcgen` by an optimized
implementation for `try (mpure_intro; trivial)`. This tactic sequence is
used to eagerly discharge VCs and in the process instantiates schematic
variables.
2025-10-21 11:32:24 +00:00
Markus Himmel
b28daa6d60 chore: rename String.endPos -> String.rawEndPos (#10853)
This PR renames `String.endPos` to `String.rawEndPos`, as in a future
release the name `String.endPos` will be taken by the function that is
currently called `String.endValidPos`.
2025-10-21 11:25:30 +00:00
Markus Himmel
196d50156a fix: logic error in String.Slice.takeWhile (#10868)
This PR fixes a bug in `String.Slice.takeWhile` which caused it to get
its bookkeeping wrong and panic. The new version only uses safe
operations on `String.Slice.Pos`.
2025-10-21 09:52:11 +00:00
Sebastian Graf
2eb44b3cdc chore: fix a typo in the docstring for SeqRight and add documentation to getLevel (#10866) 2025-10-21 09:07:24 +00:00
Sebastian Graf
916125ae1c fix: make Std.Do.Spec.forIn'_list and friends more universe polymorphic (#10865)
This PR makes the spec `Std.Do.Spec.forIn'_list` and friends more
universe polymorphic.

The regression test came from a dicussion on the public Zulip.
2025-10-21 09:04:52 +00:00
Henrik Böving
bd0b91de07 perf: reduce amount of symbols in DLLs (#10864)
This PR reduces the amount of symbols in our DLLs by cutting open a
linking cycle of the shape:

`Environment -> Compiler -> Meta -> Environment`

This is achieved by introducing a dynamic call to the compiler hidden
behind a `Ref` as previously
done in the pretty printer.
2025-10-21 09:00:56 +00:00
Sebastian Ullrich
37b78bd53d chore: more module system fixes and refinements for finishing batteries port (#10819) 2025-10-21 08:19:50 +00:00
Marc Huisinga
2e3d947e07 feat: flag on TermInfo to force rendering of term in hover (#10805)
This PR adds a field `isDisplayableTerm` to `TermInfo` and all utility
functions which create `TermInfo` that can be set to force the language
server to render the term in hover popups.
2025-10-21 08:19:20 +00:00
Markus Himmel
a5a8f2779c chore: rename String.Range to Lean.Syntax.Range (#10852)
This PR renames `String.Range` to `Lean.Syntax.Range`, to reflect that
it is not part of the standard library.
2025-10-21 07:32:25 +00:00
Mac Malone
efbbb0b230 fix: lake: recurse directories in input_dir (#10861)
This PR fixes `input_dir` tracking to also recurse through
subdirectories. The `filter` of an `input_dir` will be applied to each
file in the directory tree (the path names of directories will not be
checked).

Closes #10827.
2025-10-21 04:19:10 +00:00
Leonardo de Moura
a366cbcd20 feat: show_term for grind interactive mode (#10862)
This PR implements the `show_term` combinator in `grind` interactive
mode.
2025-10-21 02:30:16 +00:00
Kim Morrison
756fee3e96 feat: improvements to release automation for v4.25.0-rc1 (#10860)
This PR improves the release automation. We link to CI output for
building the release tag, don't give instructions for bumping downstream
repositories until the release it ready, and improve documentation and
prompts.
2025-10-21 00:59:44 +00:00
Leonardo de Moura
2ead798d87 fix: set_option auto-completion in grind mode (#10859)
This PR fixes auto-completion for `set_option` in `grind` interactive
mode.
2025-10-21 00:53:35 +00:00
Leonardo de Moura
baacf86e7f feat: improve done tactic in grind interactive mode (#10858)
This PR improves the `done` tactic in `grind` interactive mode. It now
displays the `grind` state diagnostics for all unsolved subgoals.
2025-10-21 00:25:40 +00:00
Joachim Breitner
e3a5369bd7 perf: match compilation to use exfalso early (#10851)
This PR lets match compilation use exfalso as soon as no alternatives
are left. This way, the compiler does not have to look at subsequent
case splits.
2025-10-20 12:23:23 +00:00
Markus Himmel
c981ebc546 feat: split and splitInclusive iterators are finite (#10820)
This PR shows that the iterators returned by `String.Slice.split` and
`String.Slice.splitInclusive` are finite as long as the forward matcher
iterator for the pattern is finite (which we already know for all of our
patterns).

At actually also completely redefines the iterators to avoid the inner
loop in `Internal.nextMatch` which generates inefficient code. Instead,
when encountering a mismach from the matcher, we `skip` the split
iterator.
2025-10-20 10:21:21 +00:00
Paul Reichert
71f1a6c164 feat: Iterator find? consumer and variants (#10769)
This PR adds a `find?` consumer in analogy to `List.find?` and variants
thereof.
2025-10-20 09:12:53 +00:00
Sebastian Ullrich
0d5869bb71 fix: stuck "Missing alternative name" with incremental processing (#10848)
This PR fixes an issue where adding a missing case name after the pipe
in `induction` would not remove the now-obsolete error message.

Fixes #10847
2025-10-20 08:00:48 +00:00
Leonardo de Moura
135e7e7bd3 fix: instance tactic generation at finish? (#10846)
This PR fixes a few issues on `instance only [...]` tactic generation at
`finish?`.
2025-10-20 03:10:38 +00:00
Kim Morrison
58a884ef06 chore: update actions/checkout action in lake new template (#10845)
This PR update the `lake new` template to use the current version of the
`actions/checkout` Github workflow.
2025-10-20 02:32:52 +00:00
Kim Morrison
77e72afe0a chore: tweak error message about weak options (#10844)
This PR tweaks the error message about options defined in libraries.
This was relevant for an option defined in Mathlib, but set in FLT.
2025-10-20 02:28:20 +00:00
Leonardo de Moura
823671f744 feat: set_option tactic in grind interactive mode (#10843)
This PR implements the `set_option` tactic in `grind` interactive mode.
2025-10-20 00:44:59 +00:00
Leonardo de Moura
681724a8cf feat: generate instantiate only [...] at finish? (#10841)
This PR improves the `grind` tactic generated by the `instantiate`
action in tracing mode. It also updates the syntax for the `instantiate`
tactic, making it similar to `simp`. For example:

* `instantiate only [thm1, thm2]` instantiates only theorems `thm1` and
`thm2`.
* `instantiate [thm1, thm2]` instantiates theorems marked with the
`@[grind]` attribute **and** theorems `thm1` and `thm2`.

The action produces `instantiate only [...]` tactics. Example:

```lean
/--
info: Try this:
  [apply] ⏎
    instantiate only [= Array.getElem_set]
    instantiate only [= Array.getElem_set]
-/
#guard_msgs in
example (as bs cs : Array α) (v₁ v₂ : α)
        (i₁ i₂ j : Nat)
        (h₁ : i₁ < as.size)
        (h₂ : bs = as.set i₁ v₁)
        (h₃ : i₂ < bs.size)
        (h₄ : cs = bs.set i₂ v₂)
        (h₅ : i₁ ≠ j ∧ i₂ ≠ j)
        (h₆ : j < cs.size)
        (h₇ : j < as.size) :
    cs[j] = as[j] := by
  grind => finish?
```

Recall that `finish?` replays generated tactics before suggesting them.

The `instantiate` action inspects the generated proof term to decide
which theorems to include as parameters in the `instantiate only [...]`
tactic. However, in some cases, a theorem contributes only by adding a
term to the state. In such cases, the generated tactic cannot be fully
replayed, and the action uses
`instantiate approx [<thms instantiated>]` to indicate which parts of
the tactic script are approximate. The `approx` is just a hint for
users.
2025-10-19 23:35:27 +00:00
Lean stage0 autoupdater
28dd72d514 chore: update stage0 2025-10-19 23:45:51 +00:00
Leonardo de Moura
61ee3b2711 feat: expose optionValue parser (#10839)
This PR exposes the `optionValue` parser used to implement the
`set_option` notation.
2025-10-19 22:57:47 +00:00
Leonardo de Moura
206eb73cd9 feat: finish? tactic for grind interactive mode (#10837)
This PR implements the `finish?` tactic for the `grind` interactive
mode. When it successfully closes the goal, it produces a code action
that allows the user to close the goal using explicit grind tactic
steps, i.e., without any search. It also makes explicit which solvers
have been used.

This is just the first version, we will add many "bells and whistles"
later. For example, `instantiate` steps will clearly show which theorems
have been instantiated.

Example:

```lean
/--
info: Try this:
  [apply] ⏎
    cases #b0f4
    next => cases #50fc
    next => cases #50fc <;> lia
-/
#guard_msgs in
example (p : Nat → Prop) (x y z w : Int) :
    (x = 1 ∨ x = 2) →
    (w = 1 ∨ w = 4) →
    (y = 1 ∨ (∃ x : Nat, y = 3 - x ∧ p x)) →
    (z = 1 ∨ z = 0) → x + y ≤ 6 := by
  grind => finish?
```

The anchors in the generated script are based on stable hash codes.
Moreover, users can hover over them to see the exact term used in the
case split. `grind?` will also be implemented using the new framework.
2025-10-19 03:52:32 +00:00
Leonardo de Moura
09f22203f8 feat: add SolverExtension.action and Solvers.mkAction (#10836)
This PR implements support for `Action` in the `grind` solver extensions
(`SolverExtension`). It also provides the `Solvers.mkAction` function
that constructs an `Action` using all registered solvers. The generated
action is "fair," that is, a solver cannot prevent other solvers from
making progress.
2025-10-19 00:53:45 +00:00
Leonardo de Moura
ef23782608 feat: ring action (#10834)
This PR implements the `ring` action for `grind`.
2025-10-18 22:01:51 +00:00
Leonardo de Moura
e2b5747f4b feat: evalTactic in GrindM (#10833)
This PR implements infrastructure for evaluating `grind` tactics in the
`GrindM` monad. We are going to use it to check whether auto-generated
tactics can effectively close the original goal.
2025-10-18 17:02:36 +00:00
Markus Himmel
dad541265c refactor: move operations on String.Pos.Raw to the String.Pos.Raw namespace (#10735)
This PR moves many operations involving `String.Pos.Raw` to a the
`String.Pos.Raw` namespace with the eventual aim of freeing up the
`String` namespace to contain operations using `String.ValidPos` (to be
renamed to `String.Pos`) instead.

This PR adds the `String.ValidPos.set` and `String.ValidPos.modify`
functions.

After this PR, `String.pos_lt_eq` is no longer a `simp` lemma. Add
`String.Pos.Raw.lt_iff` as a `simp` lemma if your proofs break.
2025-10-18 12:12:55 +00:00
Markus Himmel
ca7a8e18b7 refactor: rename String.split to String.splitToList (#10822)
This PR renames `String.split` to `String.splitToList`, because soon the
name `String.split` will be used by a new implementation which is
superior because it is polymorphic over the pattern kind and it returns
an iterator of slices instead of a list of strings.
2025-10-18 12:12:54 +00:00
Sebastian Ullrich
721ffe5713 chore: CI: disable tree-less clone on nightly release 2025-10-18 13:32:04 +02:00
Leonardo de Moura
c76411d6c5 feat: compact notation for inspecting grind state (#10828)
This PR implements a compact notation for inspecting the `grind` state
in interactive mode. Within a `grind` tactic block, each tactic may
optionally have a suffix of the form `| filter?`.

Examples:

```lean
instantiate | gen > 0  -- Displays terms in the `grind` state after executing `instantiate` with generation greater than zero
```

```lean
instantiate |  -- Displays the `grind` state after executing `instantiate`
```

Remark: If the user places the cursor one space before `|`, the state
*before* executing `instantiate` is displayed.
This PR removes the code that was silently displaying the `grind` state
after each tactic step, as it was too noisy.
It also updates the notation for the `first` combinator in the `grind`
tactic mode to avoid conflicts with the new syntax.
2025-10-17 19:54:23 +00:00
Joachim Breitner
c22100036c fix: more pedantic checking of inaccessible patterns (#10796)
This PR changes match compilation to reject some pattern matches that
were previously accepted due to inaccessible patterns sometimes treated
like accessible ones. Fixes #10794.
2025-10-17 17:02:54 +00:00
Sebastian Ullrich
5800ce17b3 chore: CI: upgrade all git checkouts to tree-less clones (#10814) 2025-10-17 16:23:42 +00:00
Leonardo de Moura
78ab60d045 feat: cases? tactic for grind interactive mode (#10824)
This PR implements the `cases?` tactic for the `grind` interactive mode.
It provides a convenient way to select anchors. Users can filter the
candidates using the filter language. Examples:

<img width="1454" height="399" alt="image"
src="https://github.com/user-attachments/assets/fc370c2e-97f9-4d68-93a6-f0ebf33499f8"
/>

<img width="1447" height="166" alt="image"
src="https://github.com/user-attachments/assets/6c9c3707-79f7-4c63-8007-8d0aaedecc45"
/>
2025-10-17 15:44:19 +00:00
Sofia Rodrigues
f9adafe54d feat: adds acceptSelector and modified selectors (#10667)
This PR adds more selectors for TCP and Signals.

It also fixes a problem with `Selectors` that they cannot be closures
over a promise, otherwise it causes the waiter promise to never be
dropped.
2025-10-17 14:53:46 +00:00
Sebastian Ullrich
69d8d63d58 feat: hint about inaccessible private declaration on dot notation failure (#10803)
This PR improves the error message of generalized field notation if the
issue is that the resolved declaration is not visible in the current
context.
2025-10-17 09:31:56 +00:00
Sebastian Ullrich
dc7c184ee2 chore: CI: introduce fast-ci label 2025-10-17 08:45:41 +02:00
Sebastian Ullrich
e43ff50e76 chore: CI: revert macOS tests accidentally run on PRs 2025-10-17 08:45:41 +02:00
Leonardo de Moura
4ce7ad19ce feat: lia, linarith, and ac actions (#10812)
This PR implements `lia`, `linarith`, and `ac` actions for `grind`
interactive mode.
2025-10-17 03:56:21 +00:00
Leonardo de Moura
2a70da50c1 feat: proper case-split anchor generation in splitNext for grind? and finish? (#10811)
This PR implements proper case-split anchor generation in the
`splitNext` action, which will be used to implement `grind?` and
`finish?`.
2025-10-17 03:07:13 +00:00
Kim Morrison
effde06296 chore: add public modifiers in Lean.Elab.Tactic.Induction (#10810) 2025-10-16 21:52:02 +00:00
Kim Morrison
127fe785a3 chore: add public modifiers in Lean.Elab.Tactic.Ext (#10809)
This PR restores further definitions to `public`, after #10699.
2025-10-16 21:48:41 +00:00
Sebastian Ullrich
663df8f7e8 feat: backward.privateInPublic option (#10807)
This PR introduces the `backward.privateInPublic` option to aid in
porting projects to the module system by temporarily allowing access to
private declarations from the public scope, even across modules. A
warning will be generated by such accesses unless
`backward.privateInPublic.warn` is disabled.
2025-10-16 20:51:45 +00:00
Sebastian Ullrich
428355cf02 chore: remove redundant imports in core (#10750) 2025-10-16 20:27:46 +00:00
Sebastian Ullrich
83126883d9 chore: CI: overhaul check level logic (#10806)
The logic was *still* wrong after two PRs so let's get rid of
`check-level` as a matrix entry and trust in simple bools.
2025-10-16 20:27:02 +00:00
Sebastian Ullrich
5c7b003191 chore: lean.code-workspace: fix terminal cwd (#10802) 2025-10-16 20:19:12 +00:00
Leonardo de Moura
8a1b6e0f71 feat: compress generated grind tactic sequences using <;> (#10808)
This PR implements support for compressing auto-generated `grind` tactic
sequences.
2025-10-16 18:14:33 +00:00
Leonardo de Moura
7087c4a039 feat: add splitNext grind action (#10801)
This PR implements the `splitNext` action for `grind`.
2025-10-16 17:28:14 +00:00
Rob23oba
b7ea66d8d3 fix: consider underscores in getHexNumSize (#10719)
This PR fixes `getHexNumSize` to consider underscores. Previously, only
the amount of bytes was counted, making it output 9 for `1234_abcd`
instead of the actual number of digits, which is 8.
2025-10-16 13:57:58 +00:00
Joachim Breitner
10d6232594 chore: remove test for #10766 (#10804)
the tested situation (kernel runs into deep recursion but elaborator is
happy) is not very stable and depends on, for example, stack size. This
test is not worth that hassle.
2025-10-16 11:11:29 +00:00
Wojciech Różowski
5b35d6192c feat: redefine HashSet.union and add lemmas (#10611)
This PR adds adds union operation on `DHashMap`/`HashMap`/`HashSet` and
their raw variants and provides lemmas about union operations.

---------

Co-authored-by: Paul-Lez <paul.lezeau@gmail.com>
Co-authored-by: Markus Himmel <markus@lean-fro.org>
Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
2025-10-16 08:43:01 +00:00
Joachim Breitner
8748031853 fix: only run processInaccessibleAsCtor if there is at least one constructor around (#10793)
This PR fixes #10792.
2025-10-16 08:20:55 +00:00
Marc Huisinga
ac499323af chore: add .vscode/settings.json to .gitignore (#10795)
This PR adds `.vscode/settings.json` to our `.gitignore`, which allows
Lean 4 developers to set local workspace settings. We already use the
the workspace file for settings in core, so this shouldn't cause any
problems.
2025-10-16 07:08:41 +00:00
Kim Morrison
def3c97dbf chore: make extCore and customEliminators public for Batteries (#10799)
This PR restores two declarations to `public`, that were made non-public
in #10699, apparently breaking Batteries.
2025-10-16 05:01:23 +00:00
Kim Morrison
8db3969f87 chore: remove bad grind _=_ annotation on List.contains_iff_mem (#10800) 2025-10-16 04:00:42 +00:00
Leonardo de Moura
2f93363752 feat: intro and assertAll as actions (#10798)
This PR implements the `grind` actions `intro`, `intros`, `assertNext`,
`assertAll`.
2025-10-15 19:47:48 +00:00
Marc Huisinga
4329eae8d4 fix: unknown identifier minimization (#10797)
This PR fixes a bug in the unknown identifier code actions where the
identifiers wouldn't be correctly minimized in nested namespaces. It
also fixes a bug where identifiers would sometimes be minimized to
`[anonymous]`.

The first bug was introduced in #10619.
2025-10-15 19:25:27 +00:00
Leonardo de Moura
114f7e42f1 feat: lazy message with grind state (#10791)
This PR adds a silent info message with the `grind` state in its
interactive mode. The message is shown only when there is exactly one
goal in the grind interactive mode. The condition is a workaround for
current limitations of our `InfoTree`.
2025-10-15 15:03:07 +00:00
Sebastian Ullrich
419982bd42 chore: even more module system fixes and refinements from Mathlib porting (#10726) 2025-10-15 14:59:09 +00:00
Joachim Breitner
8431088c93 fix: preserve error locations when expanding match arms (#10783)
This PR ensures that error messages such as “redundant alternative” have
the right error location even if the arms share their RHS. Fixes #10781.
2025-10-15 13:31:42 +00:00
Sebastian Ullrich
803ec8ff9d chore: CI: re-enable mistakenly deactivated tests for Linux Lake (#10788) 2025-10-15 13:20:26 +00:00
Sebastian Ullrich
c4747752fe fix: detect private references in inferred type of public def (#10762)
This PR fixes an inconsistency in the module system around defs with
elided types.
2025-10-15 12:51:54 +00:00
Joachim Breitner
ed4d453346 refactor: processLeaf: Only look at first alt (#10774)
This PR lets match compilation look only at the first remaining
alternative in `processLeaf`. At this point we have no further variables
we can split on, so if the first one isn’t applicable, match compilation
should fail.
2025-10-15 10:10:52 +00:00
David Thrane Christiansen
45df6fcd37 fix: hovers and docstrings for (co)inductive types (#10738)
This PR fixes a regression introduced by #10307, where hovering the name
of an inductive type or constructor in its own declaration didn't show
the docstring. In the process, a bug in docstring handling for
coinductive types was discovered and also fixed. Tests are added to
prevent the regression from repeating in the future.
2025-10-15 09:32:11 +00:00
Sebastian Graf
4077bf2c05 feat: implement mvcgen?, expanding to mvcgen invariants? (#10782)
This PR implements a hint tactic `mvcgen?`, expanding to `mvcgen
invariants?`

Example:
```
/--
info: Try this:
  [apply] mvcgen invariants?
---
info: Try this:
  [apply] mvcgen [mySum] invariants?
---
info: Try this:
  [apply] mvcgen +elimLets invariants?
---
info: Try this:
  [apply] mvcgen +elimLets [mySum] invariants?
-/
#guard_msgs (info) in
theorem mySum_suggest_invariant_short (l : List Nat) : mySum l = l.sum := by
  generalize h : mySum l = r
  apply Id.of_wp_run_eq h
  mvcgen?
  mvcgen? [mySum]
  mvcgen? +elimLets
  mvcgen? +elimLets [mySum]
  all_goals admit
```
2025-10-15 08:22:09 +00:00
Joachim Breitner
54a3fbf88f fix: improve error message when decide +kernel fails (#10780)
This PR improves the error message when `decide +kernel` fails in the
kernel, but not the elaborator. Fixes #10766.
2025-10-15 07:11:27 +00:00
Leonardo de Moura
746206c5e6 feat: hover information for grind anchors (#10779)
This PR implements hover information for `grind` anchors. Anchors are
stable hash codes for referencing terms in the grind state. The anchors
will be used when auto generating tactic scripts. The hover display the
following information:

1- In the `instantiate` tactic, it displays the type of the theorem
being instantiated.
<img width="952" height="125" alt="image"
src="https://github.com/user-attachments/assets/be949b87-cf9b-4f75-abe0-17751295de93"
/>

2- In the `cases` tactic, the hover information depends on the kind of
case-split.
  a) Proposition
<img width="1019" height="125" alt="image"
src="https://github.com/user-attachments/assets/253e2927-f18e-49ab-a8fc-2144657406d8"
/>

b) A hypotheses. In this case, you can opt to replace the anchor with
the hypothesis' name if it is accessible.
<img width="1019" height="178" alt="image"
src="https://github.com/user-attachments/assets/858b3751-4ef9-492d-a42f-c0743753a7de"
/>

c) A term. The hover displays just the type, by `grind` logs a silent
information with additional information
  
<img width="1376" height="148" alt="image"
src="https://github.com/user-attachments/assets/30078ca4-a886-49d9-912e-866f3567b0da"
/>
2025-10-15 02:43:11 +00:00
Leonardo de Moura
88141a0a49 feat: hygiene for grind interactive mode (#10778)
This PR ensures that `grind` interactive mode is hygienic. It also adds
tactics for renaming inaccessible names: `rename_i h_1 ... h_n` and
`next h_1 ... h_n => ..`, and `expose_names` for automatically generated
tactic scripts. The PR also adds helper functions for implementing
case-split actions.
2025-10-15 01:27:51 +00:00
Kim Morrison
b17afe0f06 feat: improvements to release automation (#10777)
This PR improves the scripts assisting with cutting Lean releases (by
reporting CI status of open PRs, and adding documentation), and adds a
`.claude/commands/release.md` prompt file so Claude can assist.
2025-10-15 00:28:26 +00:00
Paul Reichert
7632cefa87 feat: hash map iterators (#10761)
This PR provides iterators on hash maps.
2025-10-14 15:10:01 +00:00
Paul Reichert
7a47bfa208 feat: flatMap iterator combinator (#10728)
This PR introduces the `flatMap` iterator combinator. It also adds
lemmas relating `flatMap` to `toList` and `toArray`.
2025-10-14 12:50:54 +00:00
Sebastian Ullrich
ae6335f115 chore: demote Intel macOS to Tier 2 platform (#10770) 2025-10-14 12:10:06 +00:00
Paul Reichert
f58999a7a6 refactor: use Shrink stub in the iterator framework (#10725)
This PR introduces a no-op version of `Shrink`, a type that should allow
shrinking small types into smaller universes given a proof that the type
is small enough, and uses it in the iterator library. Because this type
would require special compiler support, the current version is just a
wrapper around the inner type so that the wrapper is equivalent, but not
definitionally equivalent.

While `Shrink` is unable to shrink universes right now, but introducing
it now will allow us to generalize the universes in the iterator library
with fewer breaking changes as soon as an actual `Shrink` is possible.
2025-10-14 10:22:14 +00:00
Lean stage0 autoupdater
888b59bf95 chore: update stage0 2025-10-14 08:04:41 +00:00
Markus Himmel
1dae353575 chore: duplicate some String functions ahead of deprecation (#10768)
This PR is split off from #10735 for boring bootstrapping reasons.
2025-10-14 07:36:05 +00:00
Leonardo de Moura
a4b788c332 feat: add Grind/Action.lean (#10767)
This PR implements the new control interface for implementing `grind`
search strategies. It will replace the `SearchM` framework.
2025-10-14 03:21:51 +00:00
Sebastian Ullrich
5865c41a76 chore: lean.code-workspace: always open terminal in root folder (#10745) 2025-10-13 14:12:35 +00:00
Marc Huisinga
4b0e8d88ce fix: don't display CSS color picker in Lean files in VS Code (#10757)
This PR fixes a bug in combination with VS Code where Lean code that
looks like CSS color codes would display a color picker decoration.

VS Code displays this decoration by default for all languages, not just
CSS. Due to https://github.com/microsoft/vscode/issues/91533, this
setting cannot be disabled in the client on a per-language basis.
However, we can override the default behavior by providing a color
provider of our own. This PR implements an empty color provider to
override the VS Code one.
2025-10-13 13:39:16 +00:00
Marc Huisinga
9d427fdfcf feat: "try this" messages with support for interactivity (#10524)
This PR adds support for interactivity to the combined "try this"
messages that were introduced in #9966. In doing so, it moves the link
to apply a suggestion to a separate `[apply]` button in front of the
suggestion. Hints with diffs remain unchanged, as they did not
previously support interacting with terms in the diff, either.

<img width="379" height="256" alt="Suggestion with interactive message"
src="https://github.com/user-attachments/assets/7838ebf6-0613-46e7-bc88-468a05acbf51"
/>
2025-10-13 13:39:03 +00:00
Kim Morrison
fe1e7d56f4 chore: restore #8656 (#10758)
This PR restores the change in #8656, which removed `autoImplicit =
false` from the default lake template (per previous discussions linked
there). This was accidentally reverted in #8866.
2025-10-13 10:34:01 +00:00
Markus Himmel
fbe98d76b2 fix: turn meta import into import in Init.Data.ToString (#10754)
This PR makes sure that we always properly import
`Init.Data.ToString.Name` when importing `Init`.
2025-10-13 09:20:48 +00:00
Joachim Breitner
9a5e425990 refactor: no public section in Elab.Induction (#10699)
This PR removes `public section` in `Elab.Induction`.
2025-10-13 09:02:36 +00:00
Leonardo de Moura
14ff08db6f feat: repeat tactical for grind interactive mode (#10748)
This PR implements the `repeat` tactical for the `grind` interactive
mode.
2025-10-12 22:05:58 +00:00
Sebastian Ullrich
316859e871 perf: reset InfoState.lazyAssignment before each command (#10744)
This PR fixes a performance regression introduced in #10518. More
generally, it ensures both message log and info state are per-command,
which has been the case in practice ever since the asynchronous language
driver was introduced.
2025-10-12 09:27:14 +00:00
Leonardo de Moura
47dbcd4b93 feat: finish? and grind? infrastructure (#10747)
This PR implements infrastructure for `finish?` and `grind?` tactics.
2025-10-12 02:48:16 +00:00
Leonardo de Moura
4f7d3bb692 feat: instantiate tactic parameters (#10746)
This PR implements parameters for the `instantiate` tactic in the
`grind` interactive mode. Users can now select both global and local
theorems. Local theorems are selected using anchors. It also adds the
`show_thms` tactic for displaying local theorems. Example:

```lean
example (as bs cs : Array α) (v₁ v₂ : α)
        (i₁ i₂ j : Nat)
        (h₁ : i₁ < as.size)
        (h₂ : bs = as.set i₁ v₁)
        (h₃ : i₂ < bs.size)
        (h₃ : cs = bs.set i₂ v₂)
        (h₄ : i₁ ≠ j ∧ i₂ ≠ j)
        (h₅ : j < cs.size)
        (h₆ : j < as.size)
        : cs[j] = as[j] := by
  grind =>
    instantiate = Array.getElem_set
    instantiate Array.getElem_set
```
2025-10-11 21:35:21 +00:00
Lean stage0 autoupdater
0dc862e3ed chore: update stage0 2025-10-11 05:57:21 +00:00
Mac Malone
d9ee24bf36 fix: lake: local cache w/ --old (#10741)
This PR fixes a bug where partially up-to-date files built with `--old`
could be stored in the cache as fully up-to-date. Such files are no
longer cached. In addition, builds without traces now only perform an
modification time check with `--old`. Otherwise, they are considered
out-of-date.
2025-10-11 02:20:31 +00:00
Mac Malone
0639d49a4c feat: scope output cache by platform & toolchain (#10730)
This PR changes the Lake's remote cache interface to scope cache outputs
by toolchain and/or platform were useful.

Packages that set `platformIndependent = true` will not be scoped by
platform and the core build (i.e., `bootstrap = true`) will not be
scoped by toolchain. Lake's detected platform and toolchain can be
overridden with the new `--platform` and `--toolchain` options to `cache
get` and `cache put`.

Lake no longer accepts the `--scope` option when using `cache get` with
Reservoir.. The `--repo` option must be used instead.
2025-10-11 02:17:39 +00:00
Lean stage0 autoupdater
3a26eb7281 chore: update stage0 2025-10-10 22:22:55 +00:00
Joachim Breitner
830be29422 feat: generate equational theorems uniformly (#10734)
This PR follows upon #10606 and creates equational theorems uniformly
from the unfold theorem, there is only one handler registered in
`registerGetEqnsFn`.

For now we keep `registerGetEqnsFn`, because it’s used by mathlib’s
`irreducible_def`, but I’d like to get rid of it in the long term,
relying only on `registerGetUnfoldEqnFn` for constructions that should
unfold differently.
2025-10-10 21:35:09 +00:00
Leonardo de Moura
2a8c03109a feat: improve ac, linarith, lia, and ring in grind interactive mode (#10740)
This PR improves the tactics `ac`, `linarith`, `lia`, `ring` tactics in
`grind` interactive mode. They now fail if no progress has been made.
They also generate an info message with counterexample/basis if the goal
was not closed.
2025-10-10 21:04:26 +00:00
Leonardo de Moura
07f8ab533c feat: add tactics to grind interactive mode (#10737)
This PR adds the tactics `linarith`, `ac`, `fail`, `first`, `try`,
`fail_if_success`, and `admit` to `grind` interactive mode.
2025-10-10 20:24:07 +00:00
Paul Reichert
a73ebe8a77 feat: any/all predicates for iterators (#10686)
This PR introduces `any`, `anyM`, `all` and `allM` for pure and monadic
iterators. It also provides lemmas about them.
2025-10-10 19:24:10 +00:00
Paul Reichert
3931a72573 feat: SInt ranges (#10633)
This PR provides range support for the signed finite number types
`Int{8,16,32,64}` and `ISize`. The proof obligations are handled by
reducing all of them to proofs about an internal `UpwardEnumerable`
instance for `BitVec` interpreted as signed numbers.
2025-10-10 17:07:20 +00:00
Wojciech Różowski
bf809b5298 chore: change the location of error message for coinductive predicates (#10722)
This PR changes where errors are displayed when trying to use
`coinductive` keyword when targeting things that do not live in `Prop`.
Instead of displaying the error above the first element of the mutual
block, it is displayed above the erroneous definition.

---------

Co-authored-by: Rob23oba <152706811+Rob23oba@users.noreply.github.com>
2025-10-10 16:06:18 +00:00
Joachim Breitner
4b6f07060d feat: remove support for reducible well-founded recursion (#10714)
This PR removes support for reducible well-founded recursion, a Breaking
Change. Using `@[semireducible]` on a definition by well-founded
recursion prints a warning that this is no longer effective.

With the upcoming module system, proofs are often not available. With
this change, we remove a fringe use case hat may require proofs, and
that would not be supported under the module system anyways.

At least for now, direct use of `WellFounded.fix` is not affected.

This fixes: #5192
2025-10-10 15:48:28 +00:00
David Thrane Christiansen
09092549d0 fix: Verso docstring semantic highlighting fixes (#10662)
This PR re-enables semantic tokens for Verso docstrings, after a prior
change accidentally disabled them. It also adds a test to prevent this
from happening again.

In the process, it became clear that there was a bug. The highlighting
strategy led to overlapping but not identical tokens, but the code had
previously assumed that this couldn't happen at the delta-encoding step.
So this PR additionally replaces the removal of duplicate tokens with
priority-based handling of overlapping tokens.

---------

Co-authored-by: Marc Huisinga <mhuisi@protonmail.com>
2025-10-10 11:57:02 +00:00
Joachim Breitner
1b4360c32a fix: unfold more auxillary theorems in termination checking (#10733)
This PR unfolds auxillary theorems more aggressively during termination
checking. This fixes #10721.
2025-10-10 11:09:28 +00:00
Cameron Zwarich
705dac4f77 chore: make @hargoniX code owner of the compiler (#10732) 2025-10-10 04:43:38 +00:00
Leonardo de Moura
3bab621364 feat: add grind interactive mode tactics (#10731)
This PR adds the following tactics to the `grind` interactive mode:
- `focus <grind_tac_seq>`
- `next => <grind_tac_seq>`
- `any_goals <grind_tac_seq>`
- `all_goals <grind_tac_seq>`
- `grind_tac <;> grind_tac`
- `cases <anchor>`
- `tactic => <tac_seq>`

Example:
```lean
def g (as : List Nat) :=
  match as with
  | []      => 1
  | [_]     => 2
  | _::_::_ => 3

example : g bs = 1 → g as ≠ 0 := by
  grind [g.eq_def] =>
    instantiate
    cases #ec88
    next => instantiate
    next => finish
    tactic =>
      rw [h_2] at h_1
      simp [g] at h_1
```
2025-10-10 01:17:37 +00:00
Sebastian Ullrich
526ab9caff feat: Verso and Shake (#10657)
This PR ensures Shake does not remove any imports required by Verso
docstrings
2025-10-09 16:40:29 +00:00
Rob23oba
71ddf227d2 doc: add a recommended spelling for HEq (#10717)
This PR adds a recommended spelling for heterogenous equality (`HEq`,
`≍`).
2025-10-09 10:10:23 +00:00
Markus Himmel
dca8d6d188 refactor: discipline around arithmetic of String.Pos.Raw (#10713)
This PR enforces rules around arithmetic of `String.Pos.Raw`.

Specifically, it adopts the following conventions:

- Byte indices ("ordinals") in strings should be represented using
`String.Pos.Raw`
- Amounts of bytes ("cardinals") in strings should be represented using
`Nat`.

For example, `String.Slice.utf8ByteSize` now returns `Nat` instead of
`String.Pos.Raw`, and there is a new function `String.Slice.rawEndPos`.

Finally, the `HAdd` and `HSub` instances for `String.Pos.Raw` are
reorganized. This is a **breaking change**.

The `HAdd/HSub String.Pos.Raw String.Pos.Raw String.Pos.Raw` instances
have been removed. For the use case of tracking positions relative to
some other position, we instead provide `offsetBy` and `unoffsetBy`
functions. For the use case of advancing/unadvancing a position by an
arbitrary number of bytes, we instead provide `increaseBy` and
`decreaseBy` functions. For
offsetting/unoffsetting/advancing/unadvancing a position `p` by the size
of a string `s` (resp. character `c`), use `s + p`/`p - s`/`p + s`/`p -
s` (resp. `c + p`/`p - c`/`p + c`/`p - c`).
2025-10-09 07:47:45 +00:00
Rob23oba
6f1e932542 fix: make IO.sleep opaque (#10718)
This PR makes the function `IO.sleep` opaque. Previously, the definition
of `IO.sleep` made it definitionally equivalent to `pure ()`.
2025-10-09 07:37:11 +00:00
Sebastian Graf
c32a57e580 feat: revert "feat: disable "experimental" warning for mvcgen (#10638)" (#10720)
This PR re-enables the "experimental" warning for `mvcgen` by changing
its default. The official release has been postponed to justify small
breaking changes in the semantic foundations in the near future.
2025-10-09 06:31:18 +00:00
Lean stage0 autoupdater
aa86d95c08 chore: update stage0 2025-10-08 22:00:53 +00:00
Leonardo de Moura
f9e140838e feat: hexnum parser (#10716)
This PR adds a new helper parser for implementing parsers that contain
hexadecimal numbers. We are going to use it to implement anchors in the
`grind` interactive mode.
2025-10-08 21:12:03 +00:00
3649 changed files with 36245 additions and 16220 deletions

14
.claude/CLAUDE.md Normal file
View File

@@ -0,0 +1,14 @@
When asked to implement new features:
* begin by reviewing existing relevant code and tests
* write comprehensive tests first (expecting that these will initially fail)
* and then iterate on the implementation until the tests pass.
To build Lean you should use `make -j$(nproc) -C build/release`.
To run a test you should use `cd tests/lean/run && ./test_single.sh example_test.lean`.
*Never* report success on a task unless you have verified both a clean build without errors, and that the relevant tests pass. You have to keep working until you have verified both of these.
All new tests should go in `tests/lean/run/`. Note that these tests don't have expected output, and just run on a success or failure basis. So you should use `#guard_msgs` to check for specific messages.
If you are not following best practices specific to this repository and the user expresses frustration, stop and ask them to help update this `.claude/CLAUDE.md` file with the missing guidance.

View File

@@ -0,0 +1,69 @@
# Release Management Command
Execute the release process for a given version by running the release checklist and following its instructions.
## Before Starting
**IMPORTANT**: Before beginning the release process, read the in-file documentation:
- Read `script/release_checklist.py` for what the checklist script does
- Read `script/release_steps.py` for what the release steps script does
These comments explain the scripts' behavior, which repositories get special handling, and how errors are handled.
## Arguments
- `version`: The version to release (e.g., v4.24.0)
## Process
1. Run `script/release_checklist.py {version}` to check the current status
2. **CRITICAL: If preliminary lean4 checks fail, STOP immediately and alert the user**
- Check for: release branch exists, CMake version correct, tag exists, release page exists, release notes exist
- **IMPORTANT**: The release page is created AUTOMATICALLY by CI after pushing the tag - DO NOT create it manually
- Do NOT create any PRs or proceed with repository updates if these checks fail
3. Create a todo list tracking all repositories that need updates
4. **CRITICAL RULE: You can ONLY run `release_steps.py` for a repository if `release_checklist.py` explicitly says to do so**
- The checklist output will say "Run `script/release_steps.py {version} {repo_name}` to create it"
- If a repository shows "🟡 Dependencies not ready", you CANNOT create a PR for it yet
- You MUST rerun `release_checklist.py` before attempting to create PRs for any new repositories
5. For each repository that the checklist says needs updating:
- Run `script/release_steps.py {version} {repo_name}` to create the PR
- Mark it complete when the PR is created
6. After creating PRs, notify the user which PRs need review and merging
7. **MANDATORY: Rerun `release_checklist.py` to check current status**
- Do this after creating each batch of PRs
- Do this after the user reports PRs have been merged
- NEVER assume a repository is ready without checking the checklist output
8. As PRs are merged and tagged, dependent repositories will become ready
9. Continue the cycle: run checklist → create PRs for ready repos → wait for merges → repeat
10. Continue until all repositories are updated and the release is complete
## Important Notes
- The `release_steps.py` script is idempotent - it's safe to rerun
- The `release_checklist.py` script is idempotent - it's safe to rerun
- Some repositories depend on others (e.g., mathlib4 depends on batteries, aesop, etc.)
- Wait for user to merge PRs before dependent repos can be updated
- Alert user if anything unusual or scary happens
- Use appropriate timeouts for long-running builds (verso can take 10+ minutes)
- ProofWidgets4 uses semantic versioning (v0.0.X) - it's okay to create and push the next sequential tag yourself when needed for a release
## PR Status Reporting
Every time you run `release_checklist.py`, you MUST:
1. Parse the output to identify ALL open PRs mentioned (lines with "✅ PR with title ... exists")
2. Provide a summary to the user listing ALL open PRs that need review
3. Group them by status:
- PRs for repositories that are blocked by dependencies (show these but note they're blocked)
- PRs for repositories that are ready to merge (highlight these)
4. Format the summary clearly with PR numbers and URLs
This summary should be provided EVERY time you run the checklist, not just after creating new PRs.
The user needs to see the complete picture of what's waiting for review.
## Error Handling
**CRITICAL**: If something goes wrong or a command fails:
- **DO NOT** try to manually reproduce the failing steps yourself
- **DO NOT** try to fix things by running git commands or other manual operations
- Both scripts are idempotent and designed to handle partial completion gracefully
- If a script continues to fail after retrying, report the error to the user and wait for instructions

View File

@@ -3,9 +3,6 @@ name: build-template
on:
workflow_call:
inputs:
check-level:
type: string
required: true
config:
type: string
required: true
@@ -230,7 +227,7 @@ jobs:
run: |
ulimit -c unlimited # coredumps
time ctest --preset ${{ matrix.CMAKE_PRESET || 'release' }} --test-dir build/$TARGET_STAGE -j$NPROC --output-junit test-results.xml ${{ matrix.CTEST_OPTIONS }}
if: (matrix.wasm || !matrix.cross) && (inputs.check-level >= 1 || matrix.test)
if: matrix.test
- name: Test Summary
uses: test-summary/action@v2
with:

View File

@@ -11,8 +11,8 @@ jobs:
- uses: actions/checkout@v5
with:
ref: ${{ github.event.pull_request.head.sha }}
filter: blob:none
fetch-depth: 0
filter: tree:0
- name: Find base commit
if: github.event_name == 'pull_request'

View File

@@ -31,10 +31,6 @@ jobs:
configure:
runs-on: ubuntu-latest
outputs:
# 0: PRs without special label
# 1: PRs with `merge-ci` label, merge queue checks, master commits
# 2: PRs with `release-ci` label, releases (incl. nightlies)
check-level: ${{ steps.set-level.outputs.check-level }}
# The build matrix, dynamically generated here
matrix: ${{ steps.set-matrix.outputs.matrix }}
# secondary build jobs that should not block the CI success/merge queue
@@ -110,6 +106,9 @@ jobs:
TAG_NAME="${GITHUB_REF##*/}"
echo "RELEASE_TAG=$TAG_NAME" >> "$GITHUB_OUTPUT"
# 0: PRs without special label
# 1: PRs with `merge-ci` label, merge queue checks, master commits
# 2: PRs with `release-ci` label, releases (incl. nightlies)
- name: Set check level
id: set-level
# We do not use github.event.pull_request.labels.*.name here because
@@ -117,6 +116,7 @@ jobs:
# rerun the workflow run after setting the `release-ci`/`merge-ci` labels.
run: |
check_level=0
fast=false
if [[ -n "${{ steps.set-nightly.outputs.nightly }}" || -n "${{ steps.set-release.outputs.RELEASE_TAG }}" || -n "${{ steps.set-release-custom.outputs.RELEASE_TAG }}" ]]; then
check_level=2
@@ -129,9 +129,13 @@ jobs:
elif echo "$labels" | grep -q "merge-ci"; then
check_level=1
fi
if echo "$labels" | grep -q "fast-ci"; then
fast=true
fi
fi
echo "check-level=$check_level" >> "$GITHUB_OUTPUT"
echo "fast=$fast" >> "$GITHUB_OUTPUT"
env:
GH_TOKEN: ${{ github.token }}
@@ -141,7 +145,8 @@ jobs:
with:
script: |
const level = ${{ steps.set-level.outputs.check-level }};
console.log(`level: ${level}`);
const fast = ${{ steps.set-level.outputs.fast }};
console.log(`level: ${level}, fast: ${fast}`);
// use large runners where available (original repo)
let large = ${{ github.repository == 'leanprover/lean4' }};
const isPr = "${{ github.event_name }}" == "pull_request";
@@ -152,7 +157,8 @@ jobs:
"name": "Linux LLVM",
"os": "ubuntu-latest",
"release": false,
"check-level": 2,
"enabled": level >= 2,
"test": true,
"shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
@@ -165,17 +171,19 @@ jobs:
{
// portable release build: use channel with older glibc (2.26)
"name": "Linux release",
"os": "ubuntu-latest",
// usually not a bottleneck so make exclusive to `fast-ci`
"os": large && fast ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
"release": true,
// Special handling for release jobs. We want:
// 1. To run it in PRs so developers get PR toolchains (so secondary is sufficient)
// 1. To run it in PRs so developers get PR toolchains (so secondary without tests is sufficient)
// 2. To skip it in merge queues as it takes longer than the
// Linux lake build and adds little value in the merge queue
// 3. To run it in release (obviously)
// 4. To run it for pushes to master so that pushes to master have a Linux toolchain
// available as an artifact for Grove to use.
"check-level": (isPr || isPushToMaster) ? 0 : 2,
"secondary": isPr,
"enabled": isPr || level != 1 || isPushToMaster,
"test": level >= 1,
"secondary": level == 0,
"shell": "nix develop .#oldGlibc -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
@@ -186,26 +194,28 @@ jobs:
{
"name": "Linux Lake",
"os": large ? "nscloud-ubuntu-22.04-amd64-8x16-with-cache" : "ubuntu-latest",
"check-level": 0,
"test": true,
"enabled": true,
"check-rebootstrap": level >= 1,
"check-stage3": level >= 2,
"test": true,
// NOTE: `test-speedcenter` currently seems to be broken on `ubuntu-latest`
"test-speedcenter": large && level >= 2,
// made explicit until it can be assumed to have propagated to PRs
"CMAKE_OPTIONS": "-DUSE_LAKE=ON",
// We are not warning-free yet on all platforms, start here
"CMAKE_OPTIONS": "-DLEAN_EXTRA_CXX_FLAGS=-Werror",
},
{
"name": "Linux Reldebug",
"os": "ubuntu-latest",
"check-level": 2,
"enabled": level >= 2,
"test": true,
"CMAKE_PRESET": "reldebug",
},
// TODO: suddenly started failing in CI
/*{
"name": "Linux fsanitize",
"os": "ubuntu-latest",
"check-level": 2,
"enabled": level >= 2,
"test": true,
// turn off custom allocator & symbolic functions to make LSAN do its magic
"CMAKE_PRESET": "sanitize",
// exclude seriously slow/problematic tests (laketests crash)
@@ -215,7 +225,8 @@ jobs:
"name": "macOS",
"os": "macos-15-intel",
"release": true,
"check-level": 2,
"test": false, // Tier 2 platform
"enabled": level >= 2,
"shell": "bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-apple-darwin.tar.zst",
"prepare-llvm": "../script/prepare-llvm-macos.sh lean-llvm*",
@@ -226,7 +237,7 @@ jobs:
{
"name": "macOS aarch64",
// standard GH runner only comes with 7GB so use large runner if possible when running tests
"os": large && !isPr ? "nscloud-macos-sequoia-arm64-6x14" : "macos-15",
"os": large && (fast || level >= 1) ? "nscloud-macos-sequoia-arm64-6x14" : "macos-15",
"CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-darwin_aarch64",
"release": true,
"shell": "bash -euxo pipefail {0}",
@@ -235,14 +246,16 @@ jobs:
"binary-check": "otool -L",
"tar": "gtar", // https://github.com/actions/runner-images/issues/2619
// See "Linux release" for release job levels; Grove is not a concern here
"check-level": isPr ? 0 : 2,
"secondary": isPr,
"enabled": isPr || level != 1,
"test": level >= 1,
"secondary": level == 0,
},
{
"name": "Windows",
"os": large && level == 2 ? "namespace-profile-windows-amd64-4x16" : "windows-2022",
"os": large && (fast || level == 2) ? "namespace-profile-windows-amd64-4x16" : "windows-2022",
"release": true,
"check-level": 2,
"enabled": level >= 2,
"test": true,
"shell": "msys2 {0}",
"CMAKE_OPTIONS": "-G \"Unix Makefiles\"",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-x86_64-w64-windows-gnu.tar.zst",
@@ -254,7 +267,8 @@ jobs:
"os": "nscloud-ubuntu-22.04-arm64-4x16",
"CMAKE_OPTIONS": "-DLEAN_INSTALL_SUFFIX=-linux_aarch64",
"release": true,
"check-level": 2,
"enabled": level >= 2,
"test": true,
"shell": "nix develop .#oldGlibcAArch -c bash -euxo pipefail {0}",
"llvm-url": "https://github.com/leanprover/lean-llvm/releases/download/19.1.2/lean-llvm-aarch64-linux-gnu.tar.zst",
"prepare-llvm": "../script/prepare-llvm-linux.sh lean-llvm*",
@@ -267,7 +281,7 @@ jobs:
// "CMAKE_OPTIONS": "-DSTAGE0_USE_GMP=OFF -DSTAGE0_LEAN_EXTRA_CXX_FLAGS='-m32' -DSTAGE0_LEANC_OPTS='-m32' -DSTAGE0_MMAP=OFF -DUSE_GMP=OFF -DLEAN_EXTRA_CXX_FLAGS='-m32' -DLEANC_OPTS='-m32' -DMMAP=OFF -DLEAN_INSTALL_SUFFIX=-linux_x86 -DCMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DSTAGE0_CMAKE_LIBRARY_PATH=/usr/lib/i386-linux-gnu/ -DPKG_CONFIG_EXECUTABLE=/usr/bin/i386-linux-gnu-pkg-config",
// "cmultilib": true,
// "release": true,
// "check-level": 2,
// "enabled": level >= 2,
// "cross": true,
// "shell": "bash -euxo pipefail {0}"
//}
@@ -279,7 +293,7 @@ jobs:
// "wasm": true,
// "cmultilib": true,
// "release": true,
// "check-level": 2,
// "enabled": level >= 2,
// "cross": true,
// "shell": "bash -euxo pipefail {0}",
// // Just a few selected tests because wasm is slow
@@ -293,7 +307,7 @@ jobs:
}
}
console.log(`matrix:\n${JSON.stringify(matrix, null, 2)}`);
matrix = matrix.filter((job) => level >= job["check-level"]);
matrix = matrix.filter((job) => job["enabled"]);
core.setOutput('matrix', matrix.filter((job) => !job["secondary"]));
core.setOutput('matrix-secondary', matrix.filter((job) => job["secondary"]));
@@ -303,7 +317,6 @@ jobs:
uses: ./.github/workflows/build-template.yml
with:
config: ${{needs.configure.outputs.matrix}}
check-level: ${{ needs.configure.outputs.check-level }}
nightly: ${{ needs.configure.outputs.nightly }}
LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
@@ -319,7 +332,6 @@ jobs:
uses: ./.github/workflows/build-template.yml
with:
config: ${{needs.configure.outputs.matrix-secondary}}
check-level: ${{ needs.configure.outputs.check-level }}
nightly: ${{ needs.configure.outputs.nightly }}
LEAN_VERSION_MAJOR: ${{ needs.configure.outputs.LEAN_VERSION_MAJOR }}
LEAN_VERSION_MINOR: ${{ needs.configure.outputs.LEAN_VERSION_MINOR }}
@@ -392,6 +404,8 @@ jobs:
with:
# needed for tagging
fetch-depth: 0
# Doesn't seem to be working when additionally fetching from lean4-nightly
#filter: tree:0
token: ${{ secrets.PUSH_NIGHTLY_TOKEN }}
- uses: actions/download-artifact@v5
with:

View File

@@ -48,17 +48,17 @@ jobs:
git -C lean4.git remote add origin https://github.com/${{ github.repository_owner }}/lean4.git
git -C lean4.git fetch -n origin master
git -C lean4.git fetch -n origin "${{ steps.workflow-info.outputs.sourceHeadSha }}"
# Create both the original tag and the SHA-suffixed tag
SHORT_SHA="${{ steps.workflow-info.outputs.sourceHeadSha }}"
SHORT_SHA="${SHORT_SHA:0:7}"
# Export the short SHA for use in subsequent steps
echo "SHORT_SHA=${SHORT_SHA}" >> "$GITHUB_ENV"
git -C lean4.git tag -f pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }} "${{ steps.workflow-info.outputs.sourceHeadSha }}"
git -C lean4.git tag -f pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-"${SHORT_SHA}" "${{ steps.workflow-info.outputs.sourceHeadSha }}"
git -C lean4.git remote add pr-releases https://foo:'${{ secrets.PR_RELEASES_TOKEN }}'@github.com/${{ github.repository_owner }}/lean4-pr-releases.git
git -C lean4.git push -f pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}
git -C lean4.git push -f pr-releases pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-"${SHORT_SHA}"
@@ -200,7 +200,7 @@ jobs:
-H "Accept: application/vnd.github.v3+json" \
"https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/labels" \
| jq -r '.[].name')"
if echo "$LABELS" | grep -q "^force-mathlib-ci$"; then
echo "force-mathlib-ci label detected, forcing CI despite issues"
MESSAGE="Forcing Mathlib CI because the \`force-mathlib-ci\` label is present, despite problem: $MESSAGE"
@@ -301,7 +301,7 @@ jobs:
-H "Accept: application/vnd.github.v3+json" \
"https://api.github.com/repos/leanprover/lean4/issues/${{ steps.workflow-info.outputs.pullRequestNumber }}/labels" \
| jq -r '.[].name')"
if echo "$LABELS" | grep -q "^force-manual-ci$"; then
echo "force-manual-ci label detected, forcing CI despite issues"
MESSAGE="Forcing reference manual CI because the \`force-manual-ci\` label is present, despite problem: $MESSAGE"
@@ -401,6 +401,7 @@ jobs:
token: ${{ secrets.MATHLIB4_BOT }}
ref: nightly-testing
fetch-depth: 0 # This ensures we check out all tags and branches.
filter: tree:0
- name: Check if tag exists
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.ready.outputs.mathlib_ready == 'true'
@@ -425,7 +426,7 @@ jobs:
git switch -c lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }} "$BASE"
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
git add lean-toolchain
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
else
echo "Branch already exists, updating lean-toolchain."
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
@@ -434,7 +435,7 @@ jobs:
git merge "$BASE" --strategy-option ours --no-commit --allow-unrelated-histories
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
git add lean-toolchain
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
fi
- name: Push changes
@@ -460,6 +461,7 @@ jobs:
token: ${{ secrets.MATHLIB4_BOT }}
ref: nightly-testing
fetch-depth: 0 # This ensures we check out all tags and branches.
filter: tree:0
- name: install elan
run: |
@@ -494,7 +496,7 @@ jobs:
sed -i 's,require "leanprover-community" / "batteries" @ git ".\+",require "leanprover-community" / "batteries" @ git "lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}",' lakefile.lean
lake update batteries
git add lakefile.lean lake-manifest.json
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
else
echo "Branch already exists, updating lean-toolchain and bumping Batteries."
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
@@ -505,7 +507,7 @@ jobs:
git add lean-toolchain
lake update batteries
git add lake-manifest.json
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
fi
- name: Push changes
@@ -530,6 +532,7 @@ jobs:
token: ${{ secrets.MANUAL_PR_BOT }}
ref: nightly-testing
fetch-depth: 0 # This ensures we check out all tags and branches.
filter: tree:0
- name: Check if tag in reference manual exists
if: steps.workflow-info.outputs.pullRequestNumber != '' && steps.reference-manual-ready.outputs.manual_ready == 'true'
@@ -555,7 +558,7 @@ jobs:
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
git add lean-toolchain
git add lakefile.lean lake-manifest.json
git commit -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit --allow-empty -m "Update lean-toolchain for testing https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
else
echo "Branch already exists, updating lean-toolchain."
git switch lean-pr-testing-${{ steps.workflow-info.outputs.pullRequestNumber }}
@@ -565,7 +568,7 @@ jobs:
echo "leanprover/lean4-pr-releases:pr-release-${{ steps.workflow-info.outputs.pullRequestNumber }}-${{ env.SHORT_SHA }}" > lean-toolchain
git add lean-toolchain
git add lake-manifest.json
git commit -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
git commit --allow-empty -m "Update lean-toolchain for https://github.com/leanprover/lean4/pull/${{ steps.workflow-info.outputs.pullRequestNumber }}"
fi
- name: Push changes

View File

@@ -15,6 +15,6 @@ jobs:
script: |
const msg = context.payload.pull_request? context.payload.pull_request.title : context.payload.merge_group.head_commit.message;
console.log(`Message: ${msg}`)
if (!/^(feat|fix|doc|style|refactor|test|chore|perf): .*[^.]($|\n\n)/.test(msg)) {
if (!/^(feat|fix|doc|style|refactor|test|chore|perf): (?![A-Z][a-z]).*[^.]($|\n\n)/.test(msg)) {
core.setFailed('PR title does not follow the Commit Convention (https://leanprover.github.io/lean4/doc/dev/commit_convention.html).');
}

1
.gitignore vendored
View File

@@ -20,7 +20,6 @@ tasks.json
settings.json
.gdb_history
.vscode/*
!.vscode/settings.json
script/__pycache__
*.produced.out
CMakeSettings.json

View File

@@ -7,9 +7,9 @@
/.github/ @kim-em
/RELEASES.md @kim-em
/src/kernel/ @leodemoura
/src/library/compiler/ @zwarich
/src/library/compiler/ @hargoniX
/src/lake/ @tydeu
/src/Lean/Compiler/ @leodemoura @zwarich
/src/Lean/Compiler/ @leodemoura @hargoniX
/src/Lean/Data/Lsp/ @mhuisi
/src/Lean/Elab/Deriving/ @kim-em
/src/Lean/Elab/Tactic/ @kim-em

View File

@@ -52,7 +52,7 @@ In the case of `@[extern]` all *irrelevant* types are removed first; see next se
Similarly, the signed integer types `Int8`, ..., `Int64`, `ISize` are also represented by the unsigned C types `uint8_t`, ..., `uint64_t`, `size_t`, respectively, because they have a trivial structure.
* `Nat` and `Int` are represented by `lean_object *`.
Their runtime values is either a pointer to an opaque bignum object or, if the lowest bit of the "pointer" is 1 (`lean_is_scalar`), an encoded unboxed natural number or integer (`lean_box`/`lean_unbox`).
* A universe `Sort u`, type constructor `... → Sort u`, or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
* A universe `Sort u`, type constructor `... → Sort u`, `Void α` or proposition `p : Prop` is *irrelevant* and is either statically erased (see above) or represented as a `lean_object *` with the runtime value `lean_box(0)`
* Any other type is represented by `lean_object *`.
Its runtime value is a pointer to an object of a subtype of `lean_object` (see the "Inductive types" section below) or the unboxed value `lean_box(cidx)` for the `cidx`th constructor of an inductive type if this constructor does not have any relevant parameters.
@@ -141,8 +141,8 @@ void lean_initialize_runtime_module();
void lean_initialize();
char ** lean_setup_args(int argc, char ** argv);
lean_object * initialize_A_B(uint8_t builtin, lean_object *);
lean_object * initialize_C(uint8_t builtin, lean_object *);
lean_object * initialize_A_B(uint8_t builtin);
lean_object * initialize_C(uint8_t builtin);
...
argv = lean_setup_args(argc, argv); // if using process-related functionality
@@ -152,7 +152,7 @@ lean_initialize_runtime_module();
lean_object * res;
// use same default as for Lean executables
uint8_t builtin = 1;
res = initialize_A_B(builtin, lean_io_mk_world());
res = initialize_A_B(builtin);
if (lean_io_result_is_ok(res)) {
lean_dec_ref(res);
} else {
@@ -160,7 +160,7 @@ if (lean_io_result_is_ok(res)) {
lean_dec(res);
return ...; // do not access Lean declarations if initialization failed
}
res = initialize_C(builtin, lean_io_mk_world());
res = initialize_C(builtin);
if (lean_io_result_is_ok(res)) {
...

View File

@@ -94,10 +94,8 @@ theorem List.palindrome_of_eq_reverse (h : as.reverse = as) : Palindrome as := b
next => exact Palindrome.nil
next a => exact Palindrome.single a
next a b as ih =>
have : a = b := by simp_all
subst this
have : as.reverse = as := by simp_all
exact Palindrome.sandwich a (ih this)
obtain rfl, h, - := by simpa using h
exact Palindrome.sandwich b (ih h)
/-!
We now define a function that returns `true` iff `as` is a palindrome.

View File

@@ -14,6 +14,9 @@
}
],
"settings": {
// Open terminal at root, not current workspace folder
// (there is not way to directly refer to the root folder included as `.` above)
"terminal.integrated.cwd": "${workspaceFolder:src}/..",
"files.insertFinalNewline": true,
"files.trimTrailingWhitespace": true,
"cmake.buildDirectory": "${workspaceFolder}/build/release",

View File

@@ -57,19 +57,19 @@ def main (args : List String) : IO Unit := do
sec := "\n\n" ++ sec
if insertPos?.isNone then
sec := sec ++ "\n\n"
text := text.extract 0 insertPos ++ sec ++ text.extract insertPos text.endPos
text := text.extract 0 insertPos ++ sec ++ text.extract insertPos text.rawEndPos
-- prepend each import with `public `
for imp in imps.reverse do
let insertPos := imp.raw.getPos?.get!
let prfx := if doMeta then "public meta " else "public "
text := text.extract 0 insertPos ++ prfx ++ text.extract insertPos text.endPos
text := text.extract 0 insertPos ++ prfx ++ text.extract insertPos text.rawEndPos
-- insert `module` header
let mut initText := text.extract 0 startPos
if !initText.trim.isEmpty then
-- If there is a header comment, preserve it and put `module` in the line after
initText := initText.trimRight ++ "\n"
text := initText ++ "module\n\n" ++ text.extract startPos text.endPos
text := initText ++ "module\n\n" ++ text.extract startPos text.rawEndPos
IO.FS.writeFile path text

View File

@@ -131,10 +131,11 @@ structure State where
`transDeps[i]` is the (non-reflexive) transitive closure of `mods[i].imports`. More specifically,
* `j ∈ transDeps[i].pub` if `i -(public import)->+ j`
* `j ∈ transDeps[i].priv` if `i -(import ...)-> _ -(public import)->* j`
* `j ∈ transDeps[i].priv` if `i -(import all)->+ -(public import ...)-> _ -(public import)->* j`
* `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import ...)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import ...)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ -(public meta import ...)-> _ -(public (meta)? import ...)->* j`
* `j ∈ transDeps[i].priv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].pub/priv`
* `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import)->* j`
* `j ∈ transDeps[i].metaPriv` if `i -(import ...)-> i'` and `j ∈ transDeps[i'].metaPub`
* `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].metaPub/metaPriv`
-/
transDeps : Array Needs := #[]
/--
@@ -162,10 +163,10 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
-- `j ∈ transDeps[i].priv` if `i -(import ...)-> _ -(public import)->* j`
transImps := transImps.union .priv {j} |>.union .priv (impTransImps.get .pub)
if imp.importAll then
-- `j ∈ transDeps[i].priv` if `i -(import all)->+ -(public import ...)-> _ -(public import)->* j`
transImps := transImps.union .priv (impTransImps.get .pub)
-- `j ∈ transDeps[i].priv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].pub/priv`
transImps := transImps.union .priv (impTransImps.get .pub impTransImps.get .priv)
-- `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import ...)->* j`
-- `j ∈ transDeps[i].metaPub` if `i -(public (meta)? import)->* _ -(public meta import)-> _ -(public (meta)? import)->* j`
if imp.isExported then
transImps := transImps.union .metaPub (impTransImps.get .metaPub)
if imp.isMeta then
@@ -173,10 +174,13 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
if !imp.isExported then
if imp.isMeta then
-- `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import ...)->* j`
-- `j ∈ transDeps[i].metaPriv` if `i -(meta import ...)-> _ -(public (meta)? import)->* j`
transImps := transImps.union .metaPriv {j} |>.union .metaPriv (impTransImps.get .pub impTransImps.get .metaPub)
if imp.importAll then
-- `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ -(public meta import ...)-> _ -(public (meta)? import ...)->* j`
-- `j ∈ transDeps[i].metaPriv` if `i -(import all)->+ i'` and `j ∈ transDeps[i'].metaPub/metaPriv`
transImps := transImps.union .metaPriv (impTransImps.get .metaPub impTransImps.get .metaPriv)
else
-- `j ∈ transDeps[i].metaPriv` if `i -(import ...)-> i'` and `j ∈ transDeps[i'].metaPub`
transImps := transImps.union .metaPriv (impTransImps.get .metaPub)
transImps
@@ -185,7 +189,8 @@ def addTransitiveImps (transImps : Needs) (imp : Import) (j : Nat) (impTransImps
def calcNeeds (env : Environment) (i : ModuleIdx) : Needs := Id.run do
let mut needs := default
for ci in env.header.moduleData[i]!.constants do
let pubCI? := env.setExporting true |>.find? ci.name
-- Added guard for cases like `structure` that are still exported even if private
let pubCI? := guard (!isPrivateName ci.name) *> (env.setExporting true).find? ci.name
let k := { isExported := pubCI?.isSome, isMeta := isMeta env ci.name }
needs := visitExpr k ci.type needs
if let some e := ci.value? (allowOpaque := true) then
@@ -216,7 +221,8 @@ def getExplanations (env : Environment) (i : ModuleIdx) :
Std.HashMap (ModuleIdx × NeedsKind) (Option (Name × Name)) := Id.run do
let mut deps := default
for ci in env.header.moduleData[i]!.constants do
let pubCI? := env.setExporting true |>.find? ci.name
-- Added guard for cases like `structure` that are still exported even if private
let pubCI? := guard (!isPrivateName ci.name) *> (env.setExporting true).find? ci.name
let k := { isExported := pubCI?.isSome, isMeta := isMeta env ci.name }
deps := visitExpr k ci.name ci.type deps
if let some e := ci.value? (allowOpaque := true) then
@@ -286,7 +292,7 @@ and `endPos` is the position of the end of the header.
-/
def parseHeaderFromString (text path : String) :
IO (System.FilePath × Parser.InputContext ×
TSyntaxArray ``Parser.Module.import × String.Pos) := do
TSyntax ``Parser.Module.header × String.Pos.Raw) := do
let inputCtx := Parser.mkInputContext text path
let (header, parserState, msgs) Parser.parseHeader inputCtx
if !msgs.toList.isEmpty then -- skip this file if there are parse errors
@@ -294,8 +300,8 @@ def parseHeaderFromString (text path : String) :
throw <| .userError "parse errors in file"
-- the insertion point for `add` is the first newline after the imports
let insertion := header.raw.getTailPos?.getD parserState.pos
let insertion := text.findAux (· == '\n') text.endPos insertion + 1
pure (path, inputCtx, .mk header.raw[2].getArgs, insertion)
let insertion := text.findAux (· == '\n') text.endPos insertion + '\n'
pure (path, inputCtx, header, insertion)
/-- Parse a source file to extract the location of the import lines, for edits and error messages.
@@ -304,13 +310,18 @@ and `endPos` is the position of the end of the header.
-/
def parseHeader (srcSearchPath : SearchPath) (mod : Name) :
IO (System.FilePath × Parser.InputContext ×
TSyntaxArray ``Parser.Module.import × String.Pos) := do
TSyntax ``Parser.Module.header × String.Pos.Raw) := do
-- Parse the input file
let some path srcSearchPath.findModuleWithExt "lean" mod
| throw <| .userError s!"error: failed to find source file for {mod}"
let text IO.FS.readFile path
parseHeaderFromString text path.toString
def decodeHeader : TSyntax ``Parser.Module.header Option (TSyntax `module) × Option (TSyntax `prelude) × TSyntaxArray ``Parser.Module.import
| `(Parser.Module.header| $[module%$moduleTk?]? $[prelude%$preludeTk?]? $imports*) =>
(moduleTk?.map .mk, preludeTk?.map .mk, imports)
| _ => unreachable!
def decodeImport : TSyntax ``Parser.Module.import Import
| `(Parser.Module.import| $[public%$pubTk?]? $[meta%$metaTk?]? import $[all%$allTk?]? $id) =>
{ module := id.getId, isExported := pubTk?.isSome, isMeta := metaTk?.isSome, importAll := allTk?.isSome }
@@ -326,11 +337,20 @@ def decodeImport : TSyntax ``Parser.Module.import → Import
* `addOnly`: if true, only add missing imports, do not remove unused ones
-/
def visitModule (srcSearchPath : SearchPath)
(i : Nat) (needs : Needs) (preserve : Needs) (edits : Edits)
(i : Nat) (needs : Needs) (preserve : Needs) (edits : Edits) (headerStx : TSyntax ``Parser.Module.header)
(addOnly := false) (githubStyle := false) (explain := false) : StateT State IO Edits := do
let s get
-- Do transitive reduction of `needs` in `deps`.
let mut deps := needs
let (_, prelude?, imports) := decodeHeader headerStx
if prelude?.isNone then
deps := deps.union .pub {s.env.getModuleIdx? `Init |>.get!}
for imp in imports do
if addOnly || imp.raw.getTrailing?.any (·.toString.toSlice.contains "shake: keep") then
let imp := decodeImport imp
let j := s.env.getModuleIdx? imp.module |>.get!
let k := NeedsKind.ofImport imp
deps := deps.union k {j}
for j in [0:s.mods.size] do
let transDeps := s.transDeps[j]!
for k in NeedsKind.all do
@@ -354,7 +374,8 @@ def visitModule (srcSearchPath : SearchPath)
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
else
let k := NeedsKind.ofImport imp
if !addOnly && !deps.has k j && !deps.has { k with isExported := false } j then
-- A private import should also be removed if the public version is needed
if !deps.has k j || !k.isExported && deps.has { k with isExported := true } j then
toRemove := toRemove.push imp
else
newDeps := addTransitiveImps newDeps imp j s.transDeps[j]!
@@ -385,7 +406,8 @@ def visitModule (srcSearchPath : SearchPath)
if githubStyle then
try
let (path, inputCtx, imports, endHeader) parseHeader srcSearchPath s.modNames[i]!
let (path, inputCtx, stx, endHeader) parseHeader srcSearchPath s.modNames[i]!
let (_, _, imports) := decodeHeader stx
for stx in imports do
if toRemove.any fun imp => imp == decodeImport stx then
let pos := inputCtx.fileMap.toPosition stx.raw.getPos?.get!
@@ -529,33 +551,43 @@ def main (args : List String) : IO UInt32 := do
let needs := s.mods.mapIdx fun i _ =>
Task.spawn fun _ => calcNeeds s.env i
-- Parse headers in parallel
let headers s.mods.mapIdxM fun i _ =>
BaseIO.asTask (parseHeader srcSearchPath s.modNames[i]! |>.toBaseIO)
if args.fix then
println! "The following changes will be made automatically:"
-- Check all selected modules
let mut edits : Edits :=
let mut revNeeds : Needs := default
for i in [0:s.mods.size], t in needs do
edits visitModule (addOnly := !pkg.isPrefixOf s.modNames[i]!) srcSearchPath i t.get revNeeds edits args.githubStyle args.explain
if isExtraRevModUse s.env i then
revNeeds := revNeeds.union .priv {i}
for i in [0:s.mods.size], t in needs, header in headers do
match header.get with
| .ok (_, _, stx, _) =>
edits visitModule (addOnly := !pkg.isPrefixOf s.modNames[i]!)
srcSearchPath i t.get revNeeds edits stx args.githubStyle args.explain
if isExtraRevModUse s.env i then
revNeeds := revNeeds.union .priv {i}
| .error e =>
println! e.toString
if !args.fix then
-- return error if any issues were found
return if edits.isEmpty then 0 else 1
-- Apply the edits to existing files
let count edits.foldM (init := 0) fun count mod (remove, add) => do
let mut count := 0
for mod in s.modNames, header? in headers do
let some (remove, add) := edits[mod]? | continue
let add : Array Import := add.qsortOrd
-- Parse the input file
let (path, inputCtx, imports, insertion)
try parseHeader srcSearchPath mod
catch e => println! e.toString; return count
let .ok (path, inputCtx, stx, insertion) := header?.get | continue
let (_, _, imports) := decodeHeader stx
let text := inputCtx.fileMap.source
-- Calculate the edit result
let mut pos : String.Pos := 0
let mut pos : String.Pos.Raw := 0
let mut out : String := ""
let mut seen : Std.HashSet Import := {}
for stx in imports do
@@ -563,17 +595,17 @@ def main (args : List String) : IO UInt32 := do
if remove.contains mod || seen.contains mod then
out := out ++ text.extract pos stx.raw.getPos?.get!
-- We use the end position of the syntax, but include whitespace up to the first newline
pos := text.findAux (· == '\n') text.endPos stx.raw.getTailPos?.get! + 1
pos := text.findAux (· == '\n') text.rawEndPos stx.raw.getTailPos?.get! + '\n'
seen := seen.insert mod
out := out ++ text.extract pos insertion
for mod in add do
if !seen.contains mod then
seen := seen.insert mod
out := out ++ s!"{mod}\n"
out := out ++ text.extract insertion text.endPos
out := out ++ text.extract insertion text.rawEndPos
IO.FS.writeFile path out
return count + 1
count := count + 1
-- Since we throw an error upon encountering issues, we can be sure that everything worked
-- if we reach this point of the script.

View File

@@ -1,5 +1,58 @@
#!/usr/bin/env python3
"""
Release Checklist for Lean4 and Downstream Repositories
This script validates the status of a Lean4 release across all dependent repositories.
It checks whether repositories are ready for release and identifies missing steps.
IMPORTANT: Keep this documentation up-to-date when modifying the script's behavior!
What this script does:
1. Validates preliminary Lean4 release infrastructure:
- Checks that the release branch (releases/vX.Y.0) exists
- Verifies CMake version settings are correct
- Confirms the release tag exists
- Validates the release page exists on GitHub (created automatically by CI after tag push)
- Checks the release notes page on lean-lang.org (updated while bumping the `reference-manual` repository)
**IMPORTANT: If the release page doesn't exist, the script will skip checking
downstream repositories and the master branch configuration. The preliminary
infrastructure must be in place before the release process can proceed.**
**NOTE: The GitHub release page is created AUTOMATICALLY by CI after the tag is pushed.
DO NOT create it manually. Wait for CI to complete after pushing the tag.**
2. For each downstream repository (batteries, mathlib4, etc.):
- Checks if dependencies are ready (e.g., mathlib4 depends on batteries)
- Verifies the main branch is on the target toolchain (or newer)
- Checks if a PR exists to bump the toolchain (if not yet updated)
- Validates tags exist for the release version
- Ensures tags are merged into stable branches (for non-RC releases)
- Verifies bump branches exist and are configured correctly
- Special handling for ProofWidgets4 release tags
3. Optionally automates missing steps (when not in --dry-run mode):
- Creates missing release tags using push_repo_release_tag.py
- Merges tags into stable branches using merge_remote.py
Usage:
./release_checklist.py v4.24.0 # Check release status
./release_checklist.py v4.24.0 --verbose # Show detailed debug info
./release_checklist.py v4.24.0 --dry-run # Check only, don't execute fixes
For automated release management with Claude Code:
/release v4.24.0 # Run full release process with Claude
The script reads repository configurations from release_repos.yml and reports:
- ✅ for completed requirements
- ❌ for missing requirements (with instructions to fix)
- 🟡 for repositories waiting on dependencies
- ⮕ for automated actions being taken
This script is idempotent and safe to rerun multiple times.
"""
import argparse
import yaml
import requests
@@ -76,6 +129,39 @@ def release_page_exists(repo_url, tag_name, github_token):
response = requests.get(api_url, headers=headers)
return response.status_code == 200
def get_tag_workflow_status(repo_url, tag_name, github_token):
"""Get the status of CI workflows running for a specific tag."""
api_base = repo_url.replace("https://github.com/", "https://api.github.com/repos/")
headers = {'Authorization': f'token {github_token}'} if github_token else {}
# Get workflow runs for the tag
# GitHub's workflow runs API uses the branch/tag name in the 'head_branch' field
api_url = f"{api_base}/actions/runs?event=push&head_branch={tag_name}"
response = requests.get(api_url, headers=headers)
if response.status_code != 200:
return None
data = response.json()
workflow_runs = data.get('workflow_runs', [])
if not workflow_runs:
return None
# Get the most recent workflow run for this tag
run = workflow_runs[0]
status = run.get('status')
conclusion = run.get('conclusion')
workflow_name = run.get('name', 'CI')
run_id = run.get('id')
return {
'status': status,
'conclusion': conclusion,
'workflow_name': workflow_name,
'run_id': run_id
}
def get_release_notes(tag_name):
"""Fetch release notes page title from lean-lang.org."""
# Strip -rcX suffix if present for the URL
@@ -84,20 +170,17 @@ def get_release_notes(tag_name):
try:
response = requests.get(reference_url)
response.raise_for_status() # Raise HTTPError for bad responses (4xx or 5xx)
# Extract title using regex
match = re.search(r"<title>(.*?)</title>", response.text, re.IGNORECASE | re.DOTALL)
if match:
return match.group(1).strip()
else:
print(f" ⚠️ Could not find <title> tag in {reference_url}")
return None
except requests.exceptions.RequestException as e:
print(f" ❌ Error fetching release notes from {reference_url}: {e}")
except requests.exceptions.RequestException:
return None
except Exception as e:
print(f" ❌ An unexpected error occurred while processing release notes: {e}")
except Exception:
return None
def get_branch_content(repo_url, branch, file_path, github_token):
@@ -286,6 +369,68 @@ def check_bump_branch_toolchain(url, bump_branch, github_token):
print(f" ✅ Bump branch correctly uses toolchain: {content}")
return True
def get_pr_ci_status(repo_url, pr_number, github_token):
"""Get the CI status for a pull request."""
api_base = repo_url.replace("https://github.com/", "https://api.github.com/repos/")
headers = {'Authorization': f'token {github_token}'} if github_token else {}
# Get PR details to find the head SHA
pr_response = requests.get(f"{api_base}/pulls/{pr_number}", headers=headers)
if pr_response.status_code != 200:
return "unknown", "Could not fetch PR details"
pr_data = pr_response.json()
head_sha = pr_data['head']['sha']
# Get check runs for the commit
check_runs_response = requests.get(
f"{api_base}/commits/{head_sha}/check-runs",
headers=headers
)
if check_runs_response.status_code != 200:
return "unknown", "Could not fetch check runs"
check_runs_data = check_runs_response.json()
check_runs = check_runs_data.get('check_runs', [])
if not check_runs:
# No check runs, check for status checks (legacy)
status_response = requests.get(
f"{api_base}/commits/{head_sha}/status",
headers=headers
)
if status_response.status_code == 200:
status_data = status_response.json()
state = status_data.get('state', 'unknown')
if state == 'success':
return "success", "All status checks passed"
elif state == 'failure':
return "failure", "Some status checks failed"
elif state == 'pending':
return "pending", "Status checks in progress"
return "unknown", "No CI checks found"
# Analyze check runs
conclusions = [run['conclusion'] for run in check_runs if run.get('status') == 'completed']
in_progress = [run for run in check_runs if run.get('status') in ['queued', 'in_progress']]
if in_progress:
return "pending", f"{len(in_progress)} check(s) in progress"
if not conclusions:
return "pending", "Checks queued"
if all(c == 'success' for c in conclusions):
return "success", f"All {len(conclusions)} checks passed"
failed = sum(1 for c in conclusions if c in ['failure', 'timed_out', 'action_required'])
if failed > 0:
return "failure", f"{failed} check(s) failed"
# Some checks are cancelled, skipped, or neutral
return "warning", f"Some checks did not complete normally"
def pr_exists_with_title(repo_url, title, github_token):
api_url = repo_url.replace("https://github.com/", "https://api.github.com/repos/") + "/pulls"
headers = {'Authorization': f'token {github_token}'} if github_token else {}
@@ -404,30 +549,57 @@ def main():
print(f" ❌ Short commit hash {commit_hash[:SHORT_HASH_LENGTH]} is numeric and starts with 0, causing issues for version parsing. Try regenerating the last commit to get a new hash.")
lean4_success = False
if not release_page_exists(lean_repo_url, toolchain, github_token):
print(f" ❌ Release page for {toolchain} does not exist")
release_page_ready = release_page_exists(lean_repo_url, toolchain, github_token)
if not release_page_ready:
print(f" ❌ Release page for {toolchain} does not exist (This will be created by CI.)")
# Check CI workflow status
workflow_status = get_tag_workflow_status(lean_repo_url, toolchain, github_token)
if workflow_status:
status = workflow_status['status']
conclusion = workflow_status['conclusion']
workflow_name = workflow_status['workflow_name']
run_id = workflow_status['run_id']
workflow_url = f"{lean_repo_url}/actions/runs/{run_id}"
if status == 'in_progress' or status == 'queued':
print(f" 🔄 {workflow_name} workflow is {status}: {workflow_url}")
elif status == 'completed':
if conclusion == 'success':
print(f"{workflow_name} workflow completed successfully: {workflow_url}")
elif conclusion == 'failure':
print(f"{workflow_name} workflow failed: {workflow_url}")
else:
print(f" ⚠️ {workflow_name} workflow completed with status: {conclusion}: {workflow_url}")
else:
print(f" {workflow_name} workflow status: {status}: {workflow_url}")
lean4_success = False
else:
print(f" ✅ Release page for {toolchain} exists")
# Check the actual release notes page title
# Check the actual release notes page title (informational only - does not block)
actual_title = get_release_notes(toolchain)
expected_title_prefix = f"Lean {toolchain.lstrip('v')}" # e.g., "Lean 4.19.0" or "Lean 4.19.0-rc1"
base_tag = toolchain.split('-')[0]
release_notes_url = f"https://lean-lang.org/doc/reference/latest/releases/{base_tag}/"
if actual_title is None:
# Error already printed by get_release_notes
lean4_success = False
print(f" ⚠️ Release notes not found at {release_notes_url} (this will be fixed while updating the reference-manual repository)")
elif not actual_title.startswith(expected_title_prefix):
# Construct URL for the error message (using the base tag)
base_tag = toolchain.split('-')[0]
check_url = f"https://lean-lang.org/doc/reference/latest/releases/{base_tag}/"
print(f" ❌ Release notes page title mismatch. Expected prefix '{expected_title_prefix}', got '{actual_title}'. Check {check_url}")
lean4_success = False
print(f" ⚠️ Release notes page title mismatch. Expected prefix '{expected_title_prefix}', got '{actual_title}'. Check {release_notes_url}")
else:
print(f" ✅ Release notes page title looks good ('{actual_title}').")
repo_status["lean4"] = lean4_success
# If the release page doesn't exist, skip repository checks and master branch checks
# The preliminary infrastructure must be in place first
if not release_page_exists(lean_repo_url, toolchain, github_token):
print("\n⚠️ Release process blocked: preliminary Lean4 infrastructure incomplete.")
print(" Complete the steps above, then rerun this script to proceed with downstream repositories.")
return
# Load repositories and perform further checks
print("\nChecking repositories...")
@@ -471,6 +643,19 @@ def main():
if pr_info:
pr_number, pr_url = pr_info
print(f" ✅ PR with title '{pr_title}' exists: #{pr_number} ({pr_url})")
# Check CI status
ci_status, ci_message = get_pr_ci_status(url, pr_number, github_token)
if ci_status == "success":
print(f" ✅ CI: {ci_message}")
elif ci_status == "failure":
print(f" ❌ CI: {ci_message}")
elif ci_status == "pending":
print(f" 🔄 CI: {ci_message}")
elif ci_status == "warning":
print(f" ⚠️ CI: {ci_message}")
else:
print(f" ❓ CI: {ci_message}")
else:
print(f" ❌ PR with title '{pr_title}' does not exist")
print(f" Run `script/release_steps.py {toolchain} {name}` to create it")

View File

@@ -1,30 +1,53 @@
#!/usr/bin/env python3
"""
Execute release steps for Lean4 repositories.
Execute Release Steps for Lean4 Downstream Repositories
This script helps automate the release process for Lean4 and its dependent repositories
by actually executing the step-by-step instructions for updating toolchains, creating tags,
and managing branches.
This script automates the process of updating a downstream repository to a new Lean4 release.
It handles creating branches, updating toolchains, merging changes, building, testing, and
creating pull requests.
IMPORTANT: Keep this documentation up-to-date when modifying the script's behavior!
What this script does:
1. Sets up the downstream_releases/ directory for cloning repositories
2. Clones or updates the target repository
3. Creates a branch named bump_to_{version} for the changes
4. Updates the lean-toolchain file to the target version
5. Handles repository-specific variations:
- Different dependency update mechanisms
- Special merging strategies for repositories with nightly-testing branches
- Safety checks for repositories using bump branches
- Custom build and test procedures
6. Commits the changes with message "chore: bump toolchain to {version}"
7. Builds the project (with a clean .lake cache)
8. Runs tests if available
9. Pushes the branch to GitHub
10. Creates a pull request (or reports if one already exists)
Usage:
python3 release_steps.py <version> <repo>
./release_steps.py v4.24.0 batteries # Update batteries to v4.24.0
./release_steps.py v4.24.0-rc1 mathlib4 # Update mathlib4 to v4.24.0-rc1
Arguments:
version: The version to set in the lean-toolchain file (e.g., v4.6.0)
repo: The repository name as specified in release_repos.yml
The script reads repository configurations from release_repos.yml.
Each repository has specific handling for merging, dependencies, and testing.
Example:
python3 release_steps.py v4.6.0 mathlib4
python3 release_steps.py v4.6.0 batteries
This script is idempotent - it's safe to rerun if it fails partway through.
Existing branches, commits, and PRs will be reused rather than duplicated.
The script reads repository configurations from release_repos.yml in the same directory.
Each repository may have specific requirements for:
- Branch management
- Toolchain updates
- Dependency updates
- Tagging conventions
- Stable branch handling
Error handling:
- If build or tests fail, the script continues to create the PR anyway
- Manual conflicts must be resolved by the user
- Network issues during push/PR creation are reported with manual instructions
"""
import argparse
@@ -566,8 +589,19 @@ def execute_release_steps(repo, version, config):
# Clean lake cache for a fresh build
print(blue("Cleaning lake cache..."))
run_command("rm -rf .lake", cwd=repo_path)
run_command("lake clean", cwd=repo_path)
# Check if downstream of Mathlib and get cache if so
mathlib_package_dir = repo_path / ".lake" / "packages" / "mathlib"
if mathlib_package_dir.exists():
print(blue("Project is downstream of Mathlib, fetching cache..."))
try:
run_command("lake exe cache get", cwd=repo_path, stream_output=True)
print(green("Cache fetched successfully"))
except subprocess.CalledProcessError as e:
print(yellow("Failed to fetch cache, continuing anyway..."))
print(yellow(f"Cache fetch error: {e}"))
try:
run_command("lake build", cwd=repo_path, stream_output=True)
print(green("Build completed successfully"))

View File

@@ -10,7 +10,7 @@ endif()
include(ExternalProject)
project(LEAN CXX C)
set(LEAN_VERSION_MAJOR 4)
set(LEAN_VERSION_MINOR 25)
set(LEAN_VERSION_MINOR 26)
set(LEAN_VERSION_PATCH 0)
set(LEAN_VERSION_IS_RELEASE 0) # This number is 1 in the release revision, and 0 otherwise.
set(LEAN_SPECIAL_VERSION_DESC "" CACHE STRING "Additional version description like 'nightly-2018-03-11'")

View File

@@ -14,7 +14,6 @@ public import Init.ByCases
public import Init.RCases
public import Init.Core
public import Init.Control
public import Init.Data.Basic
public import Init.WF
public import Init.WFTactics
public import Init.Data

View File

@@ -7,7 +7,6 @@ Authors: Joachim Breitner
module
prelude
public import Init.Prelude
public import Init.Tactics
public section

View File

@@ -44,3 +44,10 @@ theorem apply_ite (f : α → β) (P : Prop) [Decidable P] (x y : α) :
/-- A `dite` whose results do not actually depend on the condition may be reduced to an `ite`. -/
@[simp] theorem dite_eq_ite [Decidable P] :
(dite P (fun _ => a) (fun _ => b)) = ite P a b := rfl
-- Remark: dite and ite are "defally equal" when we ignore the proofs.
@[deprecated dite_eq_ite (since := "2025-10-29")]
theorem dif_eq_if (c : Prop) {h : Decidable c} {α : Sort u} (t : α) (e : α) : dite c (fun _ => t) (fun _ => e) = ite c t e :=
match h with
| isTrue _ => rfl
| isFalse _ => rfl

View File

@@ -181,9 +181,6 @@ theorem not_imp_iff_and_not : ¬(a → b) ↔ a ∧ ¬b := Decidable.not_imp_iff
theorem not_and_iff_not_or_not : ¬(a b) ¬a ¬b := Decidable.not_and_iff_not_or_not
@[deprecated not_and_iff_not_or_not (since := "2025-03-18")]
abbrev not_and_iff_or_not_not := @not_and_iff_not_or_not
theorem not_iff : ¬(a b) (¬a b) := Decidable.not_iff
@[simp] theorem imp_iff_left_iff : (b a b) a b := Decidable.imp_iff_left_iff

View File

@@ -45,9 +45,6 @@ instance (priority := 500) instForInOfForIn' [ForIn' m ρ α d] : ForIn m ρ α
forIn x b f = forIn' x b (fun x h => binderNameHint x f <| binderNameHint h () <| f x) := by
rfl
@[deprecated forIn_eq_forIn' (since := "2025-04-04")]
abbrev forIn_eq_forin' := @forIn_eq_forIn'
/--
Extracts the value from a `ForInStep`, ignoring whether it is `ForInStep.done` or `ForInStep.yield`.
-/

View File

@@ -6,8 +6,6 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Control.State
public import Init.Control.Except
public import Init.Data.ToString.Basic
public section

View File

@@ -10,7 +10,6 @@ module
prelude
public import Init.Control.Basic
public import Init.Control.Id
public import Init.Coe
@[expose] public section

View File

@@ -7,8 +7,6 @@ module
prelude
public import Init.Ext
public import Init.SimpLemmas
public import Init.Meta
public section
@@ -172,6 +170,7 @@ theorem bind_pure_unit [Monad m] [LawfulMonad m] {x : m PUnit} : (x >>= fun _ =>
theorem map_congr [Functor m] {x : m α} {f g : α β} (h : a, f a = g a) : (f <$> x : m β) = g <$> x := by
simp [funext h]
@[deprecated seq_eq_bind_map (since := "2025-10-26")]
theorem seq_eq_bind {α β : Type u} [Monad m] [LawfulMonad m] (mf : m (α β)) (x : m α) : mf <*> x = mf >>= fun f => f <$> x := by
rw [bind_map]
@@ -252,24 +251,9 @@ instance : LawfulMonad Id := by
@[simp] theorem run_map (x : Id α) (f : α β) : (f <$> x).run = f x.run := rfl
@[simp] theorem run_bind (x : Id α) (f : α Id β) : (x >>= f).run = (f x.run).run := rfl
@[simp] theorem run_pure (a : α) : (pure a : Id α).run = a := rfl
@[simp] theorem pure_run (a : Id α) : pure a.run = a := rfl
@[simp] theorem run_seqRight (x y : Id α) : (x *> y).run = y.run := rfl
@[simp] theorem run_seqLeft (x y : Id α) : (x <* y).run = x.run := rfl
@[simp] theorem run_seq (f : Id (α β)) (x : Id α) : (f <*> x).run = f.run x.run := rfl
-- These lemmas are bad as they abuse the defeq of `Id α` and `α`
@[deprecated run_map (since := "2025-03-05")] theorem map_eq (x : Id α) (f : α β) : f <$> x = f x := rfl
@[deprecated run_bind (since := "2025-03-05")] theorem bind_eq (x : Id α) (f : α id β) : x >>= f = f x := rfl
@[deprecated run_pure (since := "2025-03-05")] theorem pure_eq (a : α) : (pure a : Id α) = a := rfl
end Id
/-! # Option -/
instance : LawfulMonad Option := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun _ _ => rfl)
(bind_assoc := fun x _ _ => by cases x <;> rfl)
(bind_pure_comp := fun _ x => by cases x <;> rfl)
instance : LawfulApplicative Option := inferInstance
instance : LawfulFunctor Option := inferInstance

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@@ -7,14 +7,11 @@ module
prelude
public import Init.Control.Lawful.Basic
public import Init.Control.Except
import all Init.Control.Except
public import Init.Control.Option
import all Init.Control.Option
public import Init.Control.State
import all Init.Control.State
public import Init.Control.StateRef
public import Init.Ext
public section
@@ -192,12 +189,12 @@ instance [Monad m] [LawfulMonad m] : LawfulMonad (OptionT m) where
@[simp] theorem run_seq [Monad m] [LawfulMonad m] (f : OptionT m (α β)) (x : OptionT m α) :
(f <*> x).run = Option.elimM f.run (pure none) (fun f => Option.map f <$> x.run) := by
simp [seq_eq_bind, Option.elimM, Option.elim]
simp [seq_eq_bind_map, Option.elimM, Option.elim]
@[simp] theorem run_seqLeft [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) :
(x <* y).run = Option.elimM x.run (pure none)
(fun x => Option.map (Function.const β x) <$> y.run) := by
simp [seqLeft_eq, seq_eq_bind, Option.elimM, OptionT.run_bind]
simp [seqLeft_eq, seq_eq_bind_map, Option.elimM, OptionT.run_bind]
@[simp] theorem run_seqRight [Monad m] [LawfulMonad m] (x : OptionT m α) (y : OptionT m β) :
(x *> y).run = Option.elimM x.run (pure none) (Function.const α y.run) := by
@@ -222,7 +219,7 @@ instance : LawfulMonad Option := LawfulMonad.mk'
(id_map := fun x => by cases x <;> rfl)
(pure_bind := fun _ _ => by rfl)
(bind_assoc := fun a _ _ => by cases a <;> rfl)
(bind_pure_comp := bind_pure_comp)
(bind_pure_comp := fun _ x => by cases x <;> rfl)
instance : LawfulApplicative Option := inferInstance
instance : LawfulFunctor Option := inferInstance

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@@ -7,7 +7,6 @@ module
prelude
public import Init.Control.Lawful.Basic
public import Init.RCases
public import Init.ByCases
public section

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@@ -6,17 +6,13 @@ Authors: Quang Dao, Paul Reichert
module
prelude
public import Init.Control.Option
import all Init.Control.Option
public import Init.Control.Except
import all Init.Control.Except
public import Init.Control.ExceptCps
import all Init.Control.ExceptCps
public import Init.Control.StateRef
import all Init.Control.StateRef
public import Init.Control.StateCps
import all Init.Control.StateCps
public import Init.Control.Id
import all Init.Control.Id
public import Init.Control.Lawful.MonadLift.Lemmas
public import Init.Control.Lawful.Instances

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@@ -23,7 +23,7 @@ theorem monadLift_map [LawfulMonad m] [LawfulMonad n] (f : α → β) (ma : m α
theorem monadLift_seq [LawfulMonad m] [LawfulMonad n] (mf : m (α β)) (ma : m α) :
monadLift (mf <*> ma) = monadLift mf <*> (monadLift ma : n α) := by
simp only [seq_eq_bind, monadLift_map, monadLift_bind]
simp only [seq_eq_bind_map, monadLift_map, monadLift_bind]
theorem monadLift_seqLeft [LawfulMonad m] [LawfulMonad n] (x : m α) (y : m β) :
monadLift (x <* y) = (monadLift x : n α) <* (monadLift y : n β) := by

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@@ -7,7 +7,6 @@ module
prelude
public import Init.Data.Option.Basic
public import Init.Control.Basic
public import Init.Control.Except
public section
@@ -28,7 +27,7 @@ failure occurred.
/--
Executes an action that might fail in the underlying monad `m`, returning `none` in case of failure.
-/
@[always_inline, inline]
@[always_inline, inline, expose]
def OptionT.run {m : Type u Type v} {α : Type u} (x : OptionT m α) : m (Option α) :=
x
@@ -70,7 +69,7 @@ instance {m : Type u → Type v} [Pure m] : Inhabited (OptionT m α) where
/--
Recovers from failures. Typically used via the `<|>` operator.
-/
@[always_inline, inline] protected def orElse (x : OptionT m α) (y : Unit OptionT m α) : OptionT m α := OptionT.mk do
@[always_inline, inline, expose] protected def orElse (x : OptionT m α) (y : Unit OptionT m α) : OptionT m α := OptionT.mk do
match ( x) with
| some a => pure (some a)
| _ => y ()
@@ -78,7 +77,7 @@ Recovers from failures. Typically used via the `<|>` operator.
/--
A recoverable failure.
-/
@[always_inline, inline] protected def fail : OptionT m α := OptionT.mk do
@[always_inline, inline, expose] protected def fail : OptionT m α := OptionT.mk do
pure none
instance : Alternative (OptionT m) where
@@ -91,7 +90,7 @@ Converts a computation from the underlying monad into one that could fail, even
This function is typically implicitly accessed via a `MonadLiftT` instance as part of [automatic
lifting](lean-manual://section/monad-lifting).
-/
@[always_inline, inline] protected def lift (x : m α) : OptionT m α := OptionT.mk do
@[always_inline, inline, expose] protected def lift (x : m α) : OptionT m α := OptionT.mk do
return some ( x)
instance : MonadLift m (OptionT m) := OptionT.lift
@@ -101,11 +100,11 @@ instance : MonadFunctor m (OptionT m) := ⟨fun f x => f x⟩
/--
Handles failures by treating them as exceptions of type `Unit`.
-/
@[always_inline, inline] protected def tryCatch (x : OptionT m α) (handle : Unit OptionT m α) : OptionT m α := OptionT.mk do
let some a x | handle ()
@[always_inline, inline, expose] protected def tryCatch (x : OptionT m α) (handle : PUnit OptionT m α) : OptionT m α := OptionT.mk do
let some a x | handle
pure <| some a
instance : MonadExceptOf Unit (OptionT m) where
instance : MonadExceptOf PUnit (OptionT m) where
throw := fun _ => OptionT.fail
tryCatch := OptionT.tryCatch

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@@ -8,8 +8,6 @@ The Reader monad transformer for passing immutable State.
module
prelude
public import Init.Control.Basic
public import Init.Control.Id
public import Init.Control.Except
public section

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@@ -8,8 +8,6 @@ The State monad transformer.
module
prelude
public import Init.Control.Basic
public import Init.Control.Id
public import Init.Control.Except
public section

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@@ -8,7 +8,6 @@ notation, basic datatypes and type classes
module
prelude
public meta import Init.Prelude
public import Init.SizeOf
public section
@@ -601,17 +600,6 @@ export LawfulSingleton (insert_empty_eq)
attribute [simp] insert_empty_eq
@[deprecated insert_empty_eq (since := "2025-03-12")]
theorem insert_emptyc_eq [EmptyCollection β] [Insert α β] [Singleton α β]
[LawfulSingleton α β] (x : α) : (insert x : β) = singleton x :=
insert_empty_eq _
@[deprecated insert_empty_eq (since := "2025-03-12")]
theorem LawfulSingleton.insert_emptyc_eq [EmptyCollection β] [Insert α β] [Singleton α β]
[LawfulSingleton α β] (x : α) : (insert x : β) = singleton x :=
insert_empty_eq _
/-- Type class used to implement the notation `{ a ∈ c | p a }` -/
class Sep (α : outParam <| Type u) (γ : Type v) where
/-- Computes `{ a ∈ c | p a }`. -/
@@ -1096,14 +1084,6 @@ theorem of_toBoolUsing_eq_true {p : Prop} {d : Decidable p} (h : toBoolUsing d =
theorem of_toBoolUsing_eq_false {p : Prop} {d : Decidable p} (h : toBoolUsing d = false) : ¬p :=
of_decide_eq_false h
set_option linter.missingDocs false in
@[deprecated of_toBoolUsing_eq_true (since := "2025-04-04")]
abbrev ofBoolUsing_eq_true := @of_toBoolUsing_eq_true
set_option linter.missingDocs false in
@[deprecated of_toBoolUsing_eq_false (since := "2025-04-04")]
abbrev ofBoolUsing_eq_false := @of_toBoolUsing_eq_false
instance : Decidable True :=
isTrue trivial
@@ -1166,6 +1146,7 @@ end
else isFalse (fun h => absurd (h hp) hq)
else isTrue (fun h => absurd h hp)
@[inline]
instance {p q} [Decidable p] [Decidable q] : Decidable (p q) :=
if hp : p then
if hq : q then
@@ -1207,17 +1188,13 @@ theorem dif_neg {c : Prop} {h : Decidable c} (hnc : ¬c) {α : Sort u} {t : c
| isTrue hc => absurd hc hnc
| isFalse _ => rfl
-- Remark: dite and ite are "defally equal" when we ignore the proofs.
theorem dif_eq_if (c : Prop) {h : Decidable c} {α : Sort u} (t : α) (e : α) : dite c (fun _ => t) (fun _ => e) = ite c t e :=
match h with
| isTrue _ => rfl
| isFalse _ => rfl
@[macro_inline]
instance {c t e : Prop} [dC : Decidable c] [dT : Decidable t] [dE : Decidable e] : Decidable (if c then t else e) :=
match dC with
| isTrue _ => dT
| isFalse _ => dE
@[inline]
instance {c : Prop} {t : c Prop} {e : ¬c Prop} [dC : Decidable c] [dT : h, Decidable (t h)] [dE : h, Decidable (e h)] : Decidable (if h : c then t h else e h) :=
match dC with
| isTrue hc => dT hc
@@ -1368,12 +1345,12 @@ namespace Subtype
theorem exists_of_subtype {α : Type u} {p : α Prop} : { x // p x } Exists (fun x => p x)
| a, h => a, h
set_option linter.missingDocs false in
@[deprecated exists_of_subtype (since := "2025-04-04")]
abbrev existsOfSubtype := @exists_of_subtype
variable {α : Sort u} {p : α Prop}
variable {α : Type u} {p : α Prop}
protected theorem ext : {a1 a2 : {x // p x}}, val a1 = val a2 a1 = a2
| _, _, _, _, rfl => rfl
@[deprecated Subtype.ext (since := "2025-10-26")]
protected theorem eq : {a1 a2 : {x // p x}}, val a1 = val a2 a1 = a2
| _, _, _, _, rfl => rfl
@@ -1388,9 +1365,9 @@ instance {α : Type u} {p : α → Prop} [BEq α] [ReflBEq α] : ReflBEq {x : α
rfl {x} := BEq.refl x.1
instance {α : Type u} {p : α Prop} [BEq α] [LawfulBEq α] : LawfulBEq {x : α // p x} where
eq_of_beq h := Subtype.eq (eq_of_beq h)
eq_of_beq h := Subtype.ext (eq_of_beq h)
instance {α : Type u} {p : α Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
instance {α : Sort u} {p : α Prop} [DecidableEq α] : DecidableEq {x : α // p x} :=
fun a, h₁ b, h₂ =>
if h : a = b then isTrue (by subst h; exact rfl)
else isFalse (fun h' => Subtype.noConfusion h' (fun h' => absurd h' h))
@@ -1491,6 +1468,8 @@ def Prod.map {α₁ : Type u₁} {α₂ : Type u₂} {β₁ : Type v₁} {β₂
@[simp] theorem Prod.map_apply (f : α β) (g : γ δ) (x) (y) :
Prod.map f g (x, y) = (f x, g y) := rfl
-- We add `@[grind =]` to these in `Init.Data.Prod`.
@[simp] theorem Prod.map_fst (f : α β) (g : γ δ) (x) : (Prod.map f g x).1 = f x.1 := rfl
@[simp] theorem Prod.map_snd (f : α β) (g : γ δ) (x) : (Prod.map f g x).2 = g x.2 := rfl
@@ -1507,20 +1486,24 @@ protected theorem PSigma.eta {α : Sort u} {β : α → Sort v} {a₁ a₂ : α}
/-! # Universe polymorphic unit -/
theorem PUnit.ext (a b : PUnit) : a = b := by
cases a; cases b; exact rfl
@[deprecated PUnit.ext (since := "2025-10-26")]
theorem PUnit.subsingleton (a b : PUnit) : a = b := by
cases a; cases b; exact rfl
theorem PUnit.eq_punit (a : PUnit) : a = :=
PUnit.subsingleton a
PUnit.ext a
instance : Subsingleton PUnit :=
Subsingleton.intro PUnit.subsingleton
Subsingleton.intro PUnit.ext
instance : Inhabited PUnit where
default :=
instance : DecidableEq PUnit :=
fun a b => isTrue (PUnit.subsingleton a b)
fun a b => isTrue (PUnit.ext a b)
/-! # Setoid -/

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@@ -6,7 +6,6 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Basic
public import Init.Data.Nat
public import Init.Data.Bool
public import Init.Data.BitVec

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@@ -7,7 +7,6 @@ Authors: Dany Fabian
module
prelude
public import Init.Classical
public import Init.ByCases
@[expose] public section

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@@ -6,10 +6,7 @@ Authors: Joachim Breitner, Mario Carneiro
module
prelude
public import Init.Data.Array.Mem
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Count
public import Init.Data.List.Attach
import all Init.Data.List.Attach
public section
@@ -752,9 +749,6 @@ and simplifies these to the function directly taking the value.
(Array.replicate n x).unattach = Array.replicate n x.1 := by
simp [unattach]
@[deprecated unattach_replicate (since := "2025-03-18")]
abbrev unattach_mkArray := @unattach_replicate
/-! ### Well-founded recursion preprocessing setup -/
@[wf_preprocess] theorem map_wfParam {xs : Array α} {f : α β} :

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@@ -6,10 +6,6 @@ Authors: Leonardo de Moura
module
prelude
public import Init.WFTactics
public import Init.Data.Nat.Basic
public import Init.Data.Fin.Basic
public import Init.Data.UInt.BasicAux
public import Init.GetElem
public import Init.Data.List.ToArrayImpl
import all Init.Data.List.ToArrayImpl
@@ -213,20 +209,6 @@ Examples:
def replicate {α : Type u} (n : Nat) (v : α) : Array α where
toList := List.replicate n v
/--
Creates an array that contains `n` repetitions of `v`.
The corresponding `List` function is `List.replicate`.
Examples:
* `Array.mkArray 2 true = #[true, true]`
* `Array.mkArray 3 () = #[(), (), ()]`
* `Array.mkArray 0 "anything" = #[]`
-/
@[extern "lean_mk_array", deprecated replicate (since := "2025-03-18")]
def mkArray {α : Type u} (n : Nat) (v : α) : Array α where
toList := List.replicate n v
/--
Swaps two elements of an array. The modification is performed in-place when the reference to the
array is unique.
@@ -244,7 +226,7 @@ def swap (xs : Array α) (i j : @& Nat) (hi : i < xs.size := by get_elem_tactic)
let xs' := xs.set i v₂
xs'.set j v₁ (Nat.lt_of_lt_of_eq hj (size_set _).symm)
@[simp] theorem size_swap {xs : Array α} {i j : Nat} {hi hj} : (xs.swap i j hi hj).size = xs.size := by
@[simp, grind =] theorem size_swap {xs : Array α} {i j : Nat} {hi hj} : (xs.swap i j hi hj).size = xs.size := by
change ((xs.set i xs[j]).set j xs[i]
(Nat.lt_of_lt_of_eq hj (size_set _).symm)).size = xs.size
rw [size_set, size_set]
@@ -466,7 +448,7 @@ Examples:
-/
abbrev take (xs : Array α) (i : Nat) : Array α := extract xs 0 i
@[simp] theorem take_eq_extract {xs : Array α} {i : Nat} : xs.take i = xs.extract 0 i := rfl
@[simp, grind =] theorem take_eq_extract {xs : Array α} {i : Nat} : xs.take i = xs.extract 0 i := rfl
/--
Removes the first `i` elements of `xs`. If `xs` has fewer than `i` elements, the new array is empty.
@@ -480,7 +462,7 @@ Examples:
-/
abbrev drop (xs : Array α) (i : Nat) : Array α := extract xs i xs.size
@[simp] theorem drop_eq_extract {xs : Array α} {i : Nat} : xs.drop i = xs.extract i xs.size := rfl
@[simp, grind =] theorem drop_eq_extract {xs : Array α} {i : Nat} : xs.drop i = xs.extract i xs.size := rfl
@[inline]
unsafe def modifyMUnsafe [Monad m] (xs : Array α) (i : Nat) (f : α m α) : m (Array α) := do
@@ -752,8 +734,7 @@ of results.
def mapM {α : Type u} {β : Type v} {m : Type v Type w} [Monad m] (f : α m β) (as : Array α) : m (Array β) :=
-- Note: we cannot use `foldlM` here for the reference implementation because this calls
-- `bind` and `pure` too many times. (We are not assuming `m` is a `LawfulMonad`)
let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
map (i : Nat) (bs : Array β) : m (Array β) := do
let rec map (i : Nat) (bs : Array β) : m (Array β) := do
if hlt : i < as.size then
map (i+1) (bs.push ( f as[i]))
else
@@ -913,8 +894,7 @@ entire array is checked.
@[implemented_by anyMUnsafe, expose]
def anyM {α : Type u} {m : Type Type w} [Monad m] (p : α m Bool) (as : Array α) (start := 0) (stop := as.size) : m Bool :=
let any (stop : Nat) (h : stop as.size) :=
let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
loop (j : Nat) : m Bool := do
let rec loop (j : Nat) : m Bool := do
if hlt : j < stop then
have : j < as.size := Nat.lt_of_lt_of_le hlt h
if ( p as[j]) then
@@ -1252,8 +1232,7 @@ Examples:
-/
@[inline, expose]
def findIdx? {α : Type u} (p : α Bool) (as : Array α) : Option Nat :=
let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
loop (j : Nat) :=
let rec loop (j : Nat) :=
if h : j < as.size then
if p as[j] then some j else loop (j + 1)
else none
@@ -1270,8 +1249,7 @@ Examples:
-/
@[inline]
def findFinIdx? {α : Type u} (p : α Bool) (as : Array α) : Option (Fin as.size) :=
let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
loop (j : Nat) :=
let rec loop (j : Nat) :=
if h : j < as.size then
if p as[j] then some j, h else loop (j + 1)
else none
@@ -1307,7 +1285,6 @@ Examples:
@[inline, expose]
def findIdx (p : α Bool) (as : Array α) : Nat := (as.findIdx? p).getD as.size
@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
def idxOfAux [BEq α] (xs : Array α) (v : α) (i : Nat) : Option (Fin xs.size) :=
if h : i < xs.size then
if xs[i] == v then some i, h
@@ -1717,7 +1694,6 @@ Examples:
* `#[3, 2, 3, 4].popWhile (· > 2) = #[3, 2]`
* `(#[] : Array Nat).popWhile (· > 2) = #[]`
-/
@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
def popWhile (p : α Bool) (as : Array α) : Array α :=
if h : as.size > 0 then
if p (as[as.size - 1]'(Nat.sub_lt h (by decide))) then
@@ -1728,7 +1704,7 @@ def popWhile (p : α → Bool) (as : Array α) : Array α :=
as
decreasing_by simp_wf; decreasing_trivial_pre_omega
@[simp] theorem popWhile_empty {p : α Bool} :
@[simp, grind =] theorem popWhile_empty {p : α Bool} :
popWhile p #[] = #[] := by
simp [popWhile]
@@ -1742,8 +1718,7 @@ Examples:
* `#[0, 1, 2, 3, 2, 1].takeWhile (· < 0) = #[]`
-/
def takeWhile (p : α Bool) (as : Array α) : Array α :=
let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
go (i : Nat) (acc : Array α) : Array α :=
let rec go (i : Nat) (acc : Array α) : Array α :=
if h : i < as.size then
let a := as[i]
if p a then
@@ -1766,7 +1741,6 @@ Examples:
* `#["apple", "pear", "orange"].eraseIdx 1 = #["apple", "orange"]`
* `#["apple", "pear", "orange"].eraseIdx 2 = #["apple", "pear"]`
-/
@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
def eraseIdx (xs : Array α) (i : Nat) (h : i < xs.size := by get_elem_tactic) : Array α :=
if h' : i + 1 < xs.size then
let xs' := xs.swap (i + 1) i
@@ -1777,7 +1751,8 @@ termination_by xs.size - i
decreasing_by simp_wf; exact Nat.sub_succ_lt_self _ _ h
-- This is required in `Lean.Data.PersistentHashMap`.
@[simp] theorem size_eraseIdx {xs : Array α} (i : Nat) (h) : (xs.eraseIdx i h).size = xs.size - 1 := by
@[simp, grind =]
theorem size_eraseIdx {xs : Array α} (i : Nat) (h) : (xs.eraseIdx i h).size = xs.size - 1 := by
induction xs, i, h using Array.eraseIdx.induct with
| @case1 xs i h h' xs' ih =>
unfold eraseIdx
@@ -1861,8 +1836,7 @@ Examples:
* `#["tues", "thur", "sat"].insertIdx 3 "wed" = #["tues", "thur", "sat", "wed"]`
-/
@[inline] def insertIdx (as : Array α) (i : Nat) (a : α) (_ : i as.size := by get_elem_tactic) : Array α :=
let rec @[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
loop (as : Array α) (j : Fin as.size) :=
let rec loop (as : Array α) (j : Fin as.size) :=
if i < j then
let j' : Fin as.size := j-1, Nat.lt_of_le_of_lt (Nat.pred_le _) j.2
let as := as.swap j' j
@@ -1916,7 +1890,6 @@ def insertIdxIfInBounds (as : Array α) (i : Nat) (a : α) : Array α :=
else
as
@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
def isPrefixOfAux [BEq α] (as bs : Array α) (hle : as.size bs.size) (i : Nat) : Bool :=
if h : i < as.size then
let a := as[i]
@@ -1945,7 +1918,7 @@ def isPrefixOf [BEq α] (as bs : Array α) : Bool :=
else
false
@[semireducible, specialize] -- This is otherwise irreducible because it uses well-founded recursion.
@[specialize]
def zipWithMAux {m : Type v Type w} [Monad m] (as : Array α) (bs : Array β) (f : α β m γ) (i : Nat) (cs : Array γ) : m (Array γ) := do
if h : i < as.size then
let a := as[i]
@@ -2108,7 +2081,6 @@ private def allDiffAuxAux [BEq α] (as : Array α) (a : α) : forall (i : Nat),
have : i < as.size := Nat.lt_trans (Nat.lt_succ_self _) h;
a != as[i] && allDiffAuxAux as a i this
@[semireducible] -- This is otherwise irreducible because it uses well-founded recursion.
private def allDiffAux [BEq α] (as : Array α) (i : Nat) : Bool :=
if h : i < as.size then
allDiffAuxAux as as[i] i h && allDiffAux as (i+1)
@@ -2162,5 +2134,3 @@ instance [ToString α] : ToString (Array α) where
toString xs := String.Internal.append "#" (toString xs.toList)
end Array
export Array (mkArray)

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@@ -6,10 +6,8 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Nat.Linear
public import Init.NotationExtra
public section

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@@ -6,9 +6,7 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Array.Basic
public import Init.Data.Int.DivMod.Lemmas
public import Init.Omega
public section
universe u v

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@@ -8,7 +8,6 @@ module
prelude
public import Init.Data.List.TakeDrop
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public section
@@ -32,7 +31,7 @@ theorem foldlM_toList.aux [Monad m]
· cases Nat.not_le_of_gt _ (Nat.zero_add _ H)
· rename_i i; rw [Nat.succ_add] at H
simp [foldlM_toList.aux (j := j+1) H]
rw (occs := [2]) [ List.getElem_cons_drop_succ_eq_drop _]
rw (occs := [2]) [ List.getElem_cons_drop _]
simp
· rw [List.drop_of_length_le (Nat.ge_of_not_lt _)]; simp

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@@ -6,7 +6,6 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.Count
@@ -100,9 +99,6 @@ theorem countP_le_size : countP p xs ≤ xs.size := by
theorem countP_replicate {a : α} {n : Nat} : countP p (replicate n a) = if p a then n else 0 := by
simp [ List.toArray_replicate, List.countP_replicate]
@[deprecated countP_replicate (since := "2025-03-18")]
abbrev countP_mkArray := @countP_replicate
theorem boole_getElem_le_countP {xs : Array α} {i : Nat} (h : i < xs.size) :
(if p xs[i] then 1 else 0) xs.countP p := by
rcases xs with xs
@@ -263,15 +259,9 @@ theorem count_eq_size {xs : Array α} : count a xs = xs.size ↔ ∀ b ∈ xs, a
@[simp] theorem count_replicate_self {a : α} {n : Nat} : count a (replicate n a) = n := by
simp [ List.toArray_replicate]
@[deprecated count_replicate_self (since := "2025-03-18")]
abbrev count_mkArray_self := @count_replicate_self
theorem count_replicate {a b : α} {n : Nat} : count a (replicate n b) = if b == a then n else 0 := by
simp [ List.toArray_replicate, List.count_replicate]
@[deprecated count_replicate (since := "2025-03-18")]
abbrev count_mkArray := @count_replicate
theorem filter_beq {xs : Array α} (a : α) : xs.filter (· == a) = replicate (count a xs) a := by
rcases xs with xs
simp [List.filter_beq]
@@ -285,9 +275,6 @@ theorem replicate_count_eq_of_count_eq_size {xs : Array α} (h : count a xs = xs
rw [ toList_inj]
simp [List.replicate_count_eq_of_count_eq_length (by simpa using h)]
@[deprecated replicate_count_eq_of_count_eq_size (since := "2025-03-18")]
abbrev mkArray_count_eq_of_count_eq_size := @replicate_count_eq_of_count_eq_size
@[simp] theorem count_filter {xs : Array α} (h : p a) : count a (filter p xs) = count a xs := by
rcases xs with xs
simp [List.count_filter, h]

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@@ -6,11 +6,9 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.BEq
public import Init.Data.List.Nat.BEq
public import Init.ByCases
public section

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@@ -6,11 +6,8 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.Erase
public import Init.Data.List.Nat.Basic
public section
@@ -142,25 +139,16 @@ theorem eraseP_replicate {n : Nat} {a : α} {p : α → Bool} :
simp only [ List.toArray_replicate, List.eraseP_toArray, List.eraseP_replicate]
split <;> simp
@[deprecated eraseP_replicate (since := "2025-03-18")]
abbrev eraseP_mkArray := @eraseP_replicate
@[simp] theorem eraseP_replicate_of_pos {n : Nat} {a : α} (h : p a) :
(replicate n a).eraseP p = replicate (n - 1) a := by
simp only [ List.toArray_replicate, List.eraseP_toArray]
simp [h]
@[deprecated eraseP_replicate_of_pos (since := "2025-03-18")]
abbrev eraseP_mkArray_of_pos := @eraseP_replicate_of_pos
@[simp] theorem eraseP_replicate_of_neg {n : Nat} {a : α} (h : ¬p a) :
(replicate n a).eraseP p = replicate n a := by
simp only [ List.toArray_replicate, List.eraseP_toArray]
simp [h]
@[deprecated eraseP_replicate_of_neg (since := "2025-03-18")]
abbrev eraseP_mkArray_of_neg := @eraseP_replicate_of_neg
theorem eraseP_eq_iff {p} {xs : Array α} :
xs.eraseP p = ys
(( a xs, ¬ p a) xs = ys)
@@ -281,9 +269,6 @@ theorem erase_replicate [LawfulBEq α] {n : Nat} {a b : α} :
simp only [List.erase_replicate, beq_iff_eq, List.toArray_replicate]
split <;> simp
@[deprecated erase_replicate (since := "2025-03-18")]
abbrev erase_mkArray := @erase_replicate
-- The arguments `a b` are explicit,
-- so they can be specified to prevent `simp` repeatedly applying the lemma.
@[grind =]
@@ -311,17 +296,11 @@ theorem erase_eq_iff [LawfulBEq α] {a : α} {xs : Array α} :
simp only [ List.toArray_replicate, List.erase_toArray]
simp
@[deprecated erase_replicate_self (since := "2025-03-18")]
abbrev erase_mkArray_self := @erase_replicate_self
@[simp] theorem erase_replicate_ne [LawfulBEq α] {a b : α} (h : !b == a) :
(replicate n a).erase b = replicate n a := by
rw [erase_of_not_mem]
simp_all
@[deprecated erase_replicate_ne (since := "2025-03-18")]
abbrev erase_mkArray_ne := @erase_replicate_ne
end erase
/-! ### eraseIdxIfInBounds -/
@@ -432,9 +411,6 @@ theorem eraseIdx_replicate {n : Nat} {a : α} {k : Nat} {h} :
simp only [ List.toArray_replicate, List.eraseIdx_toArray]
simp [List.eraseIdx_replicate, h]
@[deprecated eraseIdx_replicate (since := "2025-03-18")]
abbrev eraseIdx_mkArray := @eraseIdx_replicate
theorem mem_eraseIdx_iff_getElem {x : α} {xs : Array α} {k} {h} : x xs.eraseIdx k h i w, i k xs[i]'w = x := by
rcases xs with xs
simp [List.mem_eraseIdx_iff_getElem, *]

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@@ -7,7 +7,6 @@ module
prelude
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.TakeDrop
public section
@@ -290,9 +289,6 @@ theorem extract_append_right {as bs : Array α} :
· simp only [size_extract, size_replicate] at h₁ h₂
simp only [getElem_extract, getElem_replicate]
@[deprecated extract_replicate (since := "2025-03-18")]
abbrev extract_mkArray := @extract_replicate
theorem extract_eq_extract_right {as : Array α} {i j j' : Nat} :
as.extract i j = as.extract i j' min (j - i) (as.size - i) = min (j' - i) (as.size - i) := by
rcases as with as
@@ -430,32 +426,20 @@ theorem popWhile_append {xs ys : Array α} :
(replicate n a).takeWhile p = (replicate n a).filter p := by
simp [ List.toArray_replicate]
@[deprecated takeWhile_replicate_eq_filter (since := "2025-03-18")]
abbrev takeWhile_mkArray_eq_filter := @takeWhile_replicate_eq_filter
theorem takeWhile_replicate {p : α Bool} :
(replicate n a).takeWhile p = if p a then replicate n a else #[] := by
simp [takeWhile_replicate_eq_filter, filter_replicate]
@[deprecated takeWhile_replicate (since := "2025-03-18")]
abbrev takeWhile_mkArray := @takeWhile_replicate
@[simp] theorem popWhile_replicate_eq_filter_not {p : α Bool} :
(replicate n a).popWhile p = (replicate n a).filter (fun a => !p a) := by
simp [ List.toArray_replicate, List.filter_reverse]
@[deprecated popWhile_replicate_eq_filter_not (since := "2025-03-18")]
abbrev popWhile_mkArray_eq_filter_not := @popWhile_replicate_eq_filter_not
theorem popWhile_replicate {p : α Bool} :
(replicate n a).popWhile p = if p a then #[] else replicate n a := by
simp only [popWhile_replicate_eq_filter_not, size_replicate, filter_replicate, Bool.not_eq_eq_eq_not,
Bool.not_true]
split <;> simp_all
@[deprecated popWhile_replicate (since := "2025-03-18")]
abbrev popWhile_mkArray := @popWhile_replicate
theorem extract_takeWhile {as : Array α} {i : Nat} :
(as.takeWhile p).extract 0 i = (as.extract 0 i).takeWhile p := by
rcases as with as

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@@ -6,7 +6,6 @@ Authors: François G. Dorais
module
prelude
public import Init.Data.List.FinRange
public import Init.Data.Array.OfFn
public section

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@@ -7,10 +7,7 @@ module
prelude
public import Init.Data.List.Nat.Find
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Attach
public import Init.Data.Array.Range
public section
@@ -132,31 +129,19 @@ theorem getElem_zero_flatten {xss : Array (Array α)} (h) :
theorem findSome?_replicate : findSome? f (replicate n a) = if n = 0 then none else f a := by
simp [ List.toArray_replicate, List.findSome?_replicate]
@[deprecated findSome?_replicate (since := "2025-03-18")]
abbrev findSome?_mkArray := @findSome?_replicate
@[simp] theorem findSome?_replicate_of_pos (h : 0 < n) : findSome? f (replicate n a) = f a := by
simp [findSome?_replicate, Nat.ne_of_gt h]
@[deprecated findSome?_replicate_of_pos (since := "2025-03-18")]
abbrev findSome?_mkArray_of_pos := @findSome?_replicate_of_pos
-- Argument is unused, but used to decide whether `simp` should unfold.
@[simp] theorem findSome?_replicate_of_isSome (_ : (f a).isSome) :
findSome? f (replicate n a) = if n = 0 then none else f a := by
simp [findSome?_replicate]
@[deprecated findSome?_replicate_of_isSome (since := "2025-03-18")]
abbrev findSome?_mkArray_of_isSome := @findSome?_replicate_of_isSome
@[simp] theorem findSome?_replicate_of_isNone (h : (f a).isNone) :
findSome? f (replicate n a) = none := by
rw [Option.isNone_iff_eq_none] at h
simp [findSome?_replicate, h]
@[deprecated findSome?_replicate_of_isNone (since := "2025-03-18")]
abbrev findSome?_mkArray_of_isNone := @findSome?_replicate_of_isNone
/-! ### find? -/
@[simp, grind =] theorem find?_empty : find? p #[] = none := rfl
@@ -321,16 +306,10 @@ theorem find?_replicate :
find? p (replicate n a) = if p a then some a else none := by
simp [find?_replicate, Nat.ne_of_gt h]
@[deprecated find?_replicate_of_size_pos (since := "2025-03-18")]
abbrev find?_mkArray_of_length_pos := @find?_replicate_of_size_pos
@[simp] theorem find?_replicate_of_pos (h : p a) :
find? p (replicate n a) = if n = 0 then none else some a := by
simp [find?_replicate, h]
@[deprecated find?_replicate_of_pos (since := "2025-03-18")]
abbrev find?_mkArray_of_pos := @find?_replicate_of_pos
@[simp] theorem find?_replicate_of_neg (h : ¬ p a) : find? p (replicate n a) = none := by
simp [find?_replicate, h]
@@ -586,9 +565,6 @@ theorem findIdx?_flatten {xss : Array (Array α)} {p : α → Bool} :
simp only [List.findIdx?_toArray]
simp
@[deprecated findIdx?_replicate (since := "2025-03-18")]
abbrev findIdx?_mkArray := @findIdx?_replicate
theorem findIdx?_eq_findSome?_zipIdx {xs : Array α} {p : α Bool} :
xs.findIdx? p = xs.zipIdx.findSome? fun a, i => if p a then some i else none := by
rcases xs with xs

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@@ -50,6 +50,6 @@ where
getLit_eq (xs : Array α) (i : Nat) (h₁ : xs.size = n) (h₂ : i < n) : xs.getLit i h₁ h₂ = getElem xs.toList i ((id (α := xs.toList.length = n) h₁) h₂) :=
rfl
go (i : Nat) (hi : i xs.size) : toListLitAux xs n hsz i hi (xs.toList.drop i) = xs.toList := by
induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.getElem_cons_drop_succ_eq_drop, *]
induction i <;> simp only [List.drop, toListLitAux, getLit_eq, List.getElem_cons_drop, *]
end Array

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@@ -7,7 +7,6 @@ module
prelude
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.InsertIdx
public section

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@@ -6,17 +6,10 @@ Authors: Mario Carneiro, Kim Morrison
module
prelude
public import Init.Data.Nat.Lemmas
public import Init.Data.List.Range
public import Init.Data.List.Nat.TakeDrop
public import Init.Data.List.Nat.Modify
public import Init.Data.List.Nat.Basic
public import Init.Data.List.Monadic
public import Init.Data.List.OfFn
public import Init.Data.Array.Mem
public import Init.Data.Array.DecidableEq
public import Init.Data.Range.Lemmas
public import Init.TacticsExtra
public import Init.Data.List.ToArray
import all Init.Data.List.Control
import all Init.Data.Array.Basic
@@ -252,12 +245,13 @@ theorem back_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.pus
replace h := List.append_inj_right' h (by simp)
simpa using h
theorem pop_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.push b) : xs = ys := by
theorem push_eq_push {a b : α} {xs ys : Array α} : xs.push a = ys.push b a = b xs = ys := by
cases xs
cases ys
simp at h
replace h := List.append_inj_left' h (by simp)
simp [h]
simp [And.comm]
theorem pop_eq_of_push_eq {a b : α} {xs ys : Array α} (h : xs.push a = ys.push b) : xs = ys :=
(push_eq_push.1 h).2
theorem push_inj_left {a : α} {xs ys : Array α} : xs.push a = ys.push a xs = ys :=
pop_eq_of_push_eq, fun h => by simp [h]
@@ -265,15 +259,6 @@ theorem push_inj_left {a : α} {xs ys : Array α} : xs.push a = ys.push a ↔ xs
theorem push_inj_right {a b : α} {xs : Array α} : xs.push a = xs.push b a = b :=
back_eq_of_push_eq, fun h => by simp [h]
theorem push_eq_push {a b : α} {xs ys : Array α} : xs.push a = ys.push b a = b xs = ys := by
constructor
· intro h
exact back_eq_of_push_eq h, pop_eq_of_push_eq h
· rintro rfl, rfl
rfl
theorem push_eq_append_singleton {as : Array α} {x : α} : as.push x = as ++ #[x] := rfl
theorem exists_push_of_ne_empty {xs : Array α} (h : xs #[]) :
(ys : Array α) (a : α), xs = ys.push a := by
rcases xs with xs
@@ -324,41 +309,23 @@ theorem singleton_inj : #[a] = #[b] ↔ a = b := by
@[simp, grind =] theorem size_replicate {n : Nat} {v : α} : (replicate n v).size = n :=
List.length_replicate ..
@[deprecated size_replicate (since := "2025-03-18")]
abbrev size_mkArray := @size_replicate
@[simp] theorem toList_replicate : (replicate n a).toList = List.replicate n a := by
simp only [replicate]
@[deprecated toList_replicate (since := "2025-03-18")]
abbrev toList_mkArray := @toList_replicate
@[simp, grind =] theorem replicate_zero : replicate 0 a = #[] := rfl
@[deprecated replicate_zero (since := "2025-03-18")]
abbrev mkArray_zero := @replicate_zero
@[grind =]
theorem replicate_succ : replicate (n + 1) a = (replicate n a).push a := by
apply toList_inj.1
simp [List.replicate_succ']
@[deprecated replicate_succ (since := "2025-03-18")]
abbrev mkArray_succ := @replicate_succ
@[simp, grind =] theorem getElem_replicate {n : Nat} {v : α} {i : Nat} (h : i < (replicate n v).size) :
(replicate n v)[i] = v := by simp [ getElem_toList]
@[deprecated getElem_replicate (since := "2025-03-18")]
abbrev getElem_mkArray := @getElem_replicate
@[grind =] theorem getElem?_replicate {n : Nat} {v : α} {i : Nat} :
(replicate n v)[i]? = if i < n then some v else none := by
simp [getElem?_def]
@[deprecated getElem?_replicate (since := "2025-03-18")]
abbrev getElem?_mkArray := @getElem?_replicate
/-! ### mem -/
@[grind ]
@@ -842,6 +809,11 @@ theorem contains_eq_true_of_mem [BEq α] [ReflBEq α] {a : α} {as : Array α} (
theorem elem_iff [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
elem a xs = true a xs := mem_of_contains_eq_true, contains_eq_true_of_mem
@[grind =]
theorem contains_iff_mem [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
xs.contains a = true a xs := mem_of_contains_eq_true, contains_eq_true_of_mem
@[deprecated contains_iff_mem (since := "2025-10-26")]
theorem contains_iff [BEq α] [LawfulBEq α] {a : α} {xs : Array α} :
xs.contains a = true a xs := mem_of_contains_eq_true, contains_eq_true_of_mem
@@ -1081,12 +1053,6 @@ theorem mem_or_eq_of_mem_setIfInBounds
cases xs
simp
@[deprecated beq_empty_eq (since := "2025-04-04")]
abbrev beq_empty_iff := @beq_empty_eq
@[deprecated empty_beq_eq (since := "2025-04-04")]
abbrev empty_beq_iff := @empty_beq_eq
@[simp, grind =] theorem push_beq_push [BEq α] {a b : α} {xs ys : Array α} :
(xs.push a == ys.push b) = (xs == ys && a == b) := by
cases xs
@@ -1107,9 +1073,6 @@ theorem size_eq_of_beq [BEq α] {xs ys : Array α} (h : xs == ys) : xs.size = ys
rw [Bool.eq_iff_iff]
simp +contextual
@[deprecated replicate_beq_replicate (since := "2025-03-18")]
abbrev mkArray_beq_mkArray := @replicate_beq_replicate
private theorem beq_of_beq_singleton [BEq α] {a b : α} : #[a] == #[b] a == b := by
intro h
have : isEqv #[a] #[b] BEq.beq = true := h
@@ -1173,7 +1136,7 @@ where
aux (i bs) :
mapM.map f xs i bs = (xs.toList.drop i).foldlM (fun bs a => bs.push <$> f a) bs := by
unfold mapM.map; split
· rw [ List.getElem_cons_drop_succ_eq_drop _]
· rw [ List.getElem_cons_drop _]
simp only [aux (i + 1), map_eq_pure_bind, List.foldlM_cons, bind_assoc,
pure_bind]
rfl
@@ -1725,9 +1688,6 @@ theorem forall_none_of_filterMap_eq_empty (h : filterMap f xs = #[]) : ∀ x ∈
cases xs
simp
@[deprecated filterMap_eq_empty_iff (since := "2025-04-04")]
abbrev filterMap_eq_nil_iff := @filterMap_eq_empty_iff
theorem filterMap_eq_push_iff {f : α Option β} {xs : Array α} {ys : Array β} {b : β} :
filterMap f xs = ys.push b as a bs,
xs = as.push a ++ bs filterMap f as = ys f a = some b ( x, x bs f x = none) := by
@@ -1890,6 +1850,9 @@ theorem getElem_of_append {xs ys zs : Array α} (eq : xs = ys.push a ++ zs) (h :
theorem push_eq_append {a : α} {as : Array α} : as.push a = as ++ #[a] := rfl
@[deprecated push_eq_append (since := "2025-10-26")]
theorem push_eq_append_singleton {as : Array α} {x : α} : as.push x = as ++ #[x] := rfl
theorem append_inj {xs₁ xs₂ ys₁ ys₂ : Array α} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) :
xs₁ = xs₂ ys₁ = ys₂ := by
rcases xs₁ with s₁
@@ -2090,11 +2053,22 @@ theorem append_eq_map_iff {f : α → β} :
| nil => simp
| cons as => induction as.toList <;> simp [*]
@[simp] theorem flatten_toArray_map {L : List (List α)} :
@[simp] theorem flatten_toArray_map_toArray {L : List (List α)} :
(L.map List.toArray).toArray.flatten = L.flatten.toArray := by
apply ext'
simp [Function.comp_def]
@[deprecated flatten_toArray_map_toArray (since := "2025-10-26")]
theorem flatten_toArray_map {L : List (List α)} :
(L.map List.toArray).toArray.flatten = L.flatten.toArray := by
simp
@[grind =]
theorem flatten_map_toArray_toArray {L : List (List α)} :
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
simp
@[deprecated flatten_map_toArray_toArray (since := "2025-10-26")]
theorem flatten_map_toArray {L : List (List α)} :
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
simp
@@ -2141,32 +2115,33 @@ theorem forall_mem_flatten {p : α → Prop} {xss : Array (Array α)} :
theorem flatten_eq_flatMap {xss : Array (Array α)} : flatten xss = xss.flatMap id := by
induction xss using array₂_induction
rw [flatten_toArray_map, List.flatten_eq_flatMap]
rw [flatten_toArray_map_toArray, List.flatten_eq_flatMap]
simp [List.flatMap_map]
@[simp, grind _=_] theorem map_flatten {f : α β} {xss : Array (Array α)} :
(flatten xss).map f = (map (map f) xss).flatten := by
induction xss using array₂_induction with
| of xss =>
simp only [flatten_toArray_map, List.map_toArray, List.map_flatten, List.map_map,
simp only [flatten_toArray_map_toArray, List.map_toArray, List.map_flatten, List.map_map,
Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map]
rw [ Function.comp_def, List.map_map, flatten_toArray_map_toArray]
@[simp, grind =] theorem filterMap_flatten {f : α Option β} {xss : Array (Array α)} {stop : Nat} (w : stop = xss.flatten.size) :
filterMap f (flatten xss) 0 stop = flatten (map (filterMap f) xss) := by
subst w
induction xss using array₂_induction
simp only [flatten_toArray_map, List.size_toArray, List.length_flatten, List.filterMap_toArray',
List.filterMap_flatten, List.map_toArray, List.map_map, Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map]
simp only [flatten_toArray_map_toArray, List.size_toArray, List.length_flatten,
List.filterMap_toArray', List.filterMap_flatten, List.map_toArray, List.map_map,
Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map_toArray]
@[simp, grind =] theorem filter_flatten {p : α Bool} {xss : Array (Array α)} {stop : Nat} (w : stop = xss.flatten.size) :
filter p (flatten xss) 0 stop = flatten (map (filter p) xss) := by
subst w
induction xss using array₂_induction
simp only [flatten_toArray_map, List.size_toArray, List.length_flatten, List.filter_toArray',
List.filter_flatten, List.map_toArray, List.map_map, Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map]
simp only [flatten_toArray_map_toArray, List.size_toArray, List.length_flatten,
List.filter_toArray', List.filter_flatten, List.map_toArray, List.map_map, Function.comp_def]
rw [ Function.comp_def, List.map_map, flatten_toArray_map_toArray]
theorem flatten_filter_not_isEmpty {xss : Array (Array α)} :
flatten (xss.filter fun xs => !xs.isEmpty) = xss.flatten := by
@@ -2189,23 +2164,23 @@ theorem flatten_filter_ne_empty [DecidablePred fun xs : Array α => xs ≠ #[]]
induction xss using array₂_induction
rcases xs with l
have this : [l.toArray] = [l].map List.toArray := by simp
simp only [List.push_toArray, flatten_toArray_map, List.append_toArray]
rw [this, List.map_append, flatten_toArray_map]
simp only [List.push_toArray, flatten_toArray_map_toArray, List.append_toArray]
rw [this, List.map_append, flatten_toArray_map_toArray]
simp
theorem flatten_flatten {xss : Array (Array (Array α))} : flatten (flatten xss) = flatten (map flatten xss) := by
induction xss using array₃_induction with
| of xss =>
rw [flatten_toArray_map]
rw [flatten_toArray_map_toArray]
have : (xss.map (fun xs => xs.map List.toArray)).flatten = xss.flatten.map List.toArray := by
induction xss with
| nil => simp
| cons xs xss ih =>
simp only [List.map_cons, List.flatten_cons, ih, List.map_append]
rw [this, flatten_toArray_map, List.flatten_flatten, List.map_toArray, Array.map_map,
rw [this, flatten_toArray_map_toArray, List.flatten_flatten, List.map_toArray, Array.map_map,
List.map_toArray, map_map, Function.comp_def]
simp only [Function.comp_apply, flatten_toArray_map]
rw [List.map_toArray, Function.comp_def, List.map_map, flatten_toArray_map]
simp only [Function.comp_apply, flatten_toArray_map_toArray]
rw [List.map_toArray, Function.comp_def, List.map_map, flatten_toArray_map_toArray]
theorem flatten_eq_push_iff {xss : Array (Array α)} {ys : Array α} {y : α} :
xss.flatten = ys.push y
@@ -2214,13 +2189,13 @@ theorem flatten_eq_push_iff {xss : Array (Array α)} {ys : Array α} {y : α} :
induction xss using array₂_induction with
| of xs =>
rcases ys with ys
rw [flatten_toArray_map, List.push_toArray, mk.injEq, List.flatten_eq_append_iff]
rw [flatten_toArray_map_toArray, List.push_toArray, mk.injEq, List.flatten_eq_append_iff]
constructor
· rintro (as, bs, rfl, rfl, h | as, bs, c, cs, ds, rfl, rfl, h)
· rw [List.singleton_eq_flatten_iff] at h
obtain xs, ys, rfl, h₁, h₂ := h
exact ((as ++ xs).map List.toArray).toArray, #[], (ys.map List.toArray).toArray, by simp,
by simpa using h₂, by rw [flatten_toArray_map]; simpa
by simpa using h₂, by rw [flatten_toArray_map_toArray]; simpa
· rw [List.singleton_eq_append_iff] at h
obtain (h₁, h₂ | h₁, h₂) := h
· simp at h₁
@@ -2265,18 +2240,12 @@ theorem eq_iff_flatten_eq {xss₁ xss₂ : Array (Array α)} :
rw [List.map_inj_right]
simp +contextual
theorem flatten_toArray_map_toArray {xss : List (List α)} :
(xss.map List.toArray).toArray.flatten = xss.flatten.toArray := by
simp
/-! ### flatMap -/
theorem flatMap_def {xs : Array α} {f : α Array β} : xs.flatMap f = flatten (map f xs) := by
rcases xs with l
simp [flatten_toArray, Function.comp_def, List.flatMap_def]
@[simp, grind =] theorem flatMap_empty {β} {f : α Array β} : (#[] : Array α).flatMap f = #[] := rfl
theorem flatMap_toList {xs : Array α} {f : α List β} :
xs.toList.flatMap f = (xs.flatMap (fun a => (f a).toArray)).toList := by
rcases xs with l
@@ -2287,6 +2256,7 @@ theorem flatMap_toList {xs : Array α} {f : α → List β} :
rcases xs with l
simp
@[deprecated List.flatMap_toArray_cons (since := "2025-10-29")]
theorem flatMap_toArray_cons {β} {f : α Array β} {a : α} {as : List α} :
(a :: as).toArray.flatMap f = f a ++ as.toArray.flatMap f := by
simp [flatMap]
@@ -2297,6 +2267,7 @@ theorem flatMap_toArray_cons {β} {f : α → Array β} {a : α} {as : List α}
intro cs
induction as generalizing cs <;> simp_all
@[deprecated List.flatMap_toArray (since := "2025-10-29")]
theorem flatMap_toArray {β} {f : α Array β} {as : List α} :
as.toArray.flatMap f = (as.flatMap (fun a => (f a).toList)).toArray := by
simp
@@ -2397,77 +2368,44 @@ theorem flatMap_eq_foldl {f : α → Array β} {xs : Array α} :
@[simp] theorem replicate_one : replicate 1 a = #[a] := rfl
@[deprecated replicate_one (since := "2025-03-18")]
abbrev mkArray_one := @replicate_one
/-- Variant of `replicate_succ` that prepends `a` at the beginning of the array. -/
theorem replicate_succ' : replicate (n + 1) a = #[a] ++ replicate n a := by
apply Array.ext'
simp [List.replicate_succ]
@[deprecated replicate_succ' (since := "2025-03-18")]
abbrev mkArray_succ' := @replicate_succ'
@[simp, grind =] theorem mem_replicate {a b : α} {n} : b replicate n a n 0 b = a := by
unfold replicate
simp only [List.mem_toArray, List.mem_replicate]
@[deprecated mem_replicate (since := "2025-03-18")]
abbrev mem_mkArray := @mem_replicate
@[grind ] theorem eq_of_mem_replicate {a b : α} {n} (h : b replicate n a) : b = a := (mem_replicate.1 h).2
@[deprecated eq_of_mem_mkArray (since := "2025-03-18")]
abbrev eq_of_mem_mkArray := @eq_of_mem_replicate
theorem forall_mem_replicate {p : α Prop} {a : α} {n} :
( b, b replicate n a p b) n = 0 p a := by
cases n <;> simp [mem_replicate]
@[deprecated forall_mem_replicate (since := "2025-03-18")]
abbrev forall_mem_mkArray := @forall_mem_replicate
@[simp] theorem replicate_succ_ne_empty {n : Nat} {a : α} : replicate (n+1) a #[] := by
simp [replicate_succ]
@[deprecated replicate_succ_ne_empty (since := "2025-03-18")]
abbrev mkArray_succ_ne_empty := @replicate_succ_ne_empty
@[simp] theorem replicate_eq_empty_iff {n : Nat} {a : α} : replicate n a = #[] n = 0 := by
cases n <;> simp
@[deprecated replicate_eq_empty_iff (since := "2025-03-18")]
abbrev mkArray_eq_empty_iff := @replicate_eq_empty_iff
@[simp] theorem replicate_inj : replicate n a = replicate m b n = m (n = 0 a = b) := by
rw [ toList_inj]
simp
@[deprecated replicate_inj (since := "2025-03-18")]
abbrev mkArray_inj := @replicate_inj
theorem eq_replicate_of_mem {a : α} {xs : Array α} (h : (b) (_ : b xs), b = a) : xs = replicate xs.size a := by
rw [ toList_inj]
simpa using List.eq_replicate_of_mem (by simpa using h)
@[deprecated eq_replicate_of_mem (since := "2025-03-18")]
abbrev eq_mkArray_of_mem := @eq_replicate_of_mem
theorem eq_replicate_iff {a : α} {n} {xs : Array α} :
xs = replicate n a xs.size = n (b) (_ : b xs), b = a := by
rw [ toList_inj]
simpa using List.eq_replicate_iff (l := xs.toList)
@[deprecated eq_replicate_iff (since := "2025-03-18")]
abbrev eq_mkArray_iff := @eq_replicate_iff
theorem map_eq_replicate_iff {xs : Array α} {f : α β} {b : β} :
xs.map f = replicate xs.size b x xs, f x = b := by
simp [eq_replicate_iff]
@[deprecated map_eq_replicate_iff (since := "2025-03-18")]
abbrev map_eq_mkArray_iff := @map_eq_replicate_iff
@[simp] theorem map_const {xs : Array α} {b : β} : map (Function.const α b) xs = replicate xs.size b :=
map_eq_replicate_iff.mpr fun _ _ => rfl
@@ -2484,143 +2422,86 @@ theorem map_const' {xs : Array α} {b : β} : map (fun _ => b) xs = replicate xs
apply Array.ext'
simp
@[deprecated set_replicate_self (since := "2025-03-18")]
abbrev set_mkArray_self := @set_replicate_self
@[simp] theorem setIfInBounds_replicate_self : (replicate n a).setIfInBounds i a = replicate n a := by
apply Array.ext'
simp
@[deprecated setIfInBounds_replicate_self (since := "2025-03-18")]
abbrev setIfInBounds_mkArray_self := @setIfInBounds_replicate_self
@[simp] theorem replicate_append_replicate : replicate n a ++ replicate m a = replicate (n + m) a := by
apply Array.ext'
simp
@[deprecated replicate_append_replicate (since := "2025-03-18")]
abbrev mkArray_append_mkArray := @replicate_append_replicate
theorem append_eq_replicate_iff {xs ys : Array α} {a : α} :
xs ++ ys = replicate n a
xs.size + ys.size = n xs = replicate xs.size a ys = replicate ys.size a := by
simp [ toList_inj, List.append_eq_replicate_iff]
@[deprecated append_eq_replicate_iff (since := "2025-03-18")]
abbrev append_eq_mkArray_iff := @append_eq_replicate_iff
theorem replicate_eq_append_iff {xs ys : Array α} {a : α} :
replicate n a = xs ++ ys
xs.size + ys.size = n xs = replicate xs.size a ys = replicate ys.size a := by
rw [eq_comm, append_eq_replicate_iff]
@[deprecated replicate_eq_append_iff (since := "2025-03-18")]
abbrev replicate_eq_mkArray_iff := @replicate_eq_append_iff
@[simp] theorem map_replicate : (replicate n a).map f = replicate n (f a) := by
apply Array.ext'
simp
@[deprecated map_replicate (since := "2025-03-18")]
abbrev map_mkArray := @map_replicate
@[grind =] theorem filter_replicate (w : stop = n) :
(replicate n a).filter p 0 stop = if p a then replicate n a else #[] := by
apply Array.ext'
simp only [w]
split <;> simp_all
@[deprecated filter_replicate (since := "2025-03-18")]
abbrev filter_mkArray := @filter_replicate
@[simp] theorem filter_replicate_of_pos (w : stop = n) (h : p a) :
(replicate n a).filter p 0 stop = replicate n a := by
simp [filter_replicate, h, w]
@[deprecated filter_replicate_of_pos (since := "2025-03-18")]
abbrev filter_mkArray_of_pos := @filter_replicate_of_pos
@[simp] theorem filter_replicate_of_neg (w : stop = n) (h : ¬ p a) :
(replicate n a).filter p 0 stop = #[] := by
simp [filter_replicate, h, w]
@[deprecated filter_replicate_of_neg (since := "2025-03-18")]
abbrev filter_mkArray_of_neg := @filter_replicate_of_neg
theorem filterMap_replicate {f : α Option β} (w : stop = n := by simp) :
(replicate n a).filterMap f 0 stop = match f a with | none => #[] | .some b => replicate n b := by
apply Array.ext'
simp only [w, size_replicate, toList_filterMap', toList_replicate, List.filterMap_replicate]
split <;> simp_all
@[deprecated filterMap_replicate (since := "2025-03-18")]
abbrev filterMap_mkArray := @filterMap_replicate
-- This is not a useful `simp` lemma because `b` is unknown.
theorem filterMap_replicate_of_some {f : α Option β} (h : f a = some b) :
(replicate n a).filterMap f = replicate n b := by
simp [filterMap_replicate, h]
@[deprecated filterMap_replicate_of_some (since := "2025-03-18")]
abbrev filterMap_mkArray_of_some := @filterMap_replicate_of_some
@[simp] theorem filterMap_replicate_of_isSome {f : α Option β} (h : (f a).isSome) :
(replicate n a).filterMap f = replicate n (Option.get _ h) := by
match w : f a, h with
| some b, _ => simp [filterMap_replicate, w]
@[deprecated filterMap_replicate_of_isSome (since := "2025-03-18")]
abbrev filterMap_mkArray_of_isSome := @filterMap_replicate_of_isSome
@[simp] theorem filterMap_replicate_of_none {f : α Option β} (h : f a = none) :
(replicate n a).filterMap f = #[] := by
simp [filterMap_replicate, h]
@[deprecated filterMap_replicate_of_none (since := "2025-03-18")]
abbrev filterMap_mkArray_of_none := @filterMap_replicate_of_none
@[simp] theorem flatten_replicate_empty : (replicate n (#[] : Array α)).flatten = #[] := by
rw [ toList_inj]
simp
@[deprecated flatten_replicate_empty (since := "2025-03-18")]
abbrev flatten_mkArray_empty := @flatten_replicate_empty
@[simp] theorem flatten_replicate_singleton : (replicate n #[a]).flatten = replicate n a := by
rw [ toList_inj]
simp
@[deprecated flatten_replicate_singleton (since := "2025-03-18")]
abbrev flatten_mkArray_singleton := @flatten_replicate_singleton
@[simp] theorem flatten_replicate_replicate : (replicate n (replicate m a)).flatten = replicate (n * m) a := by
rw [ toList_inj]
simp
@[deprecated flatten_replicate_replicate (since := "2025-03-18")]
abbrev flatten_mkArray_replicate := @flatten_replicate_replicate
theorem flatMap_replicate {f : α Array β} : (replicate n a).flatMap f = (replicate n (f a)).flatten := by
rw [ toList_inj]
simp [List.flatMap_replicate]
@[deprecated flatMap_replicate (since := "2025-03-18")]
abbrev flatMap_mkArray := @flatMap_replicate
@[simp] theorem isEmpty_replicate : (replicate n a).isEmpty = decide (n = 0) := by
rw [ List.toArray_replicate, List.isEmpty_toArray]
simp
@[deprecated isEmpty_replicate (since := "2025-03-18")]
abbrev isEmpty_mkArray := @isEmpty_replicate
@[simp] theorem sum_replicate_nat {n : Nat} {a : Nat} : (replicate n a).sum = n * a := by
rw [ List.toArray_replicate, List.sum_toArray]
simp
@[deprecated sum_replicate_nat (since := "2025-03-18")]
abbrev sum_mkArray_nat := @sum_replicate_nat
/-! ### Preliminaries about `swap` needed for `reverse`. -/
@[grind =]
@@ -2662,8 +2543,8 @@ theorem getElem?_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} : (xs.swap i
split <;> rename_i h₃
· simp only [ h₃, Nat.not_le.2 (Nat.lt_succ_self _), Nat.le_refl, false_and]
exact (List.getElem?_reverse' (Eq.trans (by simp +arith) h)).symm
simp only [Nat.succ_le, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
Nat.lt_succ.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
simp only [Nat.succ_le_iff, Nat.lt_iff_le_and_ne.trans (and_iff_left h₃),
Nat.lt_succ_iff.symm.trans (Nat.lt_iff_le_and_ne.trans (and_iff_left (Ne.symm h₂)))]
· rw [H]; split <;> rename_i h₂
· cases Nat.le_antisymm (Nat.not_lt.1 h₁) (Nat.le_trans h₂.1 h₂.2)
cases Nat.le_antisymm h₂.1 h₂.2
@@ -2678,7 +2559,7 @@ theorem getElem?_swap {xs : Array α} {i j : Nat} (hi hj) {k : Nat} : (xs.swap i
split
· rfl
· rename_i h
simp only [ show k < _ + 1 _ from Nat.lt_succ (n := xs.size - 1), this, Nat.zero_le,
simp only [ show k < _ + 1 _ from Nat.lt_succ_iff (n := xs.size - 1), this, Nat.zero_le,
true_and, Nat.not_lt] at h
rw [List.getElem?_eq_none_iff.2 _, List.getElem?_eq_none_iff.2 (xs.toList.length_reverse _)]
@@ -2807,9 +2688,6 @@ theorem flatten_reverse {xss : Array (Array α)} :
rw [ toList_inj]
simp
@[deprecated reverse_replicate (since := "2025-03-18")]
abbrev reverse_mkArray := @reverse_replicate
/-! ### extract -/
theorem extract_loop_zero {xs ys : Array α} {start : Nat} : extract.loop xs 0 start ys = ys := by
@@ -2829,8 +2707,8 @@ theorem extract_loop_eq_aux {xs ys : Array α} {size start : Nat} :
| zero => rw [extract_loop_zero, extract_loop_zero, append_empty]
| succ size ih =>
if h : start < xs.size then
rw [extract_loop_succ (h := h), ih, push_eq_append_singleton]
rw [extract_loop_succ (h := h), ih (ys := #[].push _), push_eq_append_singleton, empty_append]
rw [extract_loop_succ (h := h), ih, push_eq_append]
rw [extract_loop_succ (h := h), ih (ys := #[].push _), push_eq_append, empty_append]
rw [append_assoc]
else
rw [extract_loop_of_ge (h := Nat.le_of_not_lt h)]
@@ -3719,15 +3597,9 @@ theorem back?_replicate {a : α} {n : Nat} :
rw [replicate_eq_toArray_replicate]
simp only [List.back?_toArray, List.getLast?_replicate]
@[deprecated back?_replicate (since := "2025-03-18")]
abbrev back?_mkArray := @back?_replicate
@[simp] theorem back_replicate {xs : Array α} (w : 0 < n) : (replicate n xs).back (by simpa using w) = xs := by
simp [back_eq_getElem]
@[deprecated back_replicate (since := "2025-03-18")]
abbrev back_mkArray := @back_replicate
/-! ## Additional operations -/
/-! ### leftpad -/
@@ -3745,9 +3617,6 @@ theorem size_rightpad {n : Nat} {a : α} {xs : Array α} :
theorem elem_push_self [BEq α] [LawfulBEq α] {xs : Array α} {a : α} : (xs.push a).elem a = true := by simp
@[deprecated elem_push_self (since := "2025-04-04")]
abbrev elem_cons_self := @elem_push_self
theorem contains_eq_any_beq [BEq α] {xs : Array α} {a : α} : xs.contains a = xs.any (a == ·) := by
rcases xs with xs
simp [List.contains_eq_any_beq]
@@ -3761,11 +3630,6 @@ theorem contains_iff_exists_mem_beq [BEq α] {xs : Array α} {a : α} :
-- With `LawfulBEq α`, it would be better to use `contains_iff_mem` directly.
grind_pattern contains_iff_exists_mem_beq => xs.contains a
@[grind _=_]
theorem contains_iff_mem [BEq α] [LawfulBEq α] {xs : Array α} {a : α} :
xs.contains a a xs := by
simp
@[simp, grind =]
theorem contains_toList [BEq α] {xs : Array α} {x : α} :
xs.toList.contains x = xs.contains x := by
@@ -3825,9 +3689,6 @@ theorem pop_append {xs ys : Array α} :
@[simp, grind =] theorem pop_replicate {n : Nat} {a : α} : (replicate n a).pop = replicate (n - 1) a := by
ext <;> simp
@[deprecated pop_replicate (since := "2025-03-18")]
abbrev pop_mkArray := @pop_replicate
/-! ## Logic -/
/-! ### any / all -/
@@ -4057,16 +3918,10 @@ theorem all_filterMap {xs : Array α} {f : α → Option β} {p : β → Bool} :
(replicate n a).any f = if n = 0 then false else f a := by
induction n <;> simp_all [replicate_succ']
@[deprecated any_replicate (since := "2025-03-18")]
abbrev any_mkArray := @any_replicate
@[simp] theorem all_replicate {n : Nat} {a : α} :
(replicate n a).all f = if n = 0 then true else f a := by
induction n <;> simp_all +contextual [replicate_succ']
@[deprecated all_replicate (since := "2025-03-18")]
abbrev all_mkArray := @all_replicate
/-! ### modify -/
@[simp, grind =] theorem size_modify {xs : Array α} {i : Nat} {f : α α} : (xs.modify i f).size = xs.size := by
@@ -4241,17 +4096,11 @@ theorem replace_extract {xs : Array α} {i : Nat} :
(replicate n a).replace a b = #[b] ++ replicate (n - 1) a := by
cases n <;> simp_all [replicate_succ', replace_append]
@[deprecated replace_replicate_self (since := "2025-03-18")]
abbrev replace_mkArray_self := @replace_replicate_self
@[simp] theorem replace_replicate_ne {a b c : α} (h : !b == a) :
(replicate n a).replace b c = replicate n a := by
rw [replace_of_not_mem]
simp_all
@[deprecated replace_replicate_ne (since := "2025-03-18")]
abbrev replace_mkArray_ne := @replace_replicate_ne
end replace
/-! ### toListRev -/
@@ -4419,9 +4268,6 @@ theorem getElem!_eq_getD [Inhabited α] {xs : Array α} {i} : xs[i]! = xs.getD i
@[deprecated mem_toList_iff (since := "2025-05-26")]
theorem mem_toList {a : α} {xs : Array α} : a xs.toList a xs := mem_def.symm
@[deprecated not_mem_empty (since := "2025-03-25")]
theorem not_mem_nil (a : α) : ¬ a #[] := nofun
/-! # get lemmas -/
theorem lt_of_getElem {x : α} {xs : Array α} {i : Nat} {hidx : i < xs.size} (_ : xs[i] = x) :
@@ -4433,6 +4279,7 @@ theorem getElem_fin_eq_getElem_toList {xs : Array α} {i : Fin xs.size} : xs[i]
@[simp] theorem ugetElem_eq_getElem {xs : Array α} {i : USize} (h : i.toNat < xs.size) :
xs[i] = xs[i.toNat] := rfl
@[deprecated getElem?_eq_none (since := "2025-10-26")]
theorem getElem?_size_le {xs : Array α} {i : Nat} (h : xs.size i) : xs[i]? = none := by
simp [getElem?_neg, h]
@@ -4452,6 +4299,7 @@ theorem getElem?_push_lt {xs : Array α} {x : α} {i : Nat} (h : i < xs.size) :
(xs.push x)[i]? = some xs[i] := by
rw [getElem?_pos (xs.push x) i (size_push _ Nat.lt_succ_of_lt h), getElem_push_lt]
@[deprecated getElem?_push_size (since := "2025-10-26")]
theorem getElem?_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size]? = some x := by
rw [getElem?_pos (xs.push x) xs.size (size_push _ Nat.lt_succ_self xs.size), getElem_push_eq]
@@ -4470,12 +4318,6 @@ theorem getElem?_push_eq {xs : Array α} {x : α} : (xs.push x)[xs.size]? = some
cases xs
simp
/-! ### contains -/
@[deprecated contains_iff (since := "2025-04-07")]
abbrev contains_def [DecidableEq α] {a : α} {xs : Array α} : xs.contains a a xs :=
contains_iff
/-! ### isPrefixOf -/
@[simp, grind =] theorem isPrefixOf_toList [BEq α] {xs ys : Array α} :
@@ -4589,7 +4431,8 @@ theorem uset_toArray {l : List α} {i : USize} {a : α} {h : i.toNat < l.toArray
apply ext'
simp
@[simp, grind =] theorem flatten_toArray {L : List (List α)} :
@[deprecated Array.flatten_map_toArray_toArray (since := "2025-10-26")]
theorem flatten_toArray {L : List (List α)} :
(L.toArray.map List.toArray).flatten = L.flatten.toArray := by
apply ext'
simp

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@@ -6,9 +6,6 @@ Author: Kim Morrison
module
prelude
public import Init.Core
import Init.Data.Array.Basic
import Init.Data.Nat.Lemmas
public import Init.Data.Range.Polymorphic.Iterators
public import Init.Data.Range.Polymorphic.Nat
import Init.Data.Iterators.Consumers

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@@ -10,9 +10,7 @@ import all Init.Data.Array.Lex.Basic
public import Init.Data.Array.Lex.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.List.Lex
import Init.Data.Range.Polymorphic.Lemmas
import Init.Data.Range.Polymorphic.NatLemmas
import Init.Data.Order.Lemmas
public section
@@ -36,7 +34,18 @@ grind_pattern _root_.List.le_toArray => l₁.toArray ≤ l₂.toArray
grind_pattern lt_toList => xs.toList < ys.toList
grind_pattern le_toList => xs.toList ys.toList
@[simp]
protected theorem not_lt [LT α] {xs ys : Array α} : ¬ xs < ys ys xs := Iff.rfl
@[deprecated Array.not_lt (since := "2025-10-26")]
protected theorem not_lt_iff_ge [LT α] {xs ys : Array α} : ¬ xs < ys ys xs := Iff.rfl
@[simp]
protected theorem not_le [LT α] {xs ys : Array α} :
¬ xs ys ys < xs :=
Classical.not_not
@[deprecated Array.not_le (since := "2025-10-26")]
protected theorem not_le_iff_gt [LT α] {xs ys : Array α} :
¬ xs ys ys < xs :=
Classical.not_not
@@ -180,12 +189,6 @@ protected theorem le_total [LT α]
[i : Std.Asymm (· < · : α α Prop)] (xs ys : Array α) : xs ys ys xs :=
List.le_total xs.toList ys.toList
@[simp] protected theorem not_lt [LT α]
{xs ys : Array α} : ¬ xs < ys ys xs := Iff.rfl
@[simp] protected theorem not_le [LT α]
{xs ys : Array α} : ¬ ys xs xs < ys := Classical.not_not
protected theorem le_of_lt [LT α]
[i : Std.Asymm (· < · : α α Prop)]
{xs ys : Array α} (h : xs < ys) : xs ys :=

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@@ -6,10 +6,7 @@ Authors: Mario Carneiro, Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Attach
public import Init.Data.Array.OfFn
public import Init.Data.List.MapIdx
import all Init.Data.List.MapIdx
@@ -299,9 +296,6 @@ theorem mapFinIdx_eq_replicate_iff {xs : Array α} {f : (i : Nat) → α → (h
rw [ toList_inj]
simp [List.mapFinIdx_eq_replicate_iff]
@[deprecated mapFinIdx_eq_replicate_iff (since := "2025-03-18")]
abbrev mapFinIdx_eq_mkArray_iff := @mapFinIdx_eq_replicate_iff
@[simp, grind =] theorem mapFinIdx_reverse {xs : Array α} {f : (i : Nat) α (h : i < xs.reverse.size) β} :
xs.reverse.mapFinIdx f = (xs.mapFinIdx (fun i a h => f (xs.size - 1 - i) a (by simp; omega))).reverse := by
rcases xs with l
@@ -441,9 +435,6 @@ theorem mapIdx_eq_replicate_iff {xs : Array α} {f : Nat → α → β} {b : β}
rw [ toList_inj]
simp [List.mapIdx_eq_replicate_iff]
@[deprecated mapIdx_eq_replicate_iff (since := "2025-03-18")]
abbrev mapIdx_eq_mkArray_iff := @mapIdx_eq_replicate_iff
@[simp, grind =] theorem mapIdx_reverse {xs : Array α} {f : Nat α β} :
xs.reverse.mapIdx f = (mapIdx (fun i => f (xs.size - 1 - i)) xs).reverse := by
rcases xs with xs

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@@ -6,8 +6,6 @@ Authors: Leonardo de Moura, Joachim Breitner
module
prelude
public import Init.Data.Array.Basic
public import Init.Data.Nat.Linear
public import Init.Data.List.BasicAux
public section

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@@ -6,13 +6,9 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.List.Control
import all Init.Data.List.Control
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Attach
public import Init.Data.List.Monadic
public section

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@@ -6,11 +6,8 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Monadic
public import Init.Data.List.OfFn
public import Init.Data.List.FinRange
public section

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@@ -7,7 +7,6 @@ module
prelude
public import Init.Data.List.Nat.Perm
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
@@ -85,9 +84,6 @@ theorem Perm.size_eq {xs ys : Array α} (p : xs ~ ys) : xs.size = ys.size := by
simp only [perm_iff_toList_perm] at p
simpa using p.length_eq
@[deprecated Perm.size_eq (since := "2025-04-17")]
abbrev Perm.length_eq := @Perm.size_eq
theorem Perm.mem_iff {a : α} {xs ys : Array α} (p : xs ~ ys) : a xs a ys := by
rcases xs with xs
rcases ys with ys
@@ -108,7 +104,7 @@ grind_pattern Perm.append => xs ~ ys, as ~ bs, ys ++ bs
theorem Perm.push (x : α) {xs ys : Array α} (p : xs ~ ys) :
xs.push x ~ ys.push x := by
rw [push_eq_append_singleton]
rw [push_eq_append]
exact p.append .rfl
grind_pattern Perm.push => xs ~ ys, xs.push x

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@@ -6,14 +6,10 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Lemmas
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.OfFn
import all Init.Data.Array.OfFn
public import Init.Data.Array.MapIdx
public import Init.Data.Array.Zip
public import Init.Data.List.Nat.Range
public section

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@@ -6,7 +6,6 @@ Authors: Leonardo de Moura
module
prelude
public import Init.GetElem
public import Init.Data.Array.Basic
import Init.Data.Array.GetLit
public import Init.Data.Slice.Basic

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@@ -7,7 +7,6 @@ Authors: David Thrane Christiansen
module
prelude
public import Init.Data.Array.Basic
public import Init.Data.Array.Subarray
import all Init.Data.Array.Subarray
public import Init.Omega

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@@ -6,10 +6,8 @@ Authors: Markus Himmel
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.Lemmas
public import Init.Data.List.Nat.TakeDrop
public section

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@@ -6,10 +6,8 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Array.Basic
import all Init.Data.Array.Basic
public import Init.Data.Array.TakeDrop
public import Init.Data.List.Zip
public section
@@ -168,9 +166,6 @@ theorem zipWith_eq_append_iff {f : α → β → γ} {as : Array α} {bs : Array
zipWith f (replicate m a) (replicate n b) = replicate (min m n) (f a b) := by
simp [ List.toArray_replicate]
@[deprecated zipWith_replicate (since := "2025-03-18")]
abbrev zipWith_mkArray := @zipWith_replicate
theorem map_uncurry_zip_eq_zipWith {f : α β γ} {as : Array α} {bs : Array β} :
map (Function.uncurry f) (as.zip bs) = zipWith f as bs := by
cases as
@@ -296,9 +291,6 @@ theorem zip_eq_append_iff {as : Array α} {bs : Array β} :
zip (replicate m a) (replicate n b) = replicate (min m n) (a, b) := by
simp [ List.toArray_replicate]
@[deprecated zip_replicate (since := "2025-03-18")]
abbrev zip_mkArray := @zip_replicate
theorem zip_eq_zip_take_min {as : Array α} {bs : Array β} :
zip as bs = zip (as.take (min as.size bs.size)) (bs.take (min as.size bs.size)) := by
cases as
@@ -350,9 +342,6 @@ theorem map_zipWithAll {δ : Type _} {f : α → β} {g : Option γ → Option
zipWithAll f (replicate n a) (replicate n b) = replicate n (f (some a) (some b)) := by
simp [ List.toArray_replicate]
@[deprecated zipWithAll_replicate (since := "2025-03-18")]
abbrev zipWithAll_mkArray := @zipWithAll_replicate
/-! ### zipWithM -/
@[simp, grind =]
@@ -410,7 +399,4 @@ theorem zip_of_prod {as : Array α} {bs : Array β} {xs : Array (α × β)} (hl
unzip (replicate n (a, b)) = (replicate n a, replicate n b) := by
ext1 <;> simp
@[deprecated unzip_replicate (since := "2025-03-18")]
abbrev unzip_mkArray := @unzip_replicate
end Array

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@@ -1,18 +0,0 @@
/-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.Data.Nat.Basic
public import Init.Data.Fin.Basic
public import Init.Data.List.Basic
public import Init.Data.Char.Basic
public import Init.Data.String.Basic
public import Init.Data.Option.Basic
public import Init.Data.UInt
public import Init.Data.Repr
public import Init.Data.ToString.Basic
public import Init.Data.String.Extra

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@@ -6,11 +6,8 @@ Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex
module
prelude
public import Init.Data.Fin.Basic
public import Init.Data.Nat.Bitwise.Lemmas
public import Init.Data.Nat.Power2
public import Init.Data.Int.Bitwise.Basic
public import Init.Data.BitVec.BasicAux
@[expose] public section
@@ -206,8 +203,8 @@ If `n` is `0`, then one digit is returned. Otherwise, `⌊(n + 3) / 4⌋` digits
-- `Internal` string functions by moving this definition out to a separate file that can live
-- downstream of `Init.Data.String.Basic`.
protected def toHex {n : Nat} (x : BitVec n) : String :=
let s := (Nat.toDigits 16 x.toNat).asString
let t := (List.replicate ((n+3) / 4 - String.Internal.length s) '0').asString
let s := String.ofList (Nat.toDigits 16 x.toNat)
let t := String.ofList (List.replicate ((n+3) / 4 - String.Internal.length s) '0')
String.Internal.append t s
/-- `BitVec` representation. -/

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@@ -6,16 +6,11 @@ Authors: Harun Khan, Abdalrhman M Mohamed, Joe Hendrix, Siddharth Bhat
module
prelude
public import Init.Data.Nat.Bitwise.Basic
import all Init.Data.Nat.Bitwise.Basic
public import Init.Data.Nat.Mod
public import Init.Data.Int.DivMod
import all Init.Data.Int.DivMod
public import Init.Data.Int.LemmasAux
public import Init.Data.BitVec.Basic
import all Init.Data.BitVec.Basic
public import Init.Data.BitVec.Decidable
public import Init.Data.BitVec.Lemmas
public import Init.Data.BitVec.Folds
import Init.BinderPredicates
@@ -640,12 +635,11 @@ theorem mulRec_eq_mul_signExtend_setWidth (x y : BitVec w) (s : Nat) :
simp only [mulRec_zero_eq, ofNat_eq_ofNat, Nat.reduceAdd]
by_cases y.getLsbD 0
case pos hy =>
simp only [hy, reduceIte, setWidth_one_eq_ofBool_getLsb_zero,
ofBool_true, ofNat_eq_ofNat]
simp only [hy, reduceIte, setWidth_one, ofBool_true, ofNat_eq_ofNat]
rw [setWidth_ofNat_one_eq_ofNat_one_of_lt (by omega)]
simp
case neg hy =>
simp [hy, setWidth_one_eq_ofBool_getLsb_zero]
simp [hy, setWidth_one]
case succ s' hs =>
rw [mulRec_succ_eq, hs]
have heq :
@@ -1030,7 +1024,7 @@ theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
case neg.hrWidth =>
simp only
have hdr' : d (qr.r.shiftConcat (n.getLsbD (qr.wn - 1))) :=
BitVec.not_lt_iff_le.mp rltd
BitVec.not_lt.mp rltd
have hr' : ((qr.r.shiftConcat (n.getLsbD (qr.wn - 1)))).toNat < 2 ^ (qr.wr + 1) := by
apply toNat_shiftConcat_lt_of_lt <;> bv_omega
rw [BitVec.toNat_sub_of_le hdr']
@@ -1038,7 +1032,7 @@ theorem lawful_divSubtractShift (qr : DivModState w) (h : qr.Poised args) :
case neg.hqWidth =>
apply toNat_shiftConcat_lt_of_lt <;> omega
case neg.hdiv =>
have rltd' := (BitVec.not_lt_iff_le.mp rltd)
have rltd' := (BitVec.not_lt.mp rltd)
simp only [qr.toNat_shiftRight_sub_one_eq h,
BitVec.toNat_sub_of_le rltd',
toNat_shiftConcat_eq_of_lt (qr.wr_lt_w h) h.hrWidth]
@@ -1412,7 +1406,7 @@ theorem eq_iff_eq_of_inv (f : α → BitVec w) (g : BitVec w → α) (h : ∀ x,
have := congrArg g h'
simpa [h] using this
@[simp]
@[deprecated BitVec.ne_intMin_of_msb_eq_false (since := "2025-10-26")]
theorem ne_intMin_of_lt_of_msb_false {x : BitVec w} (hw : 0 < w) (hx : x.msb = false) :
x intMin w := by
have := toNat_lt_of_msb_false hx
@@ -1517,7 +1511,7 @@ theorem sdiv_ne_intMin_of_ne_intMin {x y : BitVec w} (h : x ≠ intMin w) :
by_cases hx : x.msb <;> by_cases hy : y.msb
<;> simp only [hx, hy, neg_ne_intMin_inj]
<;> simp only [Bool.not_eq_true] at hx hy
<;> apply ne_intMin_of_lt_of_msb_false (by omega)
<;> apply ne_intMin_of_msb_eq_false (by omega)
<;> rw [msb_udiv]
<;> try simp only [hx, Bool.false_and]
· simp [h, ne_zero_of_msb_true, hx]
@@ -1629,7 +1623,7 @@ theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w b ≠ -1
· have ry := (intMin_udiv_eq_intMin_iff b).mp
simp only [hb1, imp_false] at ry
simp [msb_udiv, ha_intMin, hb1, ry, intMin_udiv_ne_zero_of_ne_zero, hb, hb0]
· have := @BitVec.ne_intMin_of_lt_of_msb_false w ((-a) / b) wpos (by simp [ha, ha0, ha_intMin])
· have := @BitVec.ne_intMin_of_msb_eq_false w wpos ((-a) / b) (by simp [ha, ha0, ha_intMin])
simp [msb_neg, h', this, ha, ha_intMin]
rw [toInt_eq_toNat_of_msb hb, toInt_eq_neg_toNat_neg_of_msb_true ha, Int.neg_tdiv,
Int.tdiv_eq_ediv_of_nonneg (by omega), sdiv_toInt_of_msb_true_of_msb_false]
@@ -1640,7 +1634,7 @@ theorem toInt_sdiv_of_ne_or_ne (a b : BitVec w) (h : a ≠ intMin w b ≠ -1
rw [toInt_udiv_of_msb ha, toInt_eq_toNat_of_msb ha]
rw [toInt_eq_neg_toNat_neg_of_msb_true hb, Int.tdiv_neg, Int.tdiv_eq_ediv_of_nonneg (by omega)]
· apply sdiv_ne_intMin_of_ne_intMin
apply ne_intMin_of_lt_of_msb_false (by omega) ha
apply ne_intMin_of_msb_eq_false (by omega) ha
· rw [sdiv, Int.tdiv_cases, udiv_eq, neg_eq, if_pos (toInt_nonneg_of_msb_false ha),
if_pos (toInt_nonneg_of_msb_false hb), ha, hb, toInt_udiv_of_msb ha,
toInt_eq_toNat_of_msb ha, toInt_eq_toNat_of_msb hb]
@@ -1932,7 +1926,7 @@ theorem toInt_sub_neg_umod {x y : BitVec w} (hxmsb : x.msb = true) (hymsb : y.ms
rw [Int.bmod_eq_of_le (by omega) (by omega)]
simp only [toInt_eq_toNat_of_msb hymsb, BitVec.toInt_eq_neg_toNat_neg_of_msb_true hxmsb,
Int.dvd_neg] at hdvd
simp only [hdvd, reduceIte, Int.natAbs_cast]
simp only [hdvd, reduceIte, Int.natAbs_natCast]
theorem srem_zero_of_dvd {x y : BitVec w} (h : y.toInt x.toInt) :
x.srem y = 0#w := by

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@@ -6,10 +6,8 @@ Authors: Joe Hendrix, Harun Khan
module
prelude
public import Init.Data.BitVec.Basic
import all Init.Data.BitVec.Basic
public import Init.Data.BitVec.Lemmas
public import Init.Data.Nat.Lemmas
public import Init.Data.Fin.Iterate
public section
@@ -84,7 +82,7 @@ theorem iunfoldr_getLsbD' {f : Fin w → αα × Bool} (state : Nat → α)
intro i
simp only [getLsbD_cons]
have hj2 : j.val w := by simp
cases (Nat.lt_or_eq_of_le (Nat.lt_succ.mp i.isLt)) with
cases (Nat.lt_or_eq_of_le (Nat.lt_succ_iff.mp i.isLt)) with
| inl h3 => simp [(Nat.ne_of_lt h3)]
exact (ih hj2).1 i.val, h3
| inr h3 => simp [h3]

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@@ -6,25 +6,14 @@ Authors: Joe Hendrix, Harun Khan, Alex Keizer, Abdalrhman M Mohamed, Siddharth B
module
prelude
public import Init.Data.Bool
public import Init.Data.BitVec.Basic
import all Init.Data.BitVec.Basic
public import Init.Data.BitVec.BasicAux
import all Init.Data.BitVec.BasicAux
public import Init.Data.Fin.Lemmas
public import Init.Data.Nat.Lemmas
public import Init.Data.Nat.Div.Lemmas
public import Init.Data.Nat.Mod
public import Init.Data.Nat.Div.Lemmas
public import Init.Data.Int.Bitwise.Lemmas
public import Init.Data.Int.LemmasAux
public import Init.Data.Int.Pow
public import Init.Data.Int.LemmasAux
public import Init.Data.BitVec.Bootstrap
public import Init.Data.Order.Factories
public import Init.Data.List.BasicAux
import Init.Data.List.Lemmas
import Init.Data.BEq
public section
@@ -45,14 +34,6 @@ namespace BitVec
simp only [Bool.and_eq_false_imp, decide_eq_true_eq]
omega
set_option linter.missingDocs false in
@[deprecated getLsbD_of_ge (since := "2025-04-04")]
abbrev getLsbD_ge := @getLsbD_of_ge
set_option linter.missingDocs false in
@[deprecated getMsbD_of_ge (since := "2025-04-04")]
abbrev getMsbD_ge := @getMsbD_of_ge
theorem lt_of_getLsbD {x : BitVec w} {i : Nat} : getLsbD x i = true i < w := by
if h : i < w then
simp [h]
@@ -83,6 +64,7 @@ theorem getElem?_eq_none_iff {l : BitVec w} : l[n]? = none ↔ w ≤ n := by
theorem none_eq_getElem?_iff {l : BitVec w} : none = l[n]? w n := by
simp
@[simp]
theorem getElem?_eq_none {l : BitVec w} (h : w n) : l[n]? = none := getElem?_eq_none_iff.mpr h
theorem getElem?_eq (l : BitVec w) (i : Nat) :
@@ -151,9 +133,6 @@ theorem two_pow_le_toNat_of_getElem_eq_true {i : Nat} {x : BitVec w}
rw [ getElem_eq_testBit_toNat x i hi]
exact hx
@[grind =] theorem msb_eq_getMsbD (x : BitVec w) : x.msb = x.getMsbD 0 := by
simp [BitVec.msb]
@[grind =] theorem getMsb_eq_getLsb (x : BitVec w) (i : Fin w) :
x.getMsb i = x.getLsb w - 1 - i, by omega := by
simp only [getMsb, getLsb]
@@ -180,18 +159,13 @@ theorem getLsbD_eq_getMsbD (x : BitVec w) (i : Nat) : x.getLsbD i = (decide (i <
apply getLsbD_of_ge
omega
@[simp] theorem getElem?_of_ge (x : BitVec w) (i : Nat) (ge : w i) : x[i]? = none := by
@[deprecated getElem?_eq_none (since := "2025-10-29")]
theorem getElem?_of_ge (x : BitVec w) (i : Nat) (ge : w i) : x[i]? = none := by
simp [ge]
@[simp] theorem getMsb?_of_ge (x : BitVec w) (i : Nat) (ge : w i) : getMsb? x i = none := by
simp [getMsb?_eq_getLsb?]; omega
set_option linter.missingDocs false in
@[deprecated getElem?_of_ge (since := "2025-04-04")] abbrev getLsb?_ge := @getElem?_of_ge
set_option linter.missingDocs false in
@[deprecated getMsb?_of_ge (since := "2025-04-04")] abbrev getMsb?_ge := @getMsb?_of_ge
theorem lt_of_getElem?_eq_some (x : BitVec w) (i : Nat) : x[i]? = some b i < w := by
cases h : x[i]? with
| none => simp
@@ -214,18 +188,6 @@ theorem lt_of_isSome_getMsb? (x : BitVec w) (i : Nat) : (getMsb? x i).isSome →
else
simp [Nat.ge_of_not_lt h]
set_option linter.missingDocs false in
@[deprecated lt_of_getElem?_eq_some (since := "2025-04-04")]
abbrev lt_of_getLsb?_eq_some := @lt_of_getElem?_eq_some
set_option linter.missingDocs false in
@[deprecated lt_of_isSome_getElem? (since := "2025-04-04")]
abbrev lt_of_getLsb?_isSome := @lt_of_isSome_getElem?
set_option linter.missingDocs false in
@[deprecated lt_of_isSome_getMsb? (since := "2025-04-04")]
abbrev lt_of_getMsb?_isSome := @lt_of_isSome_getMsb?
theorem getMsbD_eq_getMsb?_getD (x : BitVec w) (i : Nat) :
x.getMsbD i = (x.getMsb? i).getD false := by
rw [getMsbD_eq_getLsbD]
@@ -455,12 +417,18 @@ theorem getElem?_zero_ofNat_one : (BitVec.ofNat (w+1) 1)[0]? = some true := by
-- This does not need to be a `@[simp]` theorem as it is already handled by `getElem?_eq_getElem`.
theorem getElem?_zero_ofBool (b : Bool) : (ofBool b)[0]? = some b := by
simp only [ofBool, ofNat_eq_ofNat, cond_eq_if]
simp only [ofBool, ofNat_eq_ofNat, cond_eq_ite]
split <;> simp_all
@[simp, grind =] theorem getElem_zero_ofBool (b : Bool) : (ofBool b)[0] = b := by
@[simp, grind =]
theorem getElem_ofBool_zero {b : Bool} : (ofBool b)[0] = b := by
rw [getElem_eq_iff, getElem?_zero_ofBool]
@[deprecated getElem_ofBool_zero (since := "2025-10-29")]
theorem getElem_zero_ofBool (b : Bool) : (ofBool b)[0] = b := by
simp
theorem getElem?_succ_ofBool (b : Bool) (i : Nat) : (ofBool b)[i + 1]? = none := by
simp
@@ -471,8 +439,6 @@ theorem getLsbD_ofBool (b : Bool) (i : Nat) : (ofBool b).getLsbD i = ((i = 0) &&
· simp only [ofBool, ofNat_eq_ofNat, cond_true, getLsbD_ofNat, Bool.and_true]
by_cases hi : i = 0 <;> simp [hi] <;> omega
theorem getElem_ofBool_zero {b : Bool} : (ofBool b)[0] = b := by simp
@[simp]
theorem getElem_ofBool {b : Bool} {h : i < 1}: (ofBool b)[i] = b := by
simp [ getLsbD_eq_getElem]
@@ -555,6 +521,10 @@ theorem toNat_ge_of_msb_true {x : BitVec n} (p : BitVec.msb x = true) : x.toNat
@[grind _=_] theorem msb_eq_getMsbD_zero (x : BitVec w) : x.msb = x.getMsbD 0 := by
cases w <;> simp [getMsbD_eq_getLsbD, msb_eq_getLsbD_last]
@[deprecated msb_eq_getMsbD_zero (since := "2025-10-26")]
theorem msb_eq_getMsbD (x : BitVec w) : x.msb = x.getMsbD 0 := by
simp [BitVec.msb]
/-! ### cast -/
@[simp, grind =] theorem toFin_cast (h : w = v) (x : BitVec w) :
@@ -616,7 +586,7 @@ theorem toInt_eq_toNat_bmod (x : BitVec n) : x.toInt = Int.bmod x.toNat (2^n) :=
simp only [toInt_eq_toNat_cond]
split
next g =>
rw [Int.bmod_pos] <;> simp only [Int.natCast_emod, toNat_mod_cancel]
rw [Int.bmod_eq_emod_of_lt] <;> simp only [Int.natCast_emod, toNat_mod_cancel]
omega
next g =>
rw [Int.bmod_neg] <;> simp only [Int.natCast_emod, toNat_mod_cancel]
@@ -1024,7 +994,14 @@ theorem msb_setWidth' (x : BitVec w) (h : w ≤ v) : (x.setWidth' h).msb = (deci
theorem msb_setWidth'' (x : BitVec w) : (x.setWidth (k + 1)).msb = x.getLsbD k := by
simp [BitVec.msb, getMsbD]
/-- Truncating to width 1 produces a bitvector equal to the least significant bit. -/
theorem setWidth_one {x : BitVec w} :
x.setWidth 1 = ofBool (x.getLsbD 0) := by
ext i
simp [show i = 0 by omega]
/-- zero extending a bitvector to width 1 equals the boolean of the lsb. -/
@[deprecated setWidth_one (since := "2025-10-29")]
theorem setWidth_one_eq_ofBool_getLsb_zero (x : BitVec w) :
x.setWidth 1 = BitVec.ofBool (x.getLsbD 0) := by
ext i h
@@ -1040,12 +1017,6 @@ theorem setWidth_ofNat_one_eq_ofNat_one_of_lt {v w : Nat} (hv : 0 < v) :
have hv := (@Nat.testBit_one_eq_true_iff_self_eq_zero i)
by_cases h : Nat.testBit 1 i = true <;> simp_all
/-- Truncating to width 1 produces a bitvector equal to the least significant bit. -/
theorem setWidth_one {x : BitVec w} :
x.setWidth 1 = ofBool (x.getLsbD 0) := by
ext i
simp [show i = 0 by omega]
@[simp, grind =] theorem setWidth_ofNat_of_le (h : v w) (x : Nat) : setWidth v (BitVec.ofNat w x) = BitVec.ofNat v x := by
apply BitVec.eq_of_toNat_eq
simp only [toNat_setWidth, toNat_ofNat]
@@ -1219,7 +1190,7 @@ let x' = x.extractLsb' 7 5 = _ _ 9 8 7
@[simp] theorem getLsbD_extract (hi lo : Nat) (x : BitVec n) (i : Nat) :
getLsbD (extractLsb hi lo x) i = (i (hi-lo) && getLsbD x (lo+i)) := by
simp [getLsbD, Nat.lt_succ]
simp [getLsbD, Nat.lt_succ_iff]
@[simp] theorem getLsbD_extractLsb {hi lo : Nat} {x : BitVec n} {i : Nat} :
(extractLsb hi lo x).getLsbD i = (decide (i < hi - lo + 1) && x.getLsbD (lo + i)) := by
@@ -1675,11 +1646,11 @@ theorem not_def {x : BitVec v} : ~~~x = allOnes v ^^^ x := rfl
@[simp] theorem ofInt_negSucc_eq_not_ofNat {w n : Nat} :
BitVec.ofInt w (Int.negSucc n) = ~~~.ofNat w n := by
simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_coe, toNat_eq, toNat_ofNatLT, toNat_not,
simp only [BitVec.ofInt, Int.toNat, Int.ofNat_eq_natCast, toNat_eq, toNat_ofNatLT, toNat_not,
toNat_ofNat]
cases h : Int.negSucc n % ((2 ^ w : Nat) : Int)
case ofNat =>
rw [Int.ofNat_eq_coe, Int.negSucc_emod] at h
rw [Int.ofNat_eq_natCast, Int.negSucc_emod] at h
· dsimp only
omega
· omega
@@ -1761,9 +1732,6 @@ theorem not_eq_comm {x y : BitVec w} : ~~~ x = y ↔ x = ~~~ y := by
rw [h]
simp
set_option linter.missingDocs false in
@[deprecated getMsbD_not (since := "2025-04-04")] abbrev getMsb_not := @getMsbD_not
@[simp] theorem msb_not {x : BitVec w} : (~~~x).msb = (decide (0 < w) && !x.msb) := by
simp [BitVec.msb]
@@ -2583,10 +2551,6 @@ theorem signExtend_eq_setWidth_of_le (x : BitVec w) {v : Nat} (hv : v ≤ w) :
ext i h
simp [getElem_signExtend, show i < w by omega]
@[deprecated signExtend_eq_setWidth_of_le (since := "2025-03-07")]
theorem signExtend_eq_setWidth_of_lt (x : BitVec w) {v : Nat} (hv : v w) :
x.signExtend v = x.setWidth v := signExtend_eq_setWidth_of_le x hv
/-- Sign extending to the same bitwidth is a no op. -/
@[simp] theorem signExtend_eq (x : BitVec w) : x.signExtend w = x := by
rw [signExtend_eq_setWidth_of_le _ (Nat.le_refl _), setWidth_eq]
@@ -3646,9 +3610,6 @@ theorem sub_eq_add_neg {n} (x y : BitVec n) : x - y = x + - y := by
simp only [toNat_sub, toNat_add, toNat_neg, Nat.add_mod_mod]
rw [Nat.add_comm]
set_option linter.missingDocs false in
@[deprecated sub_eq_add_neg (since := "2025-04-04")] abbrev sub_toAdd := @sub_eq_add_neg
theorem add_left_neg (x : BitVec w) : -x + x = 0#w := by
apply toInt_inj.mp
simp [toInt_neg, Int.add_left_neg]
@@ -3688,10 +3649,6 @@ theorem neg_one_eq_allOnes : -1#w = allOnes w := by
have r : (2^w - 1) < 2^w := by omega
simp [Nat.mod_eq_of_lt q, Nat.mod_eq_of_lt r]
set_option linter.missingDocs false in
@[deprecated neg_one_eq_allOnes (since := "2025-04-04")]
abbrev negOne_eq_allOnes := @neg_one_eq_allOnes
theorem neg_eq_not_add (x : BitVec w) : -x = ~~~x + 1#w := by
apply eq_of_toNat_eq
simp only [toNat_neg, toNat_add, toNat_not, toNat_ofNat, Nat.add_mod_mod]
@@ -3753,6 +3710,9 @@ theorem neg_add {x y : BitVec w} : - (x + y) = - x - y := by
apply eq_of_toInt_eq
simp [toInt_neg, toInt_add, Int.neg_add, Int.add_neg_eq_sub]
theorem sub_sub (a b c : BitVec n) : a - b - c = a - (b + c) := by
simp [BitVec.sub_eq_add_neg, BitVec.add_assoc, BitVec.neg_add]
theorem add_neg_eq_sub {x y : BitVec w} : x + - y = (x - y) := by
apply eq_of_toInt_eq
simp [toInt_neg, Int.sub_eq_add_neg]
@@ -4105,6 +4065,7 @@ protected theorem umod_lt (x : BitVec n) {y : BitVec n} : 0 < y → x % y < y :=
simp only [ofNat_eq_ofNat, lt_def, toNat_ofNat, Nat.zero_mod]
apply Nat.mod_lt
@[deprecated BitVec.not_lt (since := "2025-10-26")]
theorem not_lt_iff_le {x y : BitVec w} : (¬ x < y) y x := by
constructor <;>
(intro h; simp only [lt_def, Nat.not_lt, le_def] at h ; omega)
@@ -4121,7 +4082,7 @@ theorem not_lt_zero {x : BitVec w} : ¬x < 0#w := of_decide_eq_false rfl
theorem le_zero_iff {x : BitVec w} : x 0#w x = 0#w := by
constructor
· intro h
have : x 0 := not_lt_iff_le.mp not_lt_zero
have : x 0 := BitVec.not_lt.mp not_lt_zero
exact Eq.symm (BitVec.le_antisymm this h)
· simp_all
@@ -4144,7 +4105,7 @@ theorem not_allOnes_lt {x : BitVec w} : ¬allOnes w < x := by
theorem allOnes_le_iff {x : BitVec w} : allOnes w x x = allOnes w := by
constructor
· intro h
have : x allOnes w := not_lt_iff_le.mp not_allOnes_lt
have : x allOnes w := BitVec.not_lt.mp not_allOnes_lt
exact Eq.symm (BitVec.le_antisymm h this)
· simp_all
@@ -4690,9 +4651,6 @@ theorem zero_smod {x : BitVec w} : (0#w).smod x = 0#w := by
@[simp, grind =] theorem getLsbD_ofBoolListLE : (ofBoolListLE bs).getLsbD i = bs.getD i false := by
induction bs generalizing i <;> cases i <;> simp_all [ofBoolListLE]
set_option linter.missingDocs false in
@[deprecated getLsbD_ofBoolListLE (since := "2025-04-04")] abbrev getLsb_ofBoolListLE := @getLsbD_ofBoolListLE
@[simp, grind =] theorem getMsbD_ofBoolListLE :
(ofBoolListLE bs).getMsbD i = (decide (i < bs.length) && bs.getD (bs.length - 1 - i) false) := by
simp [getMsbD_eq_getLsbD]
@@ -4763,14 +4721,6 @@ theorem getLsbD_rotateLeftAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i
apply getLsbD_of_ge
omega
set_option linter.missingDocs false in
@[deprecated getLsbD_rotateLeftAux_of_lt (since := "2025-04-04")]
abbrev getLsbD_rotateLeftAux_of_le := @getLsbD_rotateLeftAux_of_lt
set_option linter.missingDocs false in
@[deprecated getLsbD_rotateLeftAux_of_ge (since := "2025-04-04")]
abbrev getLsbD_rotateLeftAux_of_geq := @getLsbD_rotateLeftAux_of_ge
/-- When `r < w`, we give a formula for `(x.rotateLeft r).getLsbD i`. -/
theorem getLsbD_rotateLeft_of_le {x : BitVec w} {r i : Nat} (hr: r < w) :
(x.rotateLeft r).getLsbD i =
@@ -4927,14 +4877,6 @@ theorem getLsbD_rotateRightAux_of_ge {x : BitVec w} {r : Nat} {i : Nat} (hi : i
apply getLsbD_of_ge
omega
set_option linter.missingDocs false in
@[deprecated getLsbD_rotateRightAux_of_lt (since := "2025-04-04")]
abbrev getLsbD_rotateRightAux_of_le := @getLsbD_rotateRightAux_of_lt
set_option linter.missingDocs false in
@[deprecated getLsbD_rotateRightAux_of_ge (since := "2025-04-04")]
abbrev getLsbD_rotateRightAux_of_geq := @getLsbD_rotateRightAux_of_ge
/-- `rotateRight` equals the bit fiddling definition of `rotateRightAux` when the rotation amount is
smaller than the bitwidth. -/
theorem rotateRight_eq_rotateRightAux_of_lt {x : BitVec w} {r : Nat} (hr : r < w) :

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@@ -111,35 +111,11 @@ Needed for confluence of term `(a && b) ↔ a` which reduces to `(a && b) = a` v
@[simp] theorem eq_self_and : {a b : Bool}, (a = (a && b)) (a b) := by decide
@[simp] theorem eq_and_self : {a b : Bool}, (b = (a && b)) (b a) := by decide
@[deprecated and_eq_left_iff_imp (since := "2025-04-04")]
abbrev and_iff_left_iff_imp := @and_eq_left_iff_imp
@[deprecated and_eq_right_iff_imp (since := "2025-04-04")]
abbrev and_iff_right_iff_imp := @and_eq_right_iff_imp
@[deprecated eq_self_and (since := "2025-04-04")]
abbrev iff_self_and := @eq_self_and
@[deprecated eq_and_self (since := "2025-04-04")]
abbrev iff_and_self := @eq_and_self
@[simp] theorem not_and_eq_left_iff_and : {a b : Bool}, ((!a && b) = a) !a !b := by decide
@[simp] theorem and_not_eq_right_iff_and : {a b : Bool}, ((a && !b) = b) !a !b := by decide
@[simp] theorem eq_not_self_and : {a b : Bool}, (a = (!a && b)) !a !b := by decide
@[simp] theorem eq_and_not_self : {a b : Bool}, (b = (a && !b)) !a !b := by decide
@[deprecated not_and_eq_left_iff_and (since := "2025-04-04")]
abbrev not_and_iff_left_iff_imp := @not_and_eq_left_iff_and
@[deprecated and_not_eq_right_iff_and (since := "2025-04-04")]
abbrev and_not_iff_right_iff_imp := @and_not_eq_right_iff_and
@[deprecated eq_not_self_and (since := "2025-04-04")]
abbrev iff_not_self_and := @eq_not_self_and
@[deprecated eq_and_not_self (since := "2025-04-04")]
abbrev iff_and_not_self := @eq_and_not_self
/-! ### or -/
@[simp] theorem or_self_left : (a b : Bool), (a || (a || b)) = (a || b) := by decide
@@ -169,35 +145,11 @@ Needed for confluence of term `(a || b) ↔ a` which reduces to `(a || b) = a` v
@[simp] theorem eq_self_or : {a b : Bool}, (a = (a || b)) (b a) := by decide
@[simp] theorem eq_or_self : {a b : Bool}, (b = (a || b)) (a b) := by decide
@[deprecated or_eq_left_iff_imp (since := "2025-04-04")]
abbrev or_iff_left_iff_imp := @or_eq_left_iff_imp
@[deprecated or_eq_right_iff_imp (since := "2025-04-04")]
abbrev or_iff_right_iff_imp := @or_eq_right_iff_imp
@[deprecated eq_self_or (since := "2025-04-04")]
abbrev iff_self_or := @eq_self_or
@[deprecated eq_or_self (since := "2025-04-04")]
abbrev iff_or_self := @eq_or_self
@[simp] theorem not_or_eq_left_iff_and : {a b : Bool}, ((!a || b) = a) a b := by decide
@[simp] theorem or_not_eq_right_iff_and : {a b : Bool}, ((a || !b) = b) a b := by decide
@[simp] theorem eq_not_self_or : {a b : Bool}, (a = (!a || b)) a b := by decide
@[simp] theorem eq_or_not_self : {a b : Bool}, (b = (a || !b)) a b := by decide
@[deprecated not_or_eq_left_iff_and (since := "2025-04-04")]
abbrev not_or_iff_left_iff_imp := @not_or_eq_left_iff_and
@[deprecated or_not_eq_right_iff_and (since := "2025-04-04")]
abbrev or_not_iff_right_iff_imp := @or_not_eq_right_iff_and
@[deprecated eq_not_self_or (since := "2025-04-04")]
abbrev iff_not_self_or := @eq_not_self_or
@[deprecated eq_or_not_self (since := "2025-04-04")]
abbrev iff_or_not_self := @eq_or_not_self
theorem or_comm : (x y : Bool), (x || y) = (y || x) := by decide
instance : Std.Commutative (· || ·) := or_comm
@@ -562,6 +514,7 @@ theorem exists_bool {p : Bool → Prop} : (∃ b, p b) ↔ p false p true :=
theorem cond_eq_ite {α} (b : Bool) (t e : α) : cond b t e = if b then t else e := by
cases b <;> simp
@[deprecated cond_eq_ite (since := "2025-10-29")]
theorem cond_eq_if : (bif b then x else y) = (if b then x else y) := cond_eq_ite b x y
@[simp] theorem cond_not (b : Bool) (t e : α) : cond (!b) t e = cond b e t := by
@@ -621,11 +574,6 @@ protected theorem cond_false {α : Sort u} {a b : α} : cond false a b = b := co
@[simp] theorem cond_then_self : (c b : Bool), cond c c b = (c || b) := by decide
@[simp] theorem cond_else_self : (c b : Bool), cond c b c = (c && b) := by decide
@[deprecated cond_then_not_self (since := "2025-04-04")] abbrev cond_true_not_same := @cond_then_not_self
@[deprecated cond_else_not_self (since := "2025-04-04")] abbrev cond_false_not_same := @cond_else_not_self
@[deprecated cond_then_self (since := "2025-04-04")] abbrev cond_true_same := @cond_then_self
@[deprecated cond_else_self (since := "2025-04-04")] abbrev cond_false_same := @cond_else_self
theorem cond_pos {b : Bool} {a a' : α} (h : b = true) : (bif b then a else a') = a := by
rw [h, cond_true]
@@ -665,7 +613,7 @@ theorem decide_beq_decide (p q : Prop) [dpq : Decidable (p ↔ q)] [dp : Decidab
end Bool
export Bool (cond_eq_if xor and or not)
export Bool (cond_eq_if cond_eq_ite xor and or not)
/-! ### decide -/

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@@ -6,11 +6,8 @@ Author: Leonardo de Moura
module
prelude
public import Init.Data.Array.DecidableEq
public import Init.Data.UInt.Basic
public import Init.Data.UInt.BasicAux
import all Init.Data.UInt.BasicAux
public import Init.Data.Option.Basic
public import Init.Data.Array.Extract
set_option doc.verso true
@@ -27,9 +24,6 @@ attribute [ext] ByteArray
instance : DecidableEq ByteArray :=
fun _ _ => decidable_of_decidable_of_iff ByteArray.ext_iff.symm
@[deprecated emptyWithCapacity (since := "2025-03-12")]
abbrev mkEmpty := emptyWithCapacity
instance : Inhabited ByteArray where
default := empty

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@@ -6,7 +6,6 @@ Author: Markus Himmel
module
prelude
public import Init.Prelude
public import Init.Data.List.Basic
public section

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@@ -7,10 +7,11 @@ module
prelude
public import Init.Data.ByteArray.Basic
public import Init.Data.Array.Extract
public section
namespace ByteArray
-- At present the preferred normal form for empty byte arrays is `ByteArray.empty`
@[simp]
theorem emptyc_eq_empty : ( : ByteArray) = ByteArray.empty := rfl
@@ -19,10 +20,10 @@ theorem emptyc_eq_empty : (∅ : ByteArray) = ByteArray.empty := rfl
theorem emptyWithCapacity_eq_empty : ByteArray.emptyWithCapacity 0 = ByteArray.empty := rfl
@[simp]
theorem ByteArray.data_empty : ByteArray.empty.data = #[] := rfl
theorem data_empty : ByteArray.empty.data = #[] := rfl
@[simp]
theorem ByteArray.data_extract {a : ByteArray} {b e : Nat} :
theorem data_extract {a : ByteArray} {b e : Nat} :
(a.extract b e).data = a.data.extract b e := by
simp [extract, copySlice]
by_cases b e
@@ -30,39 +31,39 @@ theorem ByteArray.data_extract {a : ByteArray} {b e : Nat} :
· rw [Array.extract_eq_empty_of_le (by omega), Array.extract_eq_empty_of_le (by omega)]
@[simp]
theorem ByteArray.extract_zero_size {b : ByteArray} : b.extract 0 b.size = b := by
theorem extract_zero_size {b : ByteArray} : b.extract 0 b.size = b := by
ext1
simp
@[simp]
theorem ByteArray.extract_same {b : ByteArray} {i : Nat} : b.extract i i = ByteArray.empty := by
theorem extract_same {b : ByteArray} {i : Nat} : b.extract i i = ByteArray.empty := by
ext1
simp [Nat.min_le_left]
theorem ByteArray.fastAppend_eq_copySlice {a b : ByteArray} :
theorem fastAppend_eq_copySlice {a b : ByteArray} :
a.fastAppend b = b.copySlice 0 a a.size b.size false := rfl
@[simp]
theorem List.toByteArray_append {l l' : List UInt8} :
theorem _root_.List.toByteArray_append {l l' : List UInt8} :
(l ++ l').toByteArray = l.toByteArray ++ l'.toByteArray := by
simp [List.toByteArray_append']
@[simp]
theorem ByteArray.toList_data_append {l l' : ByteArray} :
theorem toList_data_append {l l' : ByteArray} :
(l ++ l').data.toList = l.data.toList ++ l'.data.toList := by
simp [ append_eq]
@[simp]
theorem ByteArray.data_append {l l' : ByteArray} :
theorem data_append {l l' : ByteArray} :
(l ++ l').data = l.data ++ l'.data := by
simp [ Array.toList_inj]
@[simp]
theorem ByteArray.size_empty : ByteArray.empty.size = 0 := by
theorem size_empty : ByteArray.empty.size = 0 := by
simp [ ByteArray.size_data]
@[simp]
theorem List.data_toByteArray {l : List UInt8} :
theorem _root_.List.data_toByteArray {l : List UInt8} :
l.toByteArray.data = l.toArray := by
rw [List.toByteArray]
suffices a b, (List.toByteArray.loop a b).data = b.data ++ a.toArray by
@@ -71,153 +72,159 @@ theorem List.data_toByteArray {l : List UInt8} :
fun_induction List.toByteArray.loop a b with simp_all
@[simp]
theorem List.size_toByteArray {l : List UInt8} :
theorem _root_.List.size_toByteArray {l : List UInt8} :
l.toByteArray.size = l.length := by
simp [ ByteArray.size_data]
@[simp]
theorem List.toByteArray_nil : List.toByteArray [] = ByteArray.empty := rfl
theorem _root_.List.toByteArray_nil : List.toByteArray [] = ByteArray.empty := rfl
@[simp]
theorem ByteArray.empty_append {b : ByteArray} : ByteArray.empty ++ b = b := by
theorem empty_append {b : ByteArray} : ByteArray.empty ++ b = b := by
ext1
simp
@[simp]
theorem ByteArray.append_empty {b : ByteArray} : b ++ ByteArray.empty = b := by
theorem append_empty {b : ByteArray} : b ++ ByteArray.empty = b := by
ext1
simp
@[simp, grind =]
theorem ByteArray.size_append {a b : ByteArray} : (a ++ b).size = a.size + b.size := by
theorem size_append {a b : ByteArray} : (a ++ b).size = a.size + b.size := by
simp [ size_data]
@[simp]
theorem ByteArray.size_eq_zero_iff {a : ByteArray} : a.size = 0 a = ByteArray.empty := by
theorem size_eq_zero_iff {a : ByteArray} : a.size = 0 a = ByteArray.empty := by
refine fun h => ?_, fun h => h ByteArray.size_empty
ext1
simp [ Array.size_eq_zero_iff, h]
theorem ByteArray.getElem_eq_getElem_data {a : ByteArray} {i : Nat} {h : i < a.size} :
theorem getElem_eq_getElem_data {a : ByteArray} {i : Nat} {h : i < a.size} :
a[i] = a.data[i]'(by simpa [ size_data]) := rfl
@[simp]
theorem ByteArray.getElem_append_left {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
theorem getElem_append_left {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
(hlt : i < a.size) : (a ++ b)[i] = a[i] := by
simp only [getElem_eq_getElem_data, data_append]
rw [Array.getElem_append_left (by simpa)]
theorem ByteArray.getElem_append_right {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
theorem getElem_append_right {i : Nat} {a b : ByteArray} {h : i < (a ++ b).size}
(hle : a.size i) : (a ++ b)[i] = b[i - a.size]'(by simp_all; omega) := by
simp only [getElem_eq_getElem_data, data_append]
rw [Array.getElem_append_right (by simpa)]
simp
@[simp]
theorem List.getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.toByteArray.size} :
theorem _root_.List.getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.toByteArray.size} :
l.toByteArray[i]'h = l[i]'(by simp_all) := by
simp [ByteArray.getElem_eq_getElem_data]
theorem List.getElem_eq_getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.length} :
theorem _root_.List.getElem_eq_getElem_toByteArray {l : List UInt8} {i : Nat} {h : i < l.length} :
l[i]'h = l.toByteArray[i]'(by simp_all) := by
simp
@[simp]
theorem ByteArray.size_extract {a : ByteArray} {b e : Nat} :
theorem size_extract {a : ByteArray} {b e : Nat} :
(a.extract b e).size = min e a.size - b := by
simp [ size_data]
@[simp]
theorem ByteArray.extract_eq_empty_iff {b : ByteArray} {i j : Nat} : b.extract i j = ByteArray.empty min j b.size i := by
theorem extract_eq_empty_iff {b : ByteArray} {i j : Nat} : b.extract i j = ByteArray.empty min j b.size i := by
rw [ size_eq_zero_iff, size_extract]
omega
@[simp]
theorem ByteArray.extract_add_left {b : ByteArray} {i j : Nat} : b.extract (i + j) i = ByteArray.empty := by
theorem extract_add_left {b : ByteArray} {i j : Nat} : b.extract (i + j) i = ByteArray.empty := by
simp only [extract_eq_empty_iff]
exact Nat.le_trans (Nat.min_le_left _ _) (by simp)
@[simp]
theorem ByteArray.append_eq_empty_iff {a b : ByteArray} :
theorem append_eq_empty_iff {a b : ByteArray} :
a ++ b = ByteArray.empty a = ByteArray.empty b = ByteArray.empty := by
simp [ size_eq_zero_iff, size_append]
@[simp]
theorem List.toByteArray_eq_empty {l : List UInt8} :
theorem toByteArray_eq_empty {l : List UInt8} :
l.toByteArray = ByteArray.empty l = [] := by
simp [ ByteArray.size_eq_zero_iff]
theorem ByteArray.append_right_inj {ys₁ ys₂ : ByteArray} (xs : ByteArray) :
@[simp]
theorem append_right_inj {ys₁ ys₂ : ByteArray} (xs : ByteArray) :
xs ++ ys₁ = xs ++ ys₂ ys₁ = ys₂ := by
simp [ByteArray.ext_iff, Array.append_right_inj]
@[simp]
theorem ByteArray.extract_append_extract {a : ByteArray} {i j k : Nat} :
theorem append_left_inj {xs₁ xs₂ : ByteArray} (ys : ByteArray) :
xs₁ ++ ys = xs₂ ++ ys xs₁ = xs₂ := by
simp [ByteArray.ext_iff, Array.append_left_inj]
@[simp]
theorem extract_append_extract {a : ByteArray} {i j k : Nat} :
a.extract i j ++ a.extract j k = a.extract (min i j) (max j k) := by
ext1
simp
theorem ByteArray.extract_eq_extract_append_extract {a : ByteArray} {i k : Nat} (j : Nat)
theorem extract_eq_extract_append_extract {a : ByteArray} {i k : Nat} (j : Nat)
(hi : i j) (hk : j k) :
a.extract i k = a.extract i j ++ a.extract j k := by
simp
rw [Nat.min_eq_left hi, Nat.max_eq_right hk]
theorem ByteArray.append_inj_left {xs₁ xs₂ ys₁ ys₂ : ByteArray} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) : xs₁ = xs₂ := by
theorem append_inj_left {xs₁ xs₂ ys₁ ys₂ : ByteArray} (h : xs₁ ++ ys₁ = xs₂ ++ ys₂) (hl : xs₁.size = xs₂.size) : xs₁ = xs₂ := by
simp only [ByteArray.ext_iff, ByteArray.size_data, ByteArray.data_append] at *
exact Array.append_inj_left h hl
theorem ByteArray.extract_append_eq_right {a b : ByteArray} {i j : Nat} (hi : i = a.size) (hj : j = a.size + b.size) :
theorem extract_append_eq_right {a b : ByteArray} {i j : Nat} (hi : i = a.size) (hj : j = a.size + b.size) :
(a ++ b).extract i j = b := by
subst hi hj
ext1
simp [ size_data]
theorem ByteArray.extract_append_eq_left {a b : ByteArray} {i : Nat} (hi : i = a.size) :
theorem extract_append_eq_left {a b : ByteArray} {i : Nat} (hi : i = a.size) :
(a ++ b).extract 0 i = a := by
subst hi
ext1
simp
theorem ByteArray.extract_append_size_left {a b : ByteArray} {i : Nat} :
theorem extract_append_size_left {a b : ByteArray} {i : Nat} :
(a ++ b).extract i a.size = a.extract i a.size := by
ext1
simp
theorem ByteArray.extract_append_size_add {a b : ByteArray} {i j : Nat} :
theorem extract_append_size_add {a b : ByteArray} {i j : Nat} :
(a ++ b).extract (a.size + i) (a.size + j) = b.extract i j := by
ext1
simp
theorem ByteArray.extract_append {as bs : ByteArray} {i j : Nat} :
theorem extract_append {as bs : ByteArray} {i j : Nat} :
(as ++ bs).extract i j = as.extract i j ++ bs.extract (i - as.size) (j - as.size) := by
ext1
simp
theorem ByteArray.extract_append_size_add' {a b : ByteArray} {i j k : Nat} (h : k = a.size) :
theorem extract_append_size_add' {a b : ByteArray} {i j k : Nat} (h : k = a.size) :
(a ++ b).extract (k + i) (k + j) = b.extract i j := by
cases h
rw [extract_append_size_add]
theorem ByteArray.extract_extract {a : ByteArray} {i j k l : Nat} :
theorem extract_extract {a : ByteArray} {i j k l : Nat} :
(a.extract i j).extract k l = a.extract (i + k) (min (i + l) j) := by
ext1
simp
theorem ByteArray.getElem_extract_aux {xs : ByteArray} {start stop : Nat} (h : i < (xs.extract start stop).size) :
theorem getElem_extract_aux {xs : ByteArray} {start stop : Nat} (h : i < (xs.extract start stop).size) :
start + i < xs.size := by
rw [size_extract] at h; apply Nat.add_lt_of_lt_sub'; apply Nat.lt_of_lt_of_le h
apply Nat.sub_le_sub_right; apply Nat.min_le_right
theorem ByteArray.getElem_extract {i : Nat} {b : ByteArray} {start stop : Nat}
theorem getElem_extract {i : Nat} {b : ByteArray} {start stop : Nat}
(h) : (b.extract start stop)[i]'h = b[start + i]'(getElem_extract_aux h) := by
simp [getElem_eq_getElem_data]
theorem ByteArray.extract_eq_extract_left {a : ByteArray} {i i' j : Nat} :
theorem extract_eq_extract_left {a : ByteArray} {i i' j : Nat} :
a.extract i j = a.extract i' j min j a.size - i = min j a.size - i' := by
simp [ByteArray.ext_iff, Array.extract_eq_extract_left]
theorem ByteArray.extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 a.size) :
theorem extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 a.size) :
a.extract i (i + 1) = [a[i]].toByteArray := by
ext
· simp
@@ -226,34 +233,57 @@ theorem ByteArray.extract_add_one {a : ByteArray} {i : Nat} (ha : i + 1 ≤ a.si
obtain rfl : j = 0 := by simpa using hj'
simp [ByteArray.getElem_eq_getElem_data]
theorem ByteArray.extract_add_two {a : ByteArray} {i : Nat} (ha : i + 2 a.size) :
theorem extract_add_two {a : ByteArray} {i : Nat} (ha : i + 2 a.size) :
a.extract i (i + 2) = [a[i], a[i + 1]].toByteArray := by
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
extract_add_one (by omega), extract_add_one (by omega)]
simp [ List.toByteArray_append]
theorem ByteArray.extract_add_three {a : ByteArray} {i : Nat} (ha : i + 3 a.size) :
theorem extract_add_three {a : ByteArray} {i : Nat} (ha : i + 3 a.size) :
a.extract i (i + 3) = [a[i], a[i + 1], a[i + 2]].toByteArray := by
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
extract_add_one (by omega), extract_add_two (by omega)]
simp [ List.toByteArray_append]
theorem ByteArray.extract_add_four {a : ByteArray} {i : Nat} (ha : i + 4 a.size) :
theorem extract_add_four {a : ByteArray} {i : Nat} (ha : i + 4 a.size) :
a.extract i (i + 4) = [a[i], a[i + 1], a[i + 2], a[i + 3]].toByteArray := by
rw [extract_eq_extract_append_extract (i + 1) (by simp) (by omega),
extract_add_one (by omega), extract_add_three (by omega)]
simp [ List.toByteArray_append]
theorem ByteArray.append_assoc {a b c : ByteArray} : a ++ b ++ c = a ++ (b ++ c) := by
theorem append_assoc {a b c : ByteArray} : a ++ b ++ c = a ++ (b ++ c) := by
ext1
simp
@[simp]
theorem ByteArray.toList_empty : ByteArray.empty.toList = [] := by
theorem toList_empty : ByteArray.empty.toList = [] := by
simp [ByteArray.toList, ByteArray.toList.loop]
theorem ByteArray.copySlice_eq_append {src : ByteArray} {srcOff : Nat} {dest : ByteArray} {destOff len : Nat} {exact : Bool} :
theorem copySlice_eq_append {src : ByteArray} {srcOff : Nat} {dest : ByteArray} {destOff len : Nat} {exact : Bool} :
ByteArray.copySlice src srcOff dest destOff len exact =
dest.extract 0 destOff ++ src.extract srcOff (srcOff +len) ++ dest.extract (destOff + min len (src.data.size - srcOff)) dest.data.size := by
ext1
simp [copySlice]
@[simp]
theorem data_set {as : ByteArray} {i : Nat} {h : i < as.size} {a : UInt8} :
(as.set i a h).data = as.data.set i a (by simpa) := by
simp [set]
theorem set_eq_push_extract_append_extract {as : ByteArray} {i : Nat} (h : i < as.size) {a : UInt8} :
as.set i a h = (as.extract 0 i).push a ++ as.extract (i + 1) as.size := by
ext1
simpa using Array.set_eq_push_extract_append_extract _
@[simp]
theorem append_toByteArray_singleton {as : ByteArray} {a : UInt8} :
as ++ [a].toByteArray = as.push a := by
ext1
simp
@[simp]
theorem extract_zero_max_size {a : ByteArray} {i : Nat} : a.extract 0 (max i a.size) = a := by
ext1
simp [Nat.le_max_right]
end ByteArray

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@@ -6,7 +6,6 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Char.Basic
import all Init.Data.Char.Basic
public import Init.Data.UInt.Lemmas
@@ -14,12 +13,16 @@ public section
namespace Char
@[ext] protected theorem ext : {a b : Char} a.val = b.val a = b
@[deprecated Char.ext (since := "2025-10-26")]
protected theorem eq_of_val_eq : {a b : Char} a.val = b.val a = b
| _,_, _,_, rfl => rfl
theorem le_def {a b : Char} : a b a.1 b.1 := .rfl
theorem lt_def {a b : Char} : a < b a.1 < b.1 := .rfl
@[deprecated lt_def (since := "2025-10-26")]
theorem lt_iff_val_lt_val {a b : Char} : a < b a.val < b.val := Iff.rfl
@[simp] protected theorem not_le {a b : Char} : ¬ a b b < a := UInt32.not_le
@[simp] protected theorem not_lt {a b : Char} : ¬ a < b b a := UInt32.not_lt
@[simp] protected theorem le_refl (a : Char) : a a := by simp [le_def]
@@ -70,4 +73,9 @@ def notLTTotal : Std.Total (¬ · < · : Char → Char → Prop) where
rw [Char.ofNat, dif_pos]
rfl
@[simp]
theorem toUInt8_val {c : Char} : c.val.toUInt8 = c.toUInt8 := rfl
theorem toString_eq_singleton {c : Char} : c.toString = String.singleton c := rfl
end Char

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@@ -8,7 +8,6 @@ module
prelude
public import Init.Data.Rat.Lemmas
import Init.Data.Int.Bitwise.Lemmas
import Init.Data.Int.DivMod.Lemmas
import Init.Hints
/-!
@@ -288,7 +287,7 @@ theorem toRat_add (x y : Dyadic) : toRat (x + y) = toRat x + toRat y := by
· rename_i h
cases Int.sub_eq_iff_eq_add.mp h
rw [toRat_ofOdd_eq_mkRat, Rat.mkRat_eq_iff (NeZero.ne _) (NeZero.ne _)]
simp only [succ_eq_add_one, Int.ofNat_eq_coe, Int.add_shiftLeft, Int.shiftLeft_add,
simp only [succ_eq_add_one, Int.ofNat_eq_natCast, Int.add_shiftLeft, Int.shiftLeft_add,
Int.natCast_mul, Int.natCast_shiftLeft, Int.shiftLeft_mul_shiftLeft, Int.add_mul]
congr 2 <;> omega
· rename_i h
@@ -439,7 +438,7 @@ theorem toDyadic_mkRat (a : Int) (b : Nat) (prec : Int) :
rcases h : mkRat a b with n, d, hnz, hr
obtain m, hm, rfl, rfl := Rat.mkRat_num_den hb h
cases prec
· simp only [Rat.toDyadic, Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast,
· simp only [Rat.toDyadic, Int.ofNat_eq_natCast, Int.toNat_natCast, Int.toNat_neg_natCast,
shiftLeft_zero, Int.natCast_mul]
rw [Int.mul_comm d, Int.ediv_ediv (by simp), Int.shiftLeft_mul,
Int.mul_ediv_cancel _ (by simpa using hm)]
@@ -464,7 +463,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
rw [Rat.floor_def, Int.shiftLeft_eq, Nat.shiftLeft_eq]
match prec with
| .ofNat prec =>
simp only [Int.ofNat_eq_coe, Int.toNat_natCast, Int.toNat_neg_natCast, Nat.pow_zero,
simp only [Int.ofNat_eq_natCast, Int.toNat_natCast, Int.toNat_neg_natCast, Nat.pow_zero,
Nat.mul_one]
have : (2 ^ prec : Rat) = ((2 ^ prec : Nat) : Rat) := by simp
rw [Rat.zpow_natCast, this, Rat.mul_def']
@@ -473,7 +472,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
Rat.den_ofNat, Nat.one_pow, Nat.mul_one]
split
· simp_all
· rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
· rw [Int.ediv_ediv (Int.natCast_nonneg _)]
congr 1
rw [Int.natCast_ediv, Int.mul_ediv_cancel']
rw [Int.natCast_dvd_natCast]
@@ -496,7 +495,7 @@ theorem toRat_toDyadic (x : Rat) (prec : Int) :
simp only [this, Int.mul_one]
split
· simp_all
· rw [Int.ediv_ediv (Int.ofNat_zero_le _)]
· rw [Int.ediv_ediv (Int.natCast_nonneg _)]
congr 1
rw [Int.natCast_ediv, Int.mul_ediv_cancel']
· simp
@@ -683,9 +682,11 @@ instance : LE Dyadic where
instance : DecidableLT Dyadic := fun _ _ => inferInstanceAs (Decidable (_ = true))
instance : DecidableLE Dyadic := fun _ _ => inferInstanceAs (Decidable (_ = true))
theorem lt_iff_toRat {x y : Dyadic} : x < y x.toRat < y.toRat := blt_iff_toRat
@[simp]
theorem toRat_lt_toRat_iff {x y : Dyadic} : x.toRat < y.toRat x < y := blt_iff_toRat.symm
theorem le_iff_toRat {x y : Dyadic} : x y x.toRat y.toRat := ble_iff_toRat
@[simp]
theorem toRat_le_toRat_iff {x y : Dyadic} : x.toRat y.toRat x y := ble_iff_toRat.symm
@[simp]
protected theorem not_le {x y : Dyadic} : ¬x < y y x := by
@@ -697,20 +698,20 @@ protected theorem not_lt {x y : Dyadic} : ¬x ≤ y ↔ y < x := by
@[simp]
protected theorem le_refl (x : Dyadic) : x x := by
rw [le_iff_toRat]
rw [ toRat_le_toRat_iff]
exact Rat.le_refl
protected theorem le_trans {x y z : Dyadic} (h : x y) (h' : y z) : x z := by
rw [le_iff_toRat] at h h'
rw [ toRat_le_toRat_iff] at h h'
exact Rat.le_trans h h'
protected theorem le_antisymm {x y : Dyadic} (h : x y) (h' : y x) : x = y := by
rw [le_iff_toRat] at h h'
rw [ toRat_le_toRat_iff] at h h'
rw [ toRat_inj]
exact Rat.le_antisymm h h'
protected theorem le_total (x y : Dyadic) : x y y x := by
rw [le_iff_toRat, le_iff_toRat]
rw [ toRat_le_toRat_iff, toRat_le_toRat_iff]
exact Rat.le_total
instance : Std.LawfulOrderLT Dyadic where

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@@ -7,7 +7,6 @@ module
prelude
public import Init.Data.Dyadic.Basic
public import Init.Grind.Ring.Basic
public import Init.Grind.Ordered.Ring
/-! # Internal `grind` algebra instances for `Dyadic`. -/
@@ -53,8 +52,8 @@ instance : NoNatZeroDivisors Dyadic where
instance : OrderedRing Dyadic where
zero_lt_one := by decide
add_le_left_iff _ := by simp [le_iff_toRat, Rat.add_le_add_right]
mul_lt_mul_of_pos_left {_ _ _} := by simpa [lt_iff_toRat] using Rat.mul_lt_mul_of_pos_left
mul_lt_mul_of_pos_right {_ _ _} := by simpa [lt_iff_toRat] using Rat.mul_lt_mul_of_pos_right
add_le_left_iff _ := by simp [ toRat_le_toRat_iff, Rat.add_le_add_right]
mul_lt_mul_of_pos_left {_ _ _} := by simpa [ toRat_lt_toRat_iff] using Rat.mul_lt_mul_of_pos_left
mul_lt_mul_of_pos_right {_ _ _} := by simpa [ toRat_lt_toRat_iff] using Rat.mul_lt_mul_of_pos_right
end Dyadic

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@@ -5,7 +5,6 @@ Authors: Kim Morrison
-/
module
prelude
import Init.Data.Dyadic.Basic
import Init.Data.Dyadic.Round
import Init.Grind.Ordered.Ring
@@ -28,7 +27,7 @@ def invAtPrec (x : Dyadic) (prec : Int) : Dyadic :=
/-- For a positive dyadic `x`, `invAtPrec x prec * x ≤ 1`. -/
theorem invAtPrec_mul_le_one {x : Dyadic} (hx : 0 < x) (prec : Int) :
invAtPrec x prec * x 1 := by
rw [le_iff_toRat]
rw [ toRat_le_toRat_iff]
rw [toRat_mul]
rw [show (1 : Dyadic).toRat = (1 : Rat) from rfl]
unfold invAtPrec
@@ -40,19 +39,19 @@ theorem invAtPrec_mul_le_one {x : Dyadic} (hx : 0 < x) (prec : Int) :
simp only
have h_le : ((ofOdd n k hn).toRat.inv.toDyadic prec).toRat (ofOdd n k hn).toRat.inv := Rat.toRat_toDyadic_le
have h_pos : 0 (ofOdd n k hn).toRat := by
rw [lt_iff_toRat, toRat_zero] at hx
rw [ toRat_lt_toRat_iff, toRat_zero] at hx
exact Rat.le_of_lt hx
calc ((ofOdd n k hn).toRat.inv.toDyadic prec).toRat * (ofOdd n k hn).toRat
(ofOdd n k hn).toRat.inv * (ofOdd n k hn).toRat := Rat.mul_le_mul_of_nonneg_right h_le h_pos
_ = 1 := by
apply Rat.inv_mul_cancel
rw [lt_iff_toRat, toRat_zero] at hx
rw [ toRat_lt_toRat_iff, toRat_zero] at hx
exact Rat.ne_of_gt hx
/-- For a positive dyadic `x`, `1 < (invAtPrec x prec + 2^(-prec)) * x`. -/
theorem one_lt_invAtPrec_add_inc_mul {x : Dyadic} (hx : 0 < x) (prec : Int) :
1 < (invAtPrec x prec + ofIntWithPrec 1 prec) * x := by
rw [lt_iff_toRat]
rw [ toRat_lt_toRat_iff]
rw [toRat_mul]
rw [show (1 : Dyadic).toRat = (1 : Rat) from rfl]
unfold invAtPrec
@@ -65,12 +64,12 @@ theorem one_lt_invAtPrec_add_inc_mul {x : Dyadic} (hx : 0 < x) (prec : Int) :
have h_le : (ofOdd n k hn).toRat.inv < ((ofOdd n k hn).toRat.inv.toDyadic prec + ofIntWithPrec 1 prec).toRat :=
Rat.lt_toRat_toDyadic_add
have h_pos : 0 < (ofOdd n k hn).toRat := by
rwa [lt_iff_toRat, toRat_zero] at hx
rwa [ toRat_lt_toRat_iff, toRat_zero] at hx
calc
1 = (ofOdd n k hn).toRat.inv * (ofOdd n k hn).toRat := by
symm
apply Rat.inv_mul_cancel
rw [lt_iff_toRat, toRat_zero] at hx
rw [ toRat_lt_toRat_iff, toRat_zero] at hx
exact Rat.ne_of_gt hx
_ < ((ofOdd n k hn).toRat.inv.toDyadic prec + ofIntWithPrec 1 prec).toRat * (ofOdd n k hn).toRat :=
Rat.mul_lt_mul_of_pos_right h_le h_pos

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@@ -8,7 +8,6 @@ module
prelude
public import Init.Data.Dyadic.Basic
import all Init.Data.Dyadic.Instances
import Init.Data.Int.Bitwise.Lemmas
import Init.Grind.Ordered.Rat
import Init.Grind.Ordered.Field
@@ -29,7 +28,7 @@ theorem roundDown_le {x : Dyadic} {prec : Int} : roundDown x prec ≤ x :=
match h : k - prec with
| .ofNat l =>
dsimp
rw [ofOdd_eq_ofIntWithPrec, le_iff_toRat]
rw [ofOdd_eq_ofIntWithPrec, toRat_le_toRat_iff]
replace h : k = Int.ofNat l + prec := by omega
subst h
simp only [toRat_ofIntWithPrec_eq_mul_two_pow]
@@ -37,7 +36,7 @@ theorem roundDown_le {x : Dyadic} {prec : Int} : roundDown x prec ≤ x :=
refine Lean.Grind.OrderedRing.mul_le_mul_of_nonneg_right ?_ (Rat.zpow_nonneg (by decide))
rw [Int.shiftRight_eq_div_pow]
rw [ Lean.Grind.Field.IsOrdered.mul_le_mul_iff_of_pos_right (c := 2^(Int.ofNat l)) (Rat.zpow_pos (by decide))]
simp only [Int.natCast_pow, Int.cast_ofNat_Int, Int.ofNat_eq_coe]
simp only [Int.natCast_pow, Int.cast_ofNat_Int, Int.ofNat_eq_natCast]
rw [Rat.mul_assoc, Rat.zpow_add (by decide), Int.add_left_neg, Rat.zpow_zero, Rat.mul_one]
have : (2 : Rat) ^ (l : Int) = (2 ^ l : Int) := by
rw [Rat.zpow_natCast, Rat.intCast_pow, Rat.intCast_ofNat]

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@@ -7,7 +7,6 @@ module
prelude
public import Init.Data.Nat.Bitwise
public import Init.Data.Fin.Basic
public section

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@@ -6,7 +6,6 @@ Authors: François G. Dorais
module
prelude
public import Init.Data.Nat.Linear
public import Init.Control.Lawful.Basic
public import Init.Data.Fin.Lemmas
@@ -23,7 +22,7 @@ Example:
-/
@[inline] def foldl (n) (f : α Fin n α) (init : α) : α := loop init 0 where
/-- Inner loop for `Fin.foldl`. `Fin.foldl.loop n f x i = f (f (f x i) ...) (n-1)` -/
@[semireducible, specialize] loop (x : α) (i : Nat) : α :=
@[specialize] loop (x : α) (i : Nat) : α :=
if h : i < n then loop (f x i, h) (i+1) else x
termination_by n - i
@@ -34,7 +33,7 @@ and nesting to the right.
Example:
* `Fin.foldr 3 (·.val + ·) (0 : Nat) = (0 : Fin 3).val + ((1 : Fin 3).val + ((2 : Fin 3).val + 0))`
-/
@[inline] def foldr (n) (f : Fin n α α) (init : α) : α := loop n (Nat.le_refl n) init where
@[inline, expose] def foldr (n) (f : Fin n α α) (init : α) : α := loop n (Nat.le_refl n) init where
/-- Inner loop for `Fin.foldr`. `Fin.foldr.loop n f i x = f 0 (f ... (f (i-1) x))` -/
@[specialize] loop : (i : _) i n α α
| 0, _, x => x
@@ -65,7 +64,7 @@ Fin.foldlM n f x₀ = do
pure xₙ
```
-/
@[semireducible, specialize] loop (x : α) (i : Nat) : m α := do
@[specialize] loop (x : α) (i : Nat) : m α := do
if h : i < n then f x i, h >>= (loop · (i+1)) else pure x
termination_by n - i
decreasing_by decreasing_trivial_pre_omega
@@ -96,7 +95,7 @@ Fin.foldrM n f xₙ = do
pure x₀
```
-/
@[semireducible, specialize] loop : {i // i n} α m α
@[specialize] loop : {i // i n} α m α
| 0, _, x => pure x
| i+1, h, x => f i, h x >>= loop i, Nat.le_of_lt h

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@@ -7,7 +7,6 @@ module
prelude
public import Init.PropLemmas
public import Init.Data.Fin.Basic
public section

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@@ -8,10 +8,6 @@ module
prelude
public import Init.Data.Nat.Lemmas
public import Init.Ext
public import Init.ByCases
public import Init.Conv
public import Init.Omega
public import Init.Data.Order.Factories
import Init.Data.Order.Lemmas
@[expose] public section
@@ -161,6 +157,7 @@ theorem le_def {a b : Fin n} : a ≤ b ↔ a.1 ≤ b.1 := .rfl
theorem lt_def {a b : Fin n} : a < b a.1 < b.1 := .rfl
@[deprecated lt_def (since := "2025-10-26")]
theorem lt_iff_val_lt_val {a b : Fin n} : a < b a.val < b.val := Iff.rfl
@[simp] protected theorem not_le {a b : Fin n} : ¬ a b b < a := Nat.not_le
@@ -268,7 +265,7 @@ instance : LawfulOrderLT (Fin n) where
rw [val_rev, val_rev, Nat.sub_sub, Nat.sub_sub_self (by exact i.2), Nat.add_sub_cancel]
@[simp] theorem rev_le_rev {i j : Fin n} : rev i rev j j i := by
simp only [le_def, val_rev, Nat.sub_le_sub_iff_left (Nat.succ_le.2 j.is_lt)]
simp only [le_def, val_rev, Nat.sub_le_sub_iff_left (Nat.succ_le_iff.2 j.is_lt)]
exact Nat.succ_le_succ_iff
@[simp] theorem rev_inj {i j : Fin n} : rev i = rev j i = j :=
@@ -387,9 +384,10 @@ theorem add_one_pos (i : Fin (n + 1)) (h : i < Fin.last n) : (0 : Fin (n + 1)) <
rw [Fin.lt_def, val_add, val_zero, val_one, Nat.mod_eq_of_lt h]
exact Nat.zero_lt_succ _
@[deprecated zero_lt_one (since := "2025-10-26")]
theorem one_pos : (0 : Fin (n + 2)) < 1 := Nat.succ_pos 0
theorem zero_ne_one : (0 : Fin (n + 2)) 1 := Fin.ne_of_lt one_pos
theorem zero_ne_one : (0 : Fin (n + 2)) 1 := Fin.ne_of_lt zero_lt_one
/-! ### succ and casts into larger Fin types -/
@@ -544,12 +542,12 @@ theorem succ_cast_eq {n' : Nat} (i : Fin n) (h : n = n') :
@[simp] theorem coe_castSucc (i : Fin n) : (i.castSucc : Nat) = i := rfl
@[simp] theorem castSucc_mk (n i : Nat) (h : i < n) : castSucc i, h = i, Nat.lt.step h := rfl
@[simp] theorem castSucc_mk (n i : Nat) (h : i < n) : castSucc i, h = i, Nat.lt_succ_of_lt h := rfl
@[simp] theorem cast_castSucc {n' : Nat} {h : n + 1 = n' + 1} {i : Fin n} :
i.castSucc.cast h = (i.cast (Nat.succ.inj h)).castSucc := rfl
theorem castSucc_lt_succ (i : Fin n) : i.castSucc < i.succ :=
theorem castSucc_lt_succ {i : Fin n} : i.castSucc < i.succ :=
lt_def.2 <| by simp only [coe_castSucc, val_succ, Nat.lt_succ_self]
theorem le_castSucc_iff {i : Fin (n + 1)} {j : Fin n} : i j.castSucc i < j.succ := by
@@ -589,8 +587,12 @@ theorem castSucc_pos [NeZero n] {i : Fin n} (h : 0 < i) : 0 < i.castSucc := by
theorem castSucc_ne_zero_iff [NeZero n] {a : Fin n} : a.castSucc 0 a 0 :=
not_congr <| castSucc_eq_zero_iff
@[simp, grind _=_]
theorem castSucc_succ (i : Fin n) : i.succ.castSucc = i.castSucc.succ := rfl
@[deprecated castSucc_succ (since := "2025-10-29")]
theorem castSucc_fin_succ (n : Nat) (j : Fin n) :
j.succ.castSucc = (j.castSucc).succ := by simp [Fin.ext_iff]
j.succ.castSucc = (j.castSucc).succ := by simp
@[simp]
theorem coeSucc_eq_succ {a : Fin n} : a.castSucc + 1 = a.succ := by
@@ -598,6 +600,7 @@ theorem coeSucc_eq_succ {a : Fin n} : a.castSucc + 1 = a.succ := by
· exact a.elim0
· simp [Fin.ext_iff, add_def, Nat.mod_eq_of_lt (Nat.succ_lt_succ a.is_lt)]
@[deprecated castSucc_lt_succ (since := "2025-10-29")]
theorem lt_succ {a : Fin n} : a.castSucc < a.succ := by
rw [castSucc, lt_def, coe_castAdd, val_succ]; exact Nat.lt_succ_self a.val
@@ -701,9 +704,6 @@ theorem rev_castSucc (k : Fin n) : rev (castSucc k) = succ (rev k) := k.rev_cast
theorem rev_succ (k : Fin n) : rev (succ k) = castSucc (rev k) := k.rev_addNat 1
@[simp, grind _=_]
theorem castSucc_succ (i : Fin n) : i.succ.castSucc = i.castSucc.succ := rfl
@[simp, grind =]
theorem castLE_refl (h : n n) (i : Fin n) : i.castLE h = i := rfl
@@ -758,7 +758,7 @@ theorem pred_mk {n : Nat} (i : Nat) (h : i < n + 1) (w) : Fin.pred ⟨i, h⟩ w
| i + 1, hi, j + 1, hj, ha, hb => by simp [Fin.ext_iff]
@[simp] theorem pred_one {n : Nat} :
Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt one_pos)) = 0 := rfl
Fin.pred (1 : Fin (n + 2)) (Ne.symm (Fin.ne_of_lt zero_lt_one)) = 0 := rfl
theorem pred_add_one (i : Fin (n + 2)) (h : (i : Nat) < n + 1) :
pred (i + 1) (Fin.ne_of_gt (add_one_pos _ (lt_def.2 h))) = castLT i h := by
@@ -1141,6 +1141,7 @@ theorem mul_ofNat [NeZero n] (x : Fin n) (y : Nat) :
theorem val_mul {n : Nat} : a b : Fin n, (a * b).val = a.val * b.val % n
| _, _, _, _ => rfl
@[deprecated val_mul (since := "2025-10-26")]
theorem coe_mul {n : Nat} : a b : Fin n, ((a * b : Fin n) : Nat) = a * b % n
| _, _, _, _ => rfl

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@@ -6,8 +6,6 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Core
public import Init.Data.Int.Basic
public import Init.Data.ToString.Basic
public section

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@@ -6,9 +6,6 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Core
public import Init.Data.Int.Basic
public import Init.Data.ToString.Basic
public import Init.Data.Float
public section

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@@ -6,9 +6,7 @@ Author: Leonardo de Moura
module
prelude
public import Init.Data.Array.Basic
public import Init.Data.Float
public import Init.Data.Option.Basic
import Init.Ext
public import Init.Data.Array.DecidableEq
@@ -31,9 +29,6 @@ attribute [ext] FloatArray
def emptyWithCapacity (c : @& Nat) : FloatArray :=
{ data := #[] }
@[deprecated emptyWithCapacity (since := "2025-03-12")]
abbrev mkEmpty := emptyWithCapacity
def empty : FloatArray :=
emptyWithCapacity 0

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@@ -170,7 +170,7 @@ private def spaceUptoLine : Format → Bool → Int → Nat → SpaceResult
| text s, flatten, _, _ =>
let p := String.Internal.posOf s '\n'
let off := String.Internal.offsetOfPos s p
{ foundLine := p != s.endPos, foundFlattenedHardLine := flatten && p != s.endPos, space := off }
{ foundLine := p != s.rawEndPos, foundFlattenedHardLine := flatten && p != s.rawEndPos, space := off }
| append f₁ f₂, flatten, m, w => merge w (spaceUptoLine f₁ flatten m w) (spaceUptoLine f₂ flatten m)
| nest n f, flatten, m, w => spaceUptoLine f flatten (m - n) w
| group f _, _, m, w => spaceUptoLine f true m w
@@ -264,14 +264,14 @@ private partial def be (w : Nat) [Monad m] [MonadPrettyFormat m] : List WorkGrou
| nest n f => be w (gs' ({ i with f, indent := i.indent + n }::is))
| text s =>
let p := String.Internal.posOf s '\n'
if p == s.endPos then
if p == s.rawEndPos then
pushOutput s
endTags i.activeTags
be w (gs' is)
else
pushOutput (String.Internal.extract s {} p)
pushNewline i.indent.toNat
let is := { i with f := text (String.Internal.extract s (String.Internal.next s p) s.endPos) }::is
let is := { i with f := text (String.Internal.extract s (String.Internal.next s p) s.rawEndPos) }::is
-- after a hard line break, re-evaluate whether to flatten the remaining group
-- note that we shouldn't start flattening after a hard break outside a group
if g.fla == .disallow then
@@ -411,7 +411,6 @@ Renders a `Format` to a string.
* `column`: begin the first line wrap `column` characters earlier than usual
(this is useful when the output String will be printed starting at `column`)
-/
@[export lean_format_pretty]
def pretty (f : Format) (width : Nat := defWidth) (indent : Nat := 0) (column := 0) : String :=
let act : StateM State Unit := prettyM f width indent
State.out <| act (State.mk "" column) |>.snd

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@@ -6,9 +6,7 @@ Author: Leonardo de Moura
module
prelude
public import Init.Data.Format.Basic
public import Init.Data.Array.Basic
public import Init.Data.ToString.Basic
import Init.Data.String.Basic
public section

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@@ -9,7 +9,6 @@ prelude
public import Init.Data.Format.Macro
public import Init.Data.Format.Instances
public import Init.Meta
import Init.Data.String.Basic
import Init.Data.ToString.Name
public section

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@@ -5,7 +5,6 @@ Authors: Kim Morrison
-/
module
prelude
public import Init.Core
public import Init.Grind.Tactics
public section
namespace Function

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@@ -6,9 +6,7 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.UInt.Basic
public import Init.Data.String.Basic
public import Init.Data.ByteArray.Basic
public section
universe u

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@@ -80,7 +80,10 @@ protected theorem zero_ne_one : (0 : Int) ≠ 1 := nofun
/-! ## Coercions -/
@[simp] theorem ofNat_eq_coe : Int.ofNat n = Nat.cast n := rfl
@[simp] theorem ofNat_eq_natCast (n : Nat) : Int.ofNat n = n := rfl
@[deprecated ofNat_eq_natCast (since := "2025-10-29")]
theorem ofNat_eq_coe : Int.ofNat n = Nat.cast n := rfl
@[simp] theorem ofNat_zero : ((0 : Nat) : Int) = 0 := rfl
@@ -313,7 +316,7 @@ the logical model.
Examples:
* `(7 : Int).natAbs = 7`
* `(0 : Int).natAbs = 0`
* `((-11 : Int).natAbs = 11`
* `(-11 : Int).natAbs = 11`
-/
@[extern "lean_nat_abs", expose]
def natAbs (m : @& Int) : Nat :=
@@ -369,9 +372,6 @@ def toNat? : Int → Option Nat
| (n : Nat) => some n
| -[_+1] => none
@[deprecated toNat? (since := "2025-03-11"), inherit_doc toNat?]
abbrev toNat' := toNat?
/-! ## divisibility -/
/--

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@@ -47,10 +47,10 @@ theorem shiftRight_zero (n : Int) : n >>> 0 = n := by
simp [Int.shiftRight_eq_div_pow]
theorem le_shiftRight_of_nonpos {n : Int} {s : Nat} (h : n 0) : n n >>> s := by
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_coe]
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_natCast]
split
case _ _ _ m =>
simp only [ofNat_eq_coe] at h
simp only [ofNat_eq_natCast] at h
by_cases hm : m = 0
· simp [hm]
· omega
@@ -61,14 +61,14 @@ theorem le_shiftRight_of_nonpos {n : Int} {s : Nat} (h : n ≤ 0) : n ≤ n >>>
omega
theorem shiftRight_le_of_nonneg {n : Int} {s : Nat} (h : 0 n) : n >>> s n := by
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_coe]
simp only [Int.shiftRight_eq, Int.shiftRight, Int.ofNat_eq_natCast]
split
case _ _ _ m =>
simp only [Int.ofNat_eq_coe] at h
simp only [Int.ofNat_eq_natCast] at h
by_cases hm : m = 0
· simp [hm]
· have := Nat.shiftRight_le m s
rw [ofNat_eq_coe]
rw [ofNat_eq_natCast]
omega
case _ _ _ m =>
omega
@@ -108,7 +108,7 @@ theorem shiftLeft_succ (m : Int) (n : Nat) : m <<< (n + 1) = (m <<< n) * 2 := by
change Int.shiftLeft _ _ = Int.shiftLeft _ _ * 2
match m with
| (m : Nat) =>
dsimp only [Int.shiftLeft, Int.ofNat_eq_coe]
dsimp only [Int.shiftLeft, Int.ofNat_eq_natCast]
rw [Nat.shiftLeft_succ, Nat.mul_comm, natCast_mul, ofNat_two]
| Int.negSucc m =>
dsimp only [Int.shiftLeft]

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@@ -6,7 +6,6 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Int.DivMod.Lemmas
public import Init.Data.Int.Gcd
public section

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@@ -118,9 +118,6 @@ instance : Mod Int where
@[simp, norm_cast] theorem natCast_ediv (m n : Nat) : ((m / n) : Int) = m / n := rfl
@[deprecated natCast_ediv (since := "2025-04-17")]
theorem ofNat_ediv (m n : Nat) : ((m / n) : Int) = m / n := natCast_ediv m n
theorem ofNat_ediv_ofNat {a b : Nat} : (a / b : Int) = (a / b : Nat) := rfl
@[norm_cast]
theorem negSucc_ediv_ofNat_succ {a b : Nat} : ((-[a+1]) / (b+1) : Int) = -[a / succ b +1] := rfl

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@@ -38,7 +38,7 @@ protected theorem dvd_trans : ∀ {a b c : Int}, a b → b c → a c
refine fun a, ae => ?_, fun k, e => k, by rw [e, Int.natCast_mul]
match Int.le_total a 0 with
| .inl h =>
have := ae.symm Int.mul_nonpos_of_nonneg_of_nonpos (ofNat_zero_le _) h
have := ae.symm Int.mul_nonpos_of_nonneg_of_nonpos (natCast_nonneg _) h
rw [Nat.le_antisymm (ofNat_le.1 this) (Nat.zero_le _)]
apply Nat.dvd_zero
| .inr h => match a, eq_ofNat_of_zero_le h with
@@ -92,9 +92,6 @@ theorem ofNat_dvd_left {n : Nat} {z : Int} : (↑n : Int) z ↔ n z.natA
@[simp, norm_cast] theorem natCast_emod (m n : Nat) : ((m % n) : Int) = m % n := rfl
@[deprecated natCast_emod (since := "2025-04-17")]
theorem ofNat_emod (m n : Nat) : ((m % n) : Int) = m % n := natCast_emod m n
/-! ### mod definitions -/
theorem emod_add_mul_ediv : a b : Int, a % b + b * (a / b) = a
@@ -209,7 +206,7 @@ theorem ediv_nonneg_iff_of_pos {a b : Int} (h : 0 < b) : 0 ≤ a / b ↔ 0 ≤ a
/-! ### emod -/
theorem emod_nonneg : (a : Int) {b : Int}, b 0 0 a % b
| ofNat _, _, _ => ofNat_zero_le _
| ofNat _, _, _ => natCast_nonneg _
| -[_+1], _, H => Int.sub_nonneg_of_le <| ofNat_le.2 <| Nat.mod_lt _ (natAbs_pos.2 H)
theorem emod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : a % b < b :=
@@ -233,10 +230,6 @@ theorem emod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : a % b < b :=
@[simp] theorem mul_add_emod_self_left (a b c : Int) : (a * b + c) % a = c % a := by
rw [Int.add_comm, add_mul_emod_self_left]
@[deprecated add_mul_emod_self_right (since := "2025-04-11")]
theorem add_mul_emod_self {a b c : Int} : (a + b * c) % c = a % c :=
add_mul_emod_self_right ..
@[simp] theorem emod_add_emod (m n k : Int) : (m % n + k) % n = (m + k) % n := by
have := (add_mul_emod_self_left (m % n + k) n (m / n)).symm
rwa [Int.add_right_comm, emod_add_mul_ediv] at this

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@@ -6,13 +6,7 @@ Authors: Jeremy Avigad, Mario Carneiro, Kim Morrison, Markus Himmel
module
prelude
public import Init.Data.Int.DivMod.Bootstrap
public import Init.Data.Nat.Lemmas
public import Init.Data.Nat.Div.Lemmas
public import Init.Data.Int.Order
public import Init.Data.Int.Lemmas
public import Init.Data.Nat.Dvd
public import Init.RCases
import Init.TacticsExtra
public section
@@ -79,7 +73,7 @@ protected theorem dvd_iff_dvd_of_dvd_add {a b c : Int} (H : a b + c) : a
theorem le_of_dvd {a b : Int} (bpos : 0 < b) (H : a b) : a b :=
match a, b, eq_succ_of_zero_lt bpos, H with
| ofNat _, _, n, rfl, H => ofNat_le.2 <| Nat.le_of_dvd n.succ_pos <| ofNat_dvd.1 H
| -[_+1], _, _, rfl, _ => Int.le_trans (Int.le_of_lt <| negSucc_lt_zero _) (ofNat_zero_le _)
| -[_+1], _, _, rfl, _ => Int.le_trans (Int.le_of_lt <| negSucc_lt_zero _) (natCast_nonneg _)
theorem natAbs_dvd {a b : Int} : (a.natAbs : Int) b a b :=
match natAbs_eq a with
@@ -220,8 +214,8 @@ theorem tdiv_eq_ediv {a b : Int} :
| ofNat a, -[b+1] => simp [tdiv_eq_ediv_of_nonneg]
| -[a+1], 0 => simp
| -[a+1], ofNat (succ b) =>
simp only [tdiv, Nat.succ_eq_add_one, ofNat_eq_coe, Int.natCast_add, cast_ofNat_Int,
negSucc_not_nonneg, sign_of_add_one]
simp only [tdiv, Nat.succ_eq_add_one, ofNat_eq_natCast, Int.natCast_add, cast_ofNat_Int,
negSucc_not_nonneg, sign_natCast_add_one]
simp only [negSucc_emod_ofNat_succ_eq_zero_iff]
norm_cast
simp only [Nat.succ_eq_add_one, false_or]
@@ -231,7 +225,7 @@ theorem tdiv_eq_ediv {a b : Int} :
· rw [neg_ofNat_eq_negSucc_add_one_iff]
exact Nat.succ_div_of_mod_ne_zero h
| -[a+1], -[b+1] =>
simp only [tdiv, ofNat_eq_coe, negSucc_not_nonneg, false_or, sign_negSucc]
simp only [tdiv, ofNat_eq_natCast, negSucc_not_nonneg, false_or, sign_negSucc]
norm_cast
simp only [negSucc_ediv_negSucc]
rw [Int.natCast_add, Int.natCast_one]
@@ -262,7 +256,7 @@ theorem fdiv_eq_ediv {a b : Int} :
| 0, -[b+1] => simp
| ofNat (a + 1), -[b+1] =>
simp only [fdiv, ofNat_ediv_negSucc, negSucc_not_nonneg, negSucc_dvd, false_or]
simp only [ofNat_eq_coe, ofNat_dvd]
simp only [ofNat_eq_natCast, ofNat_dvd]
norm_cast
rw [Nat.succ_div, negSucc_eq]
split <;> rename_i h
@@ -270,7 +264,7 @@ theorem fdiv_eq_ediv {a b : Int} :
· simp [Int.neg_add]
norm_cast
| -[a+1], -[b+1] =>
simp only [fdiv, ofNat_eq_coe, negSucc_ediv_negSucc, negSucc_not_nonneg, dvd_negSucc, negSucc_dvd,
simp only [fdiv, ofNat_eq_natCast, negSucc_ediv_negSucc, negSucc_not_nonneg, dvd_negSucc, negSucc_dvd,
false_or]
norm_cast
rw [Int.natCast_add, Int.natCast_one, Nat.succ_div]
@@ -516,32 +510,29 @@ theorem ediv_neg_of_neg_of_pos {a b : Int} (Ha : a < 0) (Hb : 0 < b) : a / b < 0
match a, b, eq_negSucc_of_lt_zero Ha, eq_succ_of_zero_lt Hb with
| _, _, _, rfl, _, rfl => negSucc_lt_zero _
@[deprecated ediv_neg_of_neg_of_pos (since := "2025-03-04")]
abbrev ediv_neg' := @ediv_neg_of_neg_of_pos
theorem negSucc_ediv (m : Nat) {b : Int} (H : 0 < b) : -[m+1] / b = -(ediv m b + 1) :=
match b, eq_succ_of_zero_lt H with
| _, _, rfl => rfl
theorem ediv_nonneg {a b : Int} (Ha : 0 a) (Hb : 0 b) : 0 a / b :=
match a, b, eq_ofNat_of_zero_le Ha, eq_ofNat_of_zero_le Hb with
| _, _, _, rfl, _, rfl => ofNat_zero_le _
| _, _, _, rfl, _, rfl => natCast_nonneg _
theorem ediv_nonneg_of_nonpos_of_nonpos {a b : Int} (Ha : a 0) (Hb : b 0) : 0 a / b := by
match a, b with
| ofNat a, b =>
match Int.le_antisymm Ha (ofNat_zero_le a) with
match Int.le_antisymm Ha (natCast_nonneg a) with
| h1 =>
rw [h1, zero_ediv]
exact Int.le_refl 0
| a, ofNat b =>
match Int.le_antisymm Hb (ofNat_zero_le b) with
match Int.le_antisymm Hb (natCast_nonneg b) with
| h1 =>
rw [h1, Int.ediv_zero]
exact Int.le_refl 0
| negSucc a, negSucc b =>
rw [Int.div_def, ediv]
exact le_add_one (ediv_nonneg (ofNat_zero_le a) (Int.le_trans (ofNat_zero_le b) (le.intro 1 rfl)))
exact le_add_one (ediv_nonneg (natCast_nonneg a) (Int.le_trans (natCast_nonneg b) (le.intro 1 rfl)))
theorem ediv_pos_of_neg_of_neg {a b : Int} (ha : a < 0) (hb : b < 0) : 0 < a / b := by
rw [Int.div_def]
@@ -551,9 +542,6 @@ theorem ediv_pos_of_neg_of_neg {a b : Int} (ha : a < 0) (hb : b < 0) : 0 < a / b
theorem ediv_nonpos_of_nonneg_of_nonpos {a b : Int} (Ha : 0 a) (Hb : b 0) : a / b 0 :=
Int.nonpos_of_neg_nonneg <| Int.ediv_neg .. Int.ediv_nonneg Ha (Int.neg_nonneg_of_nonpos Hb)
@[deprecated ediv_nonpos_of_nonneg_of_nonpos (since := "2025-03-04")]
abbrev ediv_nonpos := @ediv_nonpos_of_nonneg_of_nonpos
theorem ediv_eq_zero_of_lt {a b : Int} (H1 : 0 a) (H2 : a < b) : a / b = 0 :=
match a, b, eq_ofNat_of_zero_le H1, eq_succ_of_zero_lt (Int.lt_of_le_of_lt H1 H2) with
| _, _, _, rfl, _, rfl => congrArg Nat.cast <| Nat.div_eq_of_lt <| ofNat_lt.1 H2
@@ -571,7 +559,7 @@ theorem ediv_eq_one_of_neg_of_le {a b : Int} (H1 : a < 0) (H2 : b ≤ a) : a / b
match a, b, H1, H2 with
| negSucc a', ofNat n', H1, H2 => simp [Int.negSucc_eq] at H2; omega
| negSucc a', negSucc b', H1, H2 =>
rw [Int.div_def, ediv, ofNat_eq_coe]
rw [Int.div_def, ediv, ofNat_eq_natCast]
norm_cast
rw [Nat.succ_eq_add_one, Nat.add_eq_right, Nat.div_eq_zero_iff_lt (by omega)]
simp [Int.negSucc_eq] at H2
@@ -591,7 +579,7 @@ theorem neg_one_ediv (b : Int) : -1 / b = -b.sign :=
match b with
| ofNat 0 => by simp
| ofNat (b + 1) =>
ediv_eq_neg_one_of_neg_of_le (by decide) (by simp [ofNat_eq_coe]; omega)
ediv_eq_neg_one_of_neg_of_le (by decide) (by simp [ofNat_eq_natCast]; omega)
| negSucc b =>
ediv_eq_one_of_neg_of_le (by decide) (by omega)
@@ -658,7 +646,7 @@ theorem sign_ediv (a b : Int) : sign (a / b) = if 0 ≤ a ∧ a < b.natAbs then
| (a + 1 : Nat) =>
norm_cast
simp only [Nat.le_add_left, Nat.add_lt_add_iff_right, true_and, Int.natCast_add,
cast_ofNat_Int, sign_of_add_one, Int.mul_one]
cast_ofNat_Int, sign_natCast_add_one, Int.mul_one]
split
· rw [Nat.div_eq_of_lt (by omega)]
simp
@@ -684,25 +672,15 @@ theorem ofNat_mod_ofNat (m n : Nat) : (m % n : Int) = ↑(m % n) := rfl
@[simp] theorem add_neg_mul_emod_self_right (a b c : Int) : (a + -(b * c)) % c = a % c := by
rw [Int.neg_mul_eq_neg_mul, add_mul_emod_self_right]
@[deprecated add_neg_mul_emod_self_right (since := "2025-04-11")]
theorem add_neg_mul_emod_self {a b c : Int} : (a + -(b * c)) % c = a % c :=
add_neg_mul_emod_self_right ..
@[simp] theorem add_neg_mul_emod_self_left (a b c : Int) : (a + -(b * c)) % b = a % b := by
rw [Int.neg_mul_eq_mul_neg, add_mul_emod_self_left]
@[simp] theorem add_emod_right (a b : Int) : (a + b) % b = a % b := by
have := add_mul_emod_self_left a b 1; rwa [Int.mul_one] at this
@[deprecated add_emod_right (since := "2025-04-11")]
theorem add_emod_self {a b : Int} : (a + b) % b = a % b := add_emod_right ..
@[simp] theorem add_emod_left (a b : Int) : (a + b) % a = b % a := by
rw [Int.add_comm, add_emod_right]
@[deprecated add_emod_left (since := "2025-04-11")]
theorem add_emod_self_left {a b : Int} : (a + b) % a = b % a := add_emod_left ..
@[simp] theorem sub_mul_emod_self_right (a b c : Int) : (a - b * c) % c = a % c := by
simp [Int.sub_eq_add_neg]
@@ -943,9 +921,6 @@ where
| -[_+1], 0 => Nat.zero_le _
| -[_+1], succ _ => Nat.succ_le_succ (Nat.div_le_self _ _)
@[deprecated natAbs_ediv_le_natAbs (since := "2025-03-05")]
abbrev natAbs_div_le_natAbs := natAbs_ediv_le_natAbs
theorem ediv_le_self {a : Int} (b : Int) (Ha : 0 a) : a / b a := by
have := Int.le_trans le_natAbs (ofNat_le.2 <| natAbs_ediv_le_natAbs a b)
rwa [natAbs_of_nonneg Ha] at this
@@ -978,14 +953,6 @@ theorem emod_eq_iff {a b c : Int} (hb : b ≠ 0) : a % b = c ↔ 0 ≤ c ∧ c <
rw [ dvd_iff_emod_eq_zero, Int.dvd_neg]
exact Int.dvd_mul_right a b
@[deprecated mul_ediv_cancel (since := "2025-03-05")]
theorem neg_mul_ediv_cancel (a b : Int) (h : b 0) : -(a * b) / b = -a := by
rw [neg_ediv_of_dvd (Int.dvd_mul_left a b), mul_ediv_cancel _ h]
@[deprecated mul_ediv_cancel (since := "2025-03-05")]
theorem neg_mul_ediv_cancel_left (a b : Int) (h : a 0) : -(a * b) / a = -b := by
rw [neg_ediv_of_dvd (Int.dvd_mul_right a b), mul_ediv_cancel_left _ h]
@[simp] theorem ediv_one : a : Int, a / 1 = a
| (_:Nat) => congrArg Nat.cast (Nat.div_one _)
| -[_+1] => congrArg negSucc (Nat.div_one _)
@@ -999,10 +966,6 @@ theorem ediv_minus_one (a : Int) : a / (-1) = -a := by
theorem emod_minus_one (a : Int) : a % (-1) = 0 := by
simp
@[deprecated sub_emod_right (since := "2025-04-11")]
theorem emod_sub_cancel (x y : Int) : (x - y) % y = x % y :=
sub_emod_right ..
@[simp] theorem add_neg_emod_self (a b : Int) : (a + -b) % b = a % b := by
rw [Int.add_neg_eq_sub, sub_emod_right]
@@ -1013,10 +976,6 @@ theorem emod_sub_cancel (x y : Int) : (x - y) % y = x % y :=
theorem dvd_self_sub_of_emod_eq {a b : Int} : {c : Int} a % b = c b a - c
| _, rfl => dvd_self_sub_emod
@[deprecated dvd_self_sub_of_emod_eq (since := "2025-04-12")]
theorem dvd_sub_of_emod_eq {a b : Int} : {c : Int} a % b = c b a - c :=
dvd_self_sub_of_emod_eq
theorem dvd_sub_self_of_emod_eq {a b : Int} : {c : Int} a % b = c b c - a
| _, rfl => dvd_emod_sub_self
@@ -1104,7 +1063,7 @@ theorem emod_natAbs_of_neg {x : Int} (h : x < 0) {n : Nat} (w : n ≠ 0) :
match x, h with
| -(x + 1 : Nat), _ =>
rw [Int.natAbs_neg]
rw [Int.natAbs_cast]
rw [Int.natAbs_natCast]
rw [Int.neg_emod]
simp only [Int.dvd_neg]
simp only [Int.natCast_dvd_natCast]
@@ -1312,7 +1271,7 @@ because these statements are all incorrect, and require awkward conditional off-
protected theorem tdiv_nonneg {a b : Int} (Ha : 0 a) (Hb : 0 b) : 0 a.tdiv b :=
match a, b, eq_ofNat_of_zero_le Ha, eq_ofNat_of_zero_le Hb with
| _, _, _, rfl, _, rfl => ofNat_zero_le _
| _, _, _, rfl, _, rfl => natCast_nonneg _
theorem tdiv_nonneg_of_nonpos_of_nonpos {a b : Int} (Ha : a 0) (Hb : b 0) : 0 a.tdiv b := by
rw [tdiv_eq_ediv]
@@ -1335,9 +1294,6 @@ theorem tdiv_nonneg_of_nonpos_of_nonpos {a b : Int} (Ha : a ≤ 0) (Hb : b ≤ 0
protected theorem tdiv_nonpos_of_nonneg_of_nonpos {a b : Int} (Ha : 0 a) (Hb : b 0) : a.tdiv b 0 :=
Int.nonpos_of_neg_nonneg <| Int.tdiv_neg .. Int.tdiv_nonneg Ha (Int.neg_nonneg_of_nonpos Hb)
@[deprecated Int.tdiv_nonpos_of_nonneg_of_nonpos (since := "2025-03-04")]
abbrev tdiv_nonpos := @Int.tdiv_nonpos_of_nonneg_of_nonpos
theorem tdiv_eq_zero_of_lt {a b : Int} (H1 : 0 a) (H2 : a < b) : a.tdiv b = 0 :=
match a, b, eq_ofNat_of_zero_le H1, eq_succ_of_zero_lt (Int.lt_of_le_of_lt H1 H2) with
| _, _, _, rfl, _, rfl => congrArg Nat.cast <| Nat.div_eq_of_lt <| ofNat_lt.1 H2
@@ -1433,7 +1389,7 @@ theorem tmod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : tmod a b < b :=
theorem lt_tmod_of_pos (a : Int) {b : Int} (H : 0 < b) : -b < tmod a b :=
match a, b, eq_succ_of_zero_lt H with
| ofNat _, _, n, rfl => by rw [ofNat_eq_coe, Int.natCast_succ, ofNat_tmod]; omega
| ofNat _, _, n, rfl => by rw [ofNat_eq_natCast, Int.natCast_succ, ofNat_tmod]; omega
| -[a+1], _, n, rfl => by
rw [negSucc_eq, neg_tmod, Int.natCast_add_one, Int.natCast_add_one, ofNat_tmod]
have : (a + 1) % (n + 1) < n + 1 := Nat.mod_lt _ (Nat.zero_lt_succ n)
@@ -1880,7 +1836,7 @@ theorem le_emod_self_add_one_iff {a b : Int} (h : 0 < b) : b ≤ a % b + 1 ↔ b
match b, h with
| .ofNat 1, h => simp
| .ofNat (b + 2), h =>
simp only [ofNat_eq_coe, Int.natCast_add, cast_ofNat_Int] at *
simp only [ofNat_eq_natCast, Int.natCast_add, cast_ofNat_Int] at *
constructor
· rw [dvd_iff_emod_eq_zero]
intro w
@@ -1896,16 +1852,12 @@ theorem le_emod_self_add_one_iff {a b : Int} (h : 0 < b) : b ≤ a % b + 1 ↔ b
sign_eq_one_of_pos (by omega), Int.mul_add]
omega
@[deprecated le_emod_self_add_one_iff (since := "2025-04-12")]
theorem le_mod_self_add_one_iff {a b : Int} (h : 0 < b) : b a % b + 1 b a + 1 :=
le_emod_self_add_one_iff h
theorem add_one_tdiv_of_pos {a b : Int} (h : 0 < b) :
(a + 1).tdiv b = a.tdiv b + if (0 < a + 1 b a + 1) (a < 0 b a) then 1 else 0 := by
match b, h with
| .ofNat 1, h => simp; omega
| .ofNat (b + 2), h =>
simp only [ofNat_eq_coe]
simp only [ofNat_eq_natCast]
rw [tdiv_eq_ediv, add_ediv (by omega), tdiv_eq_ediv]
simp only [Int.natCast_add, cast_ofNat_Int]
have : 1 / (b + 2 : Int) = 0 := by rw [one_ediv]; omega
@@ -2020,7 +1972,7 @@ theorem add_fdiv_of_dvd_left {a b c : Int} (H : c a) : (a + b).fdiv c = a.fd
theorem fdiv_nonneg {a b : Int} (Ha : 0 a) (Hb : 0 b) : 0 a.fdiv b :=
match a, b, eq_ofNat_of_zero_le Ha, eq_ofNat_of_zero_le Hb with
| _, _, _, rfl, _, rfl => ofNat_fdiv .. ofNat_zero_le _
| _, _, _, rfl, _, rfl => ofNat_fdiv .. natCast_nonneg _
theorem fdiv_nonneg_of_nonpos_of_nonpos {a b : Int} (Ha : a 0) (Hb : b 0) : 0 a.fdiv b := by
rw [fdiv_eq_ediv]
@@ -2035,9 +1987,6 @@ theorem fdiv_nonpos_of_nonneg_of_nonpos : ∀ {a b : Int}, 0 ≤ a → b ≤ 0
| 0, 0, _, _ | 0, -[_+1], _, _ | succ _, 0, _, _ | succ _, -[_+1], _, _ => by
simp [fdiv, negSucc_le_zero]
@[deprecated fdiv_nonpos_of_nonneg_of_nonpos (since := "2025-03-04")]
abbrev fdiv_nonpos := @fdiv_nonpos_of_nonneg_of_nonpos
theorem fdiv_neg_of_neg_of_pos : {a b : Int}, a < 0 0 < b a.fdiv b < 0
| -[_+1], succ _, _, _ => negSucc_lt_zero _
@@ -2072,8 +2021,8 @@ protected theorem fdiv_eq_of_eq_mul_right {a b c : Int}
(H1 : b 0) (H2 : a = b * c) : a.fdiv b = c := by rw [H2, Int.mul_fdiv_cancel_left _ H1]
protected theorem eq_fdiv_of_mul_eq_right {a b c : Int}
(H1 : a 0) (H2 : a * b = c) : b = c.tdiv a :=
(Int.tdiv_eq_of_eq_mul_right H1 H2.symm).symm
(H1 : a 0) (H2 : a * b = c) : b = c.fdiv a :=
(Int.fdiv_eq_of_eq_mul_right H1 H2.symm).symm
protected theorem fdiv_eq_of_eq_mul_left {a b c : Int}
(H1 : b 0) (H2 : a = c * b) : a.fdiv b = c :=
@@ -2110,20 +2059,20 @@ theorem neg_fdiv {a b : Int} : (-a).fdiv b = -(a.fdiv b) - if b = 0 b a
| ofNat (a + 1), 0 => simp
| ofNat (a + 1), ofNat (b + 1) =>
unfold fdiv
simp only [ofNat_eq_coe, Int.natCast_add, cast_ofNat_Int, Nat.succ_eq_add_one]
simp only [ofNat_eq_natCast, Int.natCast_add, cast_ofNat_Int, Nat.succ_eq_add_one]
rw [ negSucc_eq, negSucc_eq]
| ofNat (a + 1), -[b+1] =>
unfold fdiv
simp only [ofNat_eq_coe, Int.natCast_add, cast_ofNat_Int, Nat.succ_eq_add_one]
simp only [ofNat_eq_natCast, Int.natCast_add, cast_ofNat_Int, Nat.succ_eq_add_one]
rw [ negSucc_eq, neg_negSucc]
| -[a+1], 0 => simp
| -[a+1], ofNat (b + 1) =>
unfold fdiv
simp only [ofNat_eq_coe, Int.natCast_add, cast_ofNat_Int, Nat.succ_eq_add_one]
simp only [ofNat_eq_natCast, Int.natCast_add, cast_ofNat_Int, Nat.succ_eq_add_one]
rw [neg_negSucc, negSucc_eq]
| -[a+1], -[b+1] =>
unfold fdiv
simp only [ofNat_eq_coe, natCast_ediv, Nat.succ_eq_add_one, Int.natCast_add, cast_ofNat_Int]
simp only [ofNat_eq_natCast, natCast_ediv, Nat.succ_eq_add_one, Int.natCast_add, cast_ofNat_Int]
rw [neg_negSucc, neg_negSucc]
simp
@@ -2156,9 +2105,6 @@ theorem fmod_nonneg {a b : Int} (ha : 0 ≤ a) (hb : 0 ≤ b) : 0 ≤ a.fmod b :
theorem fmod_nonneg_of_pos (a : Int) {b : Int} (hb : 0 < b) : 0 a.fmod b :=
fmod_eq_emod_of_nonneg _ (Int.le_of_lt hb) emod_nonneg _ (Int.ne_of_lt hb).symm
@[deprecated fmod_nonneg_of_pos (since := "2025-03-04")]
abbrev fmod_nonneg' := @fmod_nonneg_of_pos
theorem fmod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : a.fmod b < b :=
fmod_eq_emod_of_nonneg _ (Int.le_of_lt H) emod_lt_of_pos a H
@@ -2168,10 +2114,6 @@ theorem fmod_lt_of_pos (a : Int) {b : Int} (H : 0 < b) : a.fmod b < b :=
rw [fmod_eq_emod, add_mul_emod_self_right, fmod_eq_emod]
simp
@[deprecated add_mul_fmod_self_right (since := "2025-04-11")]
theorem add_mul_fmod_self {a b c : Int} : (a + b * c).fmod c = a.fmod c :=
add_mul_fmod_self_right ..
@[simp] theorem add_mul_fmod_self_left (a b c : Int) : (a + b * c).fmod b = a.fmod b := by
rw [Int.mul_comm, Int.add_mul_fmod_self_right]
@@ -2419,7 +2361,7 @@ theorem natAbs_fdiv_le_natAbs (a b : Int) : natAbs (a.fdiv b) ≤ natAbs a := by
| 0, .negSucc b, h => simp at h
| .ofNat (a + 1), .negSucc 0, h => simp at h
| .ofNat (a + 1), .negSucc (b + 1), h =>
rw [negSucc_eq, ofNat_eq_coe]
rw [negSucc_eq, ofNat_eq_natCast]
norm_cast
rw [Int.ediv_neg, Int.sub_eq_add_neg, Int.neg_add, natAbs_neg]
norm_cast
@@ -2470,20 +2412,12 @@ theorem dvd_sub_self_of_fmod_eq {a b c : Int} (h : a.fmod b = c) :
@[simp] theorem fmod_one (a : Int) : a.fmod 1 = 0 := by
simp [fmod_def, Int.one_mul, Int.sub_self]
@[deprecated sub_fmod_right (since := "2025-04-12")]
theorem fmod_sub_cancel (x y : Int) : (x - y).fmod y = x.fmod y :=
sub_fmod_right _ _
@[simp] theorem add_neg_fmod_self (a b : Int) : (a + -b).fmod b = a.fmod b := by
rw [Int.add_neg_eq_sub, sub_fmod_right]
@[simp] theorem neg_add_fmod_self (a b : Int) : (-a + b).fmod a = b.fmod a := by
rw [Int.add_comm, add_neg_fmod_self]
@[deprecated dvd_self_sub_of_fmod_eq (since := "2025-04-12")]
theorem dvd_sub_of_fmod_eq {a b c : Int} (h : a.fmod b = c) : b a - c :=
dvd_self_sub_of_fmod_eq h
theorem fdiv_sign {a b : Int} : a.fdiv (sign b) = a * sign b := by
rw [fdiv_eq_ediv]
rcases sign_trichotomy b with h | h | h <;> simp [h]
@@ -2517,10 +2451,6 @@ theorem lt_mul_fdiv_self_add {x k : Int} (h : 0 < k) : x < k * (x.fdiv k) + k :=
theorem emod_bmod (x : Int) (n : Nat) : Int.bmod (x%n) n = Int.bmod x n := by
simp [bmod]
@[deprecated emod_bmod (since := "2025-04-11")]
theorem emod_bmod_congr (x : Int) (n : Nat) : Int.bmod (x%n) n = Int.bmod x n :=
emod_bmod ..
theorem bdiv_add_bmod (x : Int) (m : Nat) : m * bdiv x m + bmod x m = x := by
unfold bdiv bmod
split
@@ -2547,6 +2477,10 @@ theorem bmod_eq_self_sub_mul_bdiv (x : Int) (m : Nat) : bmod x m = x - m * bdiv
theorem bmod_eq_self_sub_bdiv_mul (x : Int) (m : Nat) : bmod x m = x - bdiv x m * m := by
rw [ Int.add_sub_cancel (bmod x m), bmod_add_bdiv']
theorem bmod_eq_emod_of_lt {x : Int} {m : Nat} (hx : x % m < (m + 1) / 2) : bmod x m = x % m := by
simp [bmod, hx]
@[deprecated Int.bmod_eq_emod_of_lt (since := "2025-10-29")]
theorem bmod_pos (x : Int) (m : Nat) (p : x % m < (m + 1) / 2) : bmod x m = x % m := by
simp [bmod_def, p]
@@ -2556,15 +2490,12 @@ theorem bmod_neg (x : Int) (m : Nat) (p : x % m ≥ (m + 1) / 2) : bmod x m = (x
theorem bmod_eq_emod (x : Int) (m : Nat) : bmod x m = x % m - if x % m (m + 1) / 2 then m else 0 := by
split
· rwa [bmod_neg]
· rw [bmod_pos] <;> simp_all
· rw [bmod_eq_emod_of_lt] <;> simp_all
@[simp]
theorem bmod_one (x : Int) : Int.bmod x 1 = 0 := by
simp [Int.bmod]
@[deprecated bmod_one (since := "2025-04-10")]
abbrev bmod_one_is_zero := @bmod_one
@[simp] theorem add_bmod_right (a : Int) (b : Nat) : (a + b).bmod b = a.bmod b := by
simp [bmod_def]
@@ -2607,76 +2538,36 @@ abbrev bmod_one_is_zero := @bmod_one
@[simp] theorem add_neg_mul_bmod_self_left (a : Int) (b : Nat) (c : Int) : (a + -(b * c)).bmod b = a.bmod b := by
simp [bmod_def]
@[deprecated add_bmod_right (since := "2025-04-10")]
theorem bmod_add_cancel {x : Int} {n : Nat} : Int.bmod (x + n) n = Int.bmod x n :=
add_bmod_right ..
@[deprecated add_mul_bmod_self_left (since := "2025-04-10")]
theorem bmod_add_mul_cancel (x : Int) (n : Nat) (k : Int) : Int.bmod (x + n * k) n = Int.bmod x n :=
add_mul_bmod_self_left ..
@[deprecated sub_bmod_right (since := "2025-04-10")]
theorem bmod_sub_cancel (x : Int) (n : Nat) : Int.bmod (x - n) n = Int.bmod x n :=
sub_bmod_right ..
@[deprecated sub_mul_bmod_self_left (since := "2025-04-10")]
theorem Int.bmod_sub_mul_cancel (x : Int) (n : Nat) (k : Int) : (x - n * k).bmod n = x.bmod n :=
sub_mul_bmod_self_left ..
@[simp]
theorem emod_add_bmod (x : Int) (n : Nat) : Int.bmod (x % n + y) n = Int.bmod (x + y) n := by
simp [Int.emod_def, Int.sub_eq_add_neg]
rw [Int.mul_neg, Int.add_right_comm, Int.add_mul_bmod_self_left]
@[deprecated emod_add_bmod (since := "2025-04-11")]
theorem emod_add_bmod_congr (x : Int) (n : Nat) : Int.bmod (x % n + y) n = Int.bmod (x + y) n :=
emod_add_bmod ..
@[simp]
theorem emod_sub_bmod (x : Int) (n : Nat) : Int.bmod (x % n - y) n = Int.bmod (x - y) n := by
simp only [emod_def, Int.sub_eq_add_neg]
rw [Int.mul_neg, Int.add_right_comm, Int.add_mul_bmod_self_left]
@[deprecated emod_sub_bmod (since := "2025-04-11")]
theorem emod_sub_bmod_congr (x : Int) (n : Nat) : Int.bmod (x % n - y) n = Int.bmod (x - y) n :=
emod_sub_bmod ..
@[simp]
theorem sub_emod_bmod (x : Int) (n : Nat) : Int.bmod (x - y % n) n = Int.bmod (x - y) n := by
simp only [emod_def]
rw [Int.sub_eq_add_neg, Int.neg_sub, Int.sub_eq_add_neg, Int.add_assoc, Int.add_right_comm,
Int.add_mul_bmod_self_left, Int.sub_eq_add_neg]
@[deprecated sub_emod_bmod (since := "2025-04-11")]
theorem sub_emod_bmod_congr (x : Int) (n : Nat) : Int.bmod (x - y % n) n = Int.bmod (x - y) n :=
sub_emod_bmod ..
@[simp]
theorem emod_mul_bmod (x : Int) (n : Nat) : Int.bmod (x % n * y) n = Int.bmod (x * y) n := by
simp [Int.emod_def, Int.sub_eq_add_neg]
rw [Int.mul_neg, Int.add_mul, Int.mul_assoc, Int.add_mul_bmod_self_left]
@[deprecated emod_mul_bmod (since := "2025-04-11")]
theorem emod_mul_bmod_congr (x : Int) (n : Nat) : Int.bmod (x % n * y) n = Int.bmod (x * y) n :=
emod_mul_bmod ..
@[simp]
theorem bmod_add_bmod : Int.bmod (Int.bmod x n + y) n = Int.bmod (x + y) n := by
have := (@add_mul_bmod_self_left (Int.bmod x n + y) n (bdiv x n)).symm
rwa [Int.add_right_comm, bmod_add_bdiv] at this
@[deprecated bmod_add_bmod (since := "2025-04-11")]
theorem bmod_add_bmod_congr : Int.bmod (Int.bmod x n + y) n = Int.bmod (x + y) n :=
bmod_add_bmod ..
@[simp]
theorem bmod_sub_bmod : Int.bmod (Int.bmod x n - y) n = Int.bmod (x - y) n :=
@bmod_add_bmod x n (-y)
@[deprecated bmod_sub_bmod (since := "2025-04-11")]
theorem bmod_sub_bmod_congr : Int.bmod (Int.bmod x n - y) n = Int.bmod (x - y) n :=
bmod_sub_bmod ..
theorem add_bmod_eq_add_bmod_right (i : Int)
(H : bmod x n = bmod y n) : bmod (x + i) n = bmod (y + i) n := by
rw [ bmod_add_bmod, @bmod_add_bmod y, H]
@@ -2836,9 +2727,6 @@ theorem bmod_eq_iff {a : Int} {b : Nat} {c : Int} (hb : 0 < b) :
have := bmod_lt (x := a) (m := b) hb
omega
theorem bmod_eq_emod_of_lt {x : Int} {m : Nat} (hx : x % m < (m + 1) / 2) : bmod x m = x % m := by
simp [bmod, hx]
theorem bmod_eq_neg {n : Nat} {m : Int} (hm : 0 m) (hn : n = 2 * m) : m.bmod n = -m := by
by_cases h : m = 0
· subst h; simp
@@ -2869,9 +2757,6 @@ theorem bmod_natAbs_add_one (x : Int) (w : x ≠ -1) : x.bmod (x.natAbs + 1) = -
· rw [sign_eq_one_iff_pos.2 hx]
exact by omega, by omega, -1, by omega
@[deprecated bmod_natAbs_add_one (since := "2025-04-04")]
abbrev bmod_natAbs_plus_one := @bmod_natAbs_add_one
theorem bmod_self_add_one {x : Nat} : (x : Int).bmod (x + 1) = if x = 0 then 0 else -1 := by
have := bmod_natAbs_add_one x (by omega)
simp only [natAbs_natCast] at this
@@ -2882,7 +2767,7 @@ theorem one_bmod_two : Int.bmod 1 2 = -1 := by simp
theorem one_bmod {b : Nat} (h : 3 b) : Int.bmod 1 b = 1 := by
have hb : 1 % (b : Int) = 1 := by rw [one_emod]; omega
rw [bmod_pos _ _ (by omega), hb]
rw [bmod_eq_emod_of_lt (by omega), hb]
theorem bmod_two_eq (x : Int) : x.bmod 2 = -1 x.bmod 2 = 0 := by
have := le_bmod (x := x) (m := 2) (by omega)
@@ -2992,11 +2877,6 @@ theorem bmod_eq_of_le {n : Int} {m : Nat} (hn' : -(m / 2) ≤ n) (hn : n < (m +
n.bmod m = n :=
(Nat.eq_zero_or_pos m).elim (by rintro rfl; simp) (fun hm => by simp_all [bmod_eq_iff])
@[deprecated bmod_eq_of_le (since := "2025-04-11")]
theorem bmod_eq_self_of_le {n : Int} {m : Nat} (hn' : -(m / 2) n) (hn : n < (m + 1) / 2) :
n.bmod m = n :=
bmod_eq_of_le hn' hn
theorem bmod_bmod_of_dvd {a : Int} {n m : Nat} (hnm : n m) :
(a.bmod m).bmod n = a.bmod n := by
rw [ Int.sub_eq_iff_eq_add.2 (bmod_add_bdiv a m).symm]
@@ -3007,11 +2887,6 @@ theorem bmod_eq_of_le_mul_two {x : Int} {y : Nat} (hle : -y ≤ x * 2) (hlt : x
x.bmod y = x := by
apply bmod_eq_of_le (by omega) (by omega)
@[deprecated bmod_eq_of_le_mul_two (since := "2025-04-11")]
theorem bmod_eq_self_of_le_mul_two {x : Int} {y : Nat} (hle : -y x * 2) (hlt : x * 2 < y) :
x.bmod y = x :=
bmod_eq_of_le_mul_two hle hlt
/- ### ediv -/
theorem ediv_lt_self_of_pos_of_ne_one {x y : Int} (hx : 0 < x) (hy : y 1) :
@@ -3030,7 +2905,7 @@ theorem ediv_nonneg_of_nonneg_of_nonneg {x y : Int} (hx : 0 ≤ x) (hy : 0 ≤ y
obtain xn, rfl := Int.eq_ofNat_of_zero_le (a := x) (by omega)
obtain yn, rfl := Int.eq_ofNat_of_zero_le (a := y) (by omega)
rw [ Int.natCast_ediv]
exact Int.ofNat_zero_le (xn / yn)
exact natCast_nonneg (xn / yn)
/-- When both x and y are negative we need stricter bounds on x and y
to establish the upper bound of x/y, i.e., x / y < x.natAbs.
@@ -3067,7 +2942,7 @@ theorem neg_self_le_ediv_of_nonneg_of_nonpos (x y : Int) (hx : 0 ≤ x) (hy : y
· obtain xn, rfl := Int.eq_ofNat_of_zero_le (a := x) (by omega)
obtain yn, rfl := Int.eq_negSucc_of_lt_zero (a := y) (by omega)
rw [show xn = ofNat xn by norm_cast, Int.ofNat_ediv_negSucc (a := xn)]
simp only [ofNat_eq_coe, natCast_ediv, Int.natCast_add, cast_ofNat_Int, Int.neg_le_neg_iff]
simp only [ofNat_eq_natCast, natCast_ediv, Int.natCast_add, cast_ofNat_Int, Int.neg_le_neg_iff]
norm_cast
apply Nat.le_trans (m := xn) (by exact Nat.div_le_self xn (yn + 1)) (by omega)

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@@ -6,8 +6,6 @@ Authors: Mario Carneiro, Markus Himmel
module
prelude
public import Init.Data.Int.Basic
public import Init.Data.Nat.Gcd
public import Init.Data.Nat.Lcm
public import Init.Data.Int.DivMod.Lemmas
public import Init.Data.Int.Pow

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@@ -6,8 +6,6 @@ Authors: Jeremy Avigad, Deniz Aydin, Floris van Doorn, Mario Carneiro
module
prelude
public import Init.Conv
public import Init.NotationExtra
public import Init.PropLemmas
public section
@@ -19,7 +17,7 @@ open Nat
/-! ## Definitions of basic functions -/
theorem subNatNat_of_sub_eq_zero {m n : Nat} (h : n - m = 0) : subNatNat m n = (m - n) := by
rw [subNatNat, h, ofNat_eq_coe]
rw [subNatNat, h, ofNat_eq_natCast]
theorem subNatNat_of_sub_eq_succ {m n k : Nat} (h : n - m = succ k) : subNatNat m n = -[k+1] := by
rw [subNatNat, h]
@@ -76,9 +74,6 @@ theorem negSucc_inj : negSucc m = negSucc n ↔ m = n := ⟨negSucc.inj, fun H =
theorem negSucc_eq (n : Nat) : -[n+1] = -((n : Int) + 1) := rfl
@[deprecated negSucc_eq (since := "2025-03-11")]
theorem negSucc_coe (n : Nat) : -[n+1] = -(n + 1) := rfl
@[simp] theorem negSucc_ne_zero (n : Nat) : -[n+1] 0 := nofun
@[simp] theorem zero_ne_negSucc (n : Nat) : 0 -[n+1] := nofun
@@ -134,7 +129,7 @@ theorem subNatNat_elim (m n : Nat) (motive : Nat → Nat → Int → Prop)
theorem subNatNat_add_left : subNatNat (m + n) m = n := by
unfold subNatNat
rw [Nat.sub_eq_zero_of_le (Nat.le_add_right ..), Nat.add_sub_cancel_left, ofNat_eq_coe]
rw [Nat.sub_eq_zero_of_le (Nat.le_add_right ..), Nat.add_sub_cancel_left, ofNat_eq_natCast]
theorem subNatNat_add_right : subNatNat m (m + n + 1) = negSucc n := by
simp [subNatNat, Nat.add_assoc, Nat.add_sub_cancel_left]
@@ -355,10 +350,6 @@ protected theorem add_sub_assoc (a b c : Int) : a + b - c = a + (b - c) := by
change ofNat (n - succ m) = subNatNat n (succ m)
rw [subNatNat, Nat.sub_eq_zero_of_le h]
@[deprecated negSucc_eq (since := "2025-03-11")]
theorem negSucc_coe' (n : Nat) : -[n+1] = -n - 1 := by
rw [Int.sub_eq_add_neg, Int.neg_add]; rfl
protected theorem subNatNat_eq_coe {m n : Nat} : subNatNat m n = m - n := by
apply subNatNat_elim m n fun m n i => i = m - n
· intro i n
@@ -609,6 +600,4 @@ protected theorem natCast_zero : ((0 : Nat) : Int) = (0 : Int) := rfl
protected theorem natCast_one : ((1 : Nat) : Int) = (1 : Int) := rfl
@[simp, norm_cast] theorem natAbs_cast (n : Nat) : natAbs n = n := rfl
end Int

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@@ -6,9 +6,7 @@ Authors: Kim Morrison
module
prelude
public import Init.Data.Int.Order
public import Init.Data.Int.Pow
public import Init.Omega
public section
@@ -29,28 +27,28 @@ namespace Int
natCast_nonneg _
@[simp] theorem neg_natCast_le_natCast (n m : Nat) : -(n : Int) (m : Int) :=
Int.le_trans (by simp) (ofNat_zero_le m)
Int.le_trans (by simp) (natCast_nonneg m)
@[simp] theorem neg_natCast_le_ofNat (n m : Nat) : -(n : Int) (no_index (OfNat.ofNat m)) :=
Int.le_trans (by simp) (ofNat_zero_le m)
Int.le_trans (by simp) (natCast_nonneg m)
@[simp] theorem neg_ofNat_le_ofNat (n m : Nat) : -(no_index (OfNat.ofNat n)) (no_index (OfNat.ofNat m)) :=
Int.le_trans (by simp) (ofNat_zero_le m)
Int.le_trans (by simp) (natCast_nonneg m)
@[simp] theorem neg_ofNat_le_natCast (n m : Nat) : -(no_index (OfNat.ofNat n)) (m : Int) :=
Int.le_trans (by simp) (ofNat_zero_le m)
Int.le_trans (by simp) (natCast_nonneg m)
theorem neg_lt_self_iff {n : Int} : -n < n 0 < n := by
omega
@[deprecated ofNat_add_ofNat (since := "2025-10-26")]
protected theorem ofNat_add_out (m n : Nat) : m + n = ((m + n) : Int) := rfl
@[deprecated ofNat_mul_ofNat (since := "2025-10-26")]
protected theorem ofNat_mul_out (m n : Nat) : m * n = ((m * n) : Int) := rfl
protected theorem ofNat_add_one_out (n : Nat) : n + (1 : Int) = (Nat.succ n) := rfl
@[simp] theorem ofNat_eq_natCast (n : Nat) : Int.ofNat n = n := rfl
@[norm_cast] theorem natCast_inj {m n : Nat} : (m : Int) = (n : Int) m = n := ofNat_inj
@[norm_cast]
@@ -64,8 +62,6 @@ theorem natCast_succ_pos (n : Nat) : 0 < (n.succ : Int) := natCast_pos.2 n.succ_
@[simp high] theorem natCast_nonpos_iff {n : Nat} : (n : Int) 0 n = 0 := by omega
@[simp] theorem sign_natCast_add_one (n : Nat) : sign (n + 1) = 1 := rfl
@[simp, norm_cast] theorem cast_id {n : Int} : Int.cast n = n := rfl
@[simp] theorem ble'_eq_true (a b : Int) : (Int.ble' a b = true) = (a b) := by
@@ -86,7 +82,7 @@ theorem natCast_succ_pos (n : Nat) : 0 < (n.succ : Int) := natCast_pos.2 n.succ_
symm
simp only [Int.toNat]
split <;> rename_i x a
· simp only [Int.ofNat_eq_coe]
· simp only [Int.ofNat_eq_natCast]
split <;> rename_i y b h
· simp at h
omega
@@ -120,14 +116,8 @@ theorem pos_iff_toNat_pos {n : Int} : 0 < n ↔ 0 < n.toNat := by
theorem natCast_toNat_eq_self {a : Int} : a.toNat = a 0 a := by omega
@[deprecated natCast_toNat_eq_self (since := "2025-04-16")]
theorem ofNat_toNat_eq_self {a : Int} : a.toNat = a 0 a := natCast_toNat_eq_self
theorem eq_natCast_toNat {a : Int} : a = a.toNat 0 a := by omega
@[deprecated eq_natCast_toNat (since := "2025-04-16")]
theorem eq_ofNat_toNat {a : Int} : a = a.toNat 0 a := eq_natCast_toNat
theorem toNat_le_toNat {n m : Int} (h : n m) : n.toNat m.toNat := by omega
theorem toNat_lt_toNat {n m : Int} (hn : 0 < m) : n.toNat < m.toNat n < m := by omega

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@@ -4,23 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
module
prelude
public import Init.ByCases
public import Init.Data.Prod
public import Init.Data.Int.Lemmas
public import Init.Data.Int.LemmasAux
public import Init.Data.Int.DivMod.Bootstrap
public import Init.Data.Int.Cooper
public import Init.Data.Int.Gcd
import all Init.Data.Int.Gcd
public import Init.Data.RArray
public import Init.Data.AC
import all Init.Data.AC
import Init.LawfulBEqTactics
public section
namespace Int.Linear
/-! Helper definitions and theorems for constructing linear arithmetic proofs. -/
@@ -28,8 +19,7 @@ namespace Int.Linear
abbrev Var := Nat
abbrev Context := Lean.RArray Int
@[expose]
def Var.denote (ctx : Context) (v : Var) : Int :=
abbrev Var.denote (ctx : Context) (v : Var) : Int :=
ctx.get v
inductive Expr where
@@ -42,8 +32,7 @@ inductive Expr where
| mulR (a : Expr) (k : Int)
deriving Inhabited, @[expose] BEq
@[expose]
def Expr.denote (ctx : Context) : Expr Int
abbrev Expr.denote (ctx : Context) : Expr Int
| .add a b => denote ctx a + denote ctx b
| .sub a b => denote ctx a - denote ctx b
| .neg a => - denote ctx a
@@ -52,6 +41,9 @@ def Expr.denote (ctx : Context) : Expr → Int
| .mulL k e => k * denote ctx e
| .mulR e k => denote ctx e * k
set_option allowUnsafeReducibility true
attribute [semireducible] Var.denote Expr.denote
inductive Poly where
| num (k : Int)
| add (k : Int) (v : Var) (p : Poly)
@@ -74,35 +66,36 @@ protected noncomputable def Poly.beq' (p₁ : Poly) : Poly → Bool :=
intro _ _; subst k₁ v₁
simp [ ih p₂, Bool.and'_eq_and]; rfl
@[expose]
def Poly.denote (ctx : Context) (p : Poly) : Int :=
abbrev Poly.denote (ctx : Context) (p : Poly) : Int :=
match p with
| .num k => k
| .add k v p => k * v.denote ctx + denote ctx p
noncomputable abbrev Poly.denote'.go (ctx : Context) (p : Poly) : Int Int :=
Poly.rec
(fun k r => Bool.rec
(r + k)
r
(Int.beq' k 0))
(fun k v _ ih r => Bool.rec
(ih (r + k * v.denote ctx))
(ih (r + v.denote ctx))
(Int.beq' k 1))
p
/--
Similar to `Poly.denote`, but produces a denotation better for `simp +arith`.
Remark: we used to convert `Poly` back into `Expr` to achieve that.
-/
@[expose] noncomputable def Poly.denote' (ctx : Context) (p : Poly) : Int :=
noncomputable abbrev Poly.denote' (ctx : Context) (p : Poly) : Int :=
Poly.rec (fun k => k)
(fun k v p _ => Bool.rec
(go p (k * v.denote ctx))
(go p (v.denote ctx))
(denote'.go ctx p (k * v.denote ctx))
(denote'.go ctx p (v.denote ctx))
(Int.beq' k 1))
p
where
go (p : Poly) : Int Int :=
Poly.rec
(fun k r => Bool.rec
(r + k)
r
(Int.beq' k 0))
(fun k v _ ih r => Bool.rec
(ih (r + k * v.denote ctx))
(ih (r + v.denote ctx))
(Int.beq' k 1))
p
attribute [semireducible] Poly.denote Poly.denote' Poly.denote'.go
@[simp] theorem Poly.denote'_go_eq_denote (ctx : Context) (p : Poly) (r : Int) : denote'.go ctx p r = p.denote ctx + r := by
induction p generalizing r
@@ -1097,7 +1090,7 @@ theorem eq_unsat_coeff (ctx : Context) (p : Poly) (k : Int) : eq_unsat_coeff_cer
induction p
next => rfl
next a y p ih =>
simp [coeff_k, coeff, cond_eq_if]; split
simp [coeff_k, coeff, cond_eq_ite]; split
next h => simp [h]
next h => rw [ Nat.beq_eq, Bool.not_eq_true] at h; simp [h, ih]; rfl

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@@ -6,11 +6,8 @@ Authors: Leonardo de Moura
module
prelude
public import Init.Data.Int.Lemmas
public import Init.Data.Int.DivMod
public import Init.Data.Int.Linear
public import Init.GrindInstances.ToInt
public import Init.Data.RArray
public section

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@@ -62,8 +62,6 @@ protected theorem le_total (a b : Int) : a ≤ b b ≤ a :=
let k, (hk : m + k = n) := Nat.le.dest h
le.intro k (by rw [ hk]; rfl)
@[simp] theorem ofNat_zero_le (n : Nat) : 0 (n : Int) := ofNat_le.2 n.zero_le
theorem eq_ofNat_of_zero_le {a : Int} (h : 0 a) : n : Nat, a = n := by
have t := le.dest_sub h; rwa [Int.sub_zero] at t
@@ -88,8 +86,12 @@ theorem lt.dest {a b : Int} (h : a < b) : ∃ n : Nat, a + Nat.succ n = b :=
@[deprecated natCast_pos (since := "2025-05-13"), simp high]
theorem ofNat_pos {n : Nat} : 0 < (n : Int) 0 < n := ofNat_lt
@[simp]
theorem natCast_nonneg (n : Nat) : 0 (n : Int) := _
@[deprecated natCast_nonneg (since := "2025-10-26")]
theorem ofNat_zero_le (n : Nat) : 0 (n : Int) := ofNat_le.2 n.zero_le
@[deprecated natCast_nonneg (since := "2025-05-13")]
theorem ofNat_nonneg (n : Nat) : 0 (n : Int) := _
@@ -234,13 +236,10 @@ theorem eq_natAbs_of_nonneg {a : Int} (h : 0 ≤ a) : a = natAbs a := by
let n, e := eq_ofNat_of_zero_le h
rw [e]; rfl
@[deprecated eq_natAbs_of_nonneg (since := "2025-03-11")]
abbrev eq_natAbs_of_zero_le := @eq_natAbs_of_nonneg
theorem le_natAbs {a : Int} : a natAbs a :=
match Int.le_total 0 a with
| .inl h => by rw [eq_natAbs_of_nonneg h]; apply Int.le_refl
| .inr h => Int.le_trans h (ofNat_zero_le _)
| .inr h => Int.le_trans h (natCast_nonneg _)
@[simp] theorem negSucc_lt_zero (n : Nat) : -[n+1] < 0 :=
Int.not_le.1 fun h => let _, h := eq_ofNat_of_zero_le h; nomatch h
@@ -468,10 +467,10 @@ protected theorem max_lt {a b c : Int} : max a b < c ↔ a < c ∧ b < c := by
simpa using Int.max_le (a := a + 1) (b := b + 1) (c := c)
@[simp] theorem ofNat_max_zero (n : Nat) : (max (n : Int) 0) = n := by
rw [Int.max_eq_left (ofNat_zero_le n)]
rw [Int.max_eq_left (natCast_nonneg n)]
@[simp] theorem zero_max_ofNat (n : Nat) : (max 0 (n : Int)) = n := by
rw [Int.max_eq_right (ofNat_zero_le n)]
rw [Int.max_eq_right (natCast_nonneg n)]
@[simp] theorem negSucc_max_zero (n : Nat) : (max (Int.negSucc n) 0) = 0 := by
rw [Int.max_eq_right (negSucc_le_zero _)]
@@ -554,8 +553,8 @@ protected theorem mul_le_mul_of_nonpos_left {a b c : Int}
@[simp, norm_cast] theorem natAbs_natCast (n : Nat) : natAbs n = n := rfl
@[deprecated natAbs_natCast (since := "2025-04-16")]
theorem natAbs_ofNat (n : Nat) : natAbs n = n := natAbs_natCast n
@[deprecated natAbs_natCast (since := "2025-10-26")]
theorem natAbs_cast (n : Nat) : natAbs n = n := rfl
/-
TODO: rename `natAbs_ofNat'` to `natAbs_ofNat` once the current deprecated alias
@@ -605,6 +604,9 @@ theorem natAbs_of_nonneg {a : Int} (H : 0 ≤ a) : (natAbs a : Int) = a :=
match a, eq_ofNat_of_zero_le H with
| _, _, rfl => rfl
theorem ofNat_natAbs_of_nonneg {a : Int} (h : 0 a) : (natAbs a : Int) = a :=
natAbs_of_nonneg h
theorem ofNat_natAbs_of_nonpos {a : Int} (H : a 0) : (natAbs a : Int) = -a := by
rw [ natAbs_neg, natAbs_of_nonneg (Int.neg_nonneg_of_nonpos H)]
@@ -631,7 +633,7 @@ theorem eq_zero_of_dvd_of_natAbs_lt_natAbs {d n : Int} (h : d n) (h₁ : n.n
/-! ### toNat -/
theorem toNat_eq_max : a : Int, (toNat a : Int) = max a 0
| (n : Nat) => (Int.max_eq_left (ofNat_zero_le n)).symm
| (n : Nat) => (Int.max_eq_left (natCast_nonneg n)).symm
| -[n+1] => (Int.max_eq_right (Int.le_of_lt (negSucc_lt_zero n))).symm
@[simp] theorem toNat_zero : (0 : Int).toNat = 0 := rfl
@@ -643,17 +645,11 @@ theorem toNat_of_nonneg {a : Int} (h : 0 ≤ a) : (toNat a : Int) = a := by
@[simp] theorem toNat_natCast (n : Nat) : toNat n = n := rfl
@[deprecated toNat_natCast (since := "2025-04-16")]
theorem toNat_ofNat (n : Nat) : toNat n = n := rfl
@[simp] theorem toNat_negSucc (n : Nat) : (Int.negSucc n).toNat = 0 := by
simp [toNat]
@[simp] theorem toNat_natCast_add_one {n : Nat} : ((n : Int) + 1).toNat = n + 1 := rfl
@[deprecated toNat_natCast_add_one (since := "2025-04-16")]
theorem toNat_ofNat_add_one {n : Nat} : ((n : Int) + 1).toNat = n + 1 := toNat_natCast_add_one
@[simp] theorem ofNat_toNat (a : Int) : (a.toNat : Int) = max a 0 := by
match a with
| (n : Nat) => simp
@@ -714,9 +710,6 @@ theorem mem_toNat? : ∀ {a : Int} {n : Nat}, toNat? a = some n ↔ a = n
| (m : Nat), n => by simp [toNat?, Int.ofNat_inj]
| -[m+1], n => by constructor <;> nofun
@[deprecated mem_toNat? (since := "2025-03-11")]
abbrev mem_toNat' := @mem_toNat?
/-! ## Order properties of the integers -/
protected theorem le_of_not_le {a b : Int} : ¬ a b b a := (Int.le_total a b).resolve_left
@@ -725,7 +718,7 @@ protected theorem le_of_not_le {a b : Int} : ¬ a ≤ b → b ≤ a := (Int.le_t
simp only [Int.not_lt, iff_false]; constructor
theorem eq_negSucc_of_lt_zero : {a : Int}, a < 0 n : Nat, a = -[n+1]
| ofNat _, h => absurd h (Int.not_lt.2 (ofNat_zero_le _))
| ofNat _, h => absurd h (Int.not_lt.2 (natCast_nonneg _))
| -[n+1], _ => n, rfl
protected theorem lt_of_add_lt_add_left {a b c : Int} (h : a + b < a + c) : b < c := by
@@ -793,10 +786,10 @@ theorem add_one_le_iff {a b : Int} : a + 1 ≤ b ↔ a < b := .rfl
theorem lt_add_one_iff {a b : Int} : a < b + 1 a b := Int.add_le_add_iff_right _
@[simp] theorem succ_ofNat_pos (n : Nat) : 0 < (n : Int) + 1 :=
lt_add_one_iff.mpr (ofNat_zero_le _)
lt_add_one_iff.mpr (natCast_nonneg _)
theorem not_ofNat_neg (n : Nat) : ¬((n : Int) < 0) :=
Int.not_lt.mpr (ofNat_zero_le ..)
Int.not_lt.mpr (natCast_nonneg ..)
theorem le_add_one {a b : Int} (h : a b) : a b + 1 :=
Int.le_of_lt (Int.lt_add_one_iff.2 h)
@@ -1247,7 +1240,11 @@ protected theorem neg_of_mul_pos_right {a b : Int}
@[simp] theorem sign_one : sign 1 = 1 := rfl
theorem sign_neg_one : sign (-1) = -1 := rfl
@[simp] theorem sign_of_add_one (x : Nat) : Int.sign (x + 1) = 1 := rfl
@[simp] theorem sign_natCast_add_one (n : Nat) : sign (n + 1) = 1 := rfl
@[deprecated sign_natCast_add_one (since := "2025-10-26")]
theorem sign_of_add_one (x : Nat) : Int.sign (x + 1) = 1 := rfl
@[simp] theorem sign_negSucc (x : Nat) : Int.sign (Int.negSucc x) = -1 := rfl
theorem natAbs_sign (z : Int) : z.sign.natAbs = if z = 0 then 0 else 1 :=
@@ -1256,17 +1253,9 @@ theorem natAbs_sign (z : Int) : z.sign.natAbs = if z = 0 then 0 else 1 :=
theorem natAbs_sign_of_ne_zero {z : Int} (hz : z 0) : z.sign.natAbs = 1 := by
rw [Int.natAbs_sign, if_neg hz]
@[deprecated natAbs_sign_of_ne_zero (since := "2025-04-16")]
theorem natAbs_sign_of_nonzero {z : Int} (hz : z 0) : z.sign.natAbs = 1 :=
natAbs_sign_of_ne_zero hz
theorem sign_natCast_of_ne_zero {n : Nat} (hn : n 0) : Int.sign n = 1 :=
match n, Nat.exists_eq_succ_of_ne_zero hn with
| _, n, rfl => Int.sign_of_add_one n
@[deprecated sign_natCast_of_ne_zero (since := "2025-04-16")]
theorem sign_ofNat_of_nonzero {n : Nat} (hn : n 0) : Int.sign n = 1 :=
sign_natCast_of_ne_zero hn
| _, n, rfl => Int.sign_natCast_add_one n
@[simp] theorem sign_neg (z : Int) : Int.sign (-z) = -Int.sign z := by
match z with | 0 | succ _ | -[_+1] => rfl
@@ -1322,8 +1311,6 @@ theorem neg_of_sign_eq_neg_one : ∀ {a : Int}, sign a = -1 → a < 0
exact Int.le_add_one (natCast_nonneg _)
| .negSucc _ => simp +decide [sign]
@[deprecated sign_nonneg_iff (since := "2025-03-11")] abbrev sign_nonneg := @sign_nonneg_iff
@[simp] theorem sign_pos_iff : 0 < sign x 0 < x := by
match x with
| 0
@@ -1406,9 +1393,6 @@ theorem natAbs_add_of_nonpos {a b : Int} (ha : a ≤ 0) (hb : b ≤ 0) :
natAbs_add_of_nonneg (Int.neg_nonneg_of_nonpos ha) (Int.neg_nonneg_of_nonpos hb),
natAbs_neg (-a), natAbs_neg (-b)]
@[deprecated negSucc_eq (since := "2025-03-11")]
theorem negSucc_eq' (m : Nat) : -[m+1] = -m - 1 := by simp only [negSucc_eq, Int.neg_add]; rfl
theorem natAbs_lt_natAbs_of_nonneg_of_lt {a b : Int}
(w₁ : 0 a) (w₂ : a < b) : a.natAbs < b.natAbs :=
match a, b, eq_ofNat_of_zero_le w₁, eq_ofNat_of_zero_le (Int.le_trans w₁ (Int.le_of_lt w₂)) with
@@ -1417,9 +1401,6 @@ theorem natAbs_lt_natAbs_of_nonneg_of_lt {a b : Int}
theorem natAbs_eq_iff_mul_eq_zero : natAbs a = n (a - n) * (a + n) = 0 := by
rw [natAbs_eq_iff, Int.mul_eq_zero, Int.sub_neg, Int.sub_eq_zero, Int.sub_eq_zero]
@[deprecated natAbs_eq_iff_mul_eq_zero (since := "2025-03-11")]
abbrev eq_natAbs_iff_mul_eq_zero := @natAbs_eq_iff_mul_eq_zero
instance instIsLinearOrder : IsLinearOrder Int := by
apply IsLinearOrder.of_le
case le_antisymm => constructor; apply Int.le_antisymm

View File

@@ -6,7 +6,6 @@ Authors: Jeremy Avigad, Deniz Aydin, Floris van Doorn, Mario Carneiro
module
prelude
public import Init.Data.Int.Lemmas
public import Init.Data.Nat.Lemmas
public section
@@ -50,10 +49,6 @@ protected theorem pow_ne_zero {n : Int} {m : Nat} : n ≠ 0 → n ^ m ≠ 0 := b
instance {n : Int} {m : Nat} [NeZero n] : NeZero (n ^ m) := Int.pow_ne_zero (NeZero.ne _)
-- This can't be removed until the next update-stage0
@[deprecated Nat.pow_pos (since := "2025-02-17")]
abbrev _root_.Nat.pos_pow_of_pos := @Nat.pow_pos
@[simp, norm_cast]
protected theorem natCast_pow (b n : Nat) : ((b^n : Nat) : Int) = (b : Int) ^ n := by
match n with

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