chore: update domain

This commit is contained in:
Sebastian Ullrich 2023-09-20 18:28:05 +02:00 committed by Leonardo de Moura
parent 4114ffa273
commit dc60150b5a
19 changed files with 46 additions and 46 deletions

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@ -54,8 +54,8 @@ We don't want to waste your time by you implementing a feature and then us not b
## How to Contribute
* Always follow the [commit convention](https://leanprover.github.io/lean4/doc/dev/commit_convention.html).
* Always follow the [commit convention](https://lean-lang.org/lean4/doc/dev/commit_convention.html).
* Follow the style of the surrounding code. When in doubt, look at other files using the particular syntax as well.
* Make sure your code is documented.
* New features or bug fixes should come with appropriate tests.
* Ensure all tests work before submitting a PR; see [Development Setup](https://leanprover.github.io/lean4/doc/make/index.html#development-setup) and [Fixing Tests](https://leanprover.github.io/lean4/doc/dev/fixing_tests.html).
* Ensure all tests work before submitting a PR; see [Development Setup](https://lean-lang.org/lean4/doc/make/index.html#development-setup) and [Fixing Tests](https://lean-lang.org/lean4/doc/dev/fixing_tests.html).

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@ -8,18 +8,18 @@ and have just begun regular [stable point releases](https://github.com/leanprove
- [Quickstart](https://github.com/leanprover/lean4/blob/master/doc/quickstart.md)
- [Walkthrough installation video](https://www.youtube.com/watch?v=yZo6k48L0VY)
- [Quick tour video](https://youtu.be/zyXtbb_eYbY)
- [Homepage](https://leanprover.github.io)
- [Theorem Proving Tutorial](https://leanprover.github.io/theorem_proving_in_lean4/)
- [Functional Programming in Lean](https://leanprover.github.io/functional_programming_in_lean/)
- [Manual](https://leanprover.github.io/lean4/doc/)
- [Homepage](https://lean-lang.org)
- [Theorem Proving Tutorial](https://lean-lang.org/theorem_proving_in_lean4/)
- [Functional Programming in Lean](https://lean-lang.org/functional_programming_in_lean/)
- [Manual](https://lean-lang.org/lean4/doc/)
- [Release notes](RELEASES.md) starting at v4.0.0-m3
- [Examples](https://leanprover.github.io/lean4/doc/examples.html)
- [Examples](https://lean-lang.org/lean4/doc/examples.html)
- [External Contribution Guidelines](https://github.com/leanprover/lean4/blob/master/doc/contributions.md)
- [FAQ](https://leanprover.github.io/lean4/doc/faq.html)
- [FAQ](https://lean-lang.org/lean4/doc/faq.html)
# Installation
See [Setting Up Lean](https://leanprover.github.io/lean4/doc/setup.html).
See [Setting Up Lean](https://lean-lang.org/lean4/doc/setup.html).
# Contributing
@ -27,4 +27,4 @@ Please read our [Contribution Guidelines](CONTRIBUTING.md) first.
# Building from Source
See [Building Lean](https://leanprover.github.io/lean4/doc/make/index.html).
See [Building Lean](https://lean-lang.org/lean4/doc/make/index.html).

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@ -11,4 +11,4 @@ the following command executes a simple set of examples
% bin/lean examples/ex.lean
For more information on Lean and supported editors, please see https://leanprover.github.io/documentation/.
For more information on Lean and supported editors, please see https://lean-lang.org/documentation/.

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@ -1,6 +1,6 @@
# Documentation
The Lean `doc` folder contains the [Lean Manual](https://leanprover.github.io/lean4/doc/) and is
The Lean `doc` folder contains the [Lean Manual](https://lean-lang.org/lean4/doc/) and is
authored in a combination of markdown (`*.md`) files and literate Lean files. The .lean files are
preprocessed using a tool called [LeanInk](https://github.com/leanprover/leanink) and
[Alectryon](https://github.com/Kha/alectryon) which produces a generated markdown file. We then run
@ -83,7 +83,7 @@ Then run the following:
```
This will put the HTML in a `out` folder so you can load `out/index.html` in your web browser and
it should look like https://leanprover.github.io/lean4/doc/.
it should look like https://lean-lang.org/lean4/doc/.
1. It is also handy to use e.g. [`mdbook watch`](https://rust-lang.github.io/mdBook/cli/watch.html)
in the `doc/` folder so that it keeps the html up to date while you are editing.

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@ -27,7 +27,7 @@ It is a good place to interact with other Lean users.
### Should I use Lean to teach a course?
Lean has been used to teach courses on logic, type theory and programming languages at CMU and the University of Washington.
The lecture notes for the CMU course [Logic and Proof](https://leanprover.github.io/logic_and_proof) are available online,
The lecture notes for the CMU course [Logic and Proof](https://lean-lang.org/logic_and_proof) are available online,
but they are for Lean 3.
If you decide to teach a course using Lean, we suggest you prepare all material before the beginning of the course, and
make sure that Lean attends all your needs. You should not expect we will fix bugs and/or add features needed for your course.

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@ -1,7 +1,7 @@
Functional Programming in Lean
=======================
The goal of [this book](https://leanprover.github.io/functional_programming_in_lean/) is to be an accessible introduction to using Lean 4 as a programming language.
The goal of [this book](https://lean-lang.org/functional_programming_in_lean/) is to be an accessible introduction to using Lean 4 as a programming language.
It should be useful both to people who want to use Lean as a general-purpose programming language and to mathematicians who want to develop larger-scale proof automation but do not have a background in functional programming.
It does not assume any background with functional programming, though it's probably not a good first book on programming in general.
New content will be added once per month until it's done.

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@ -1,3 +1,3 @@
# Inductive Types
[Theorem Proving in Lean](https://leanprover.github.io/theorem_proving_in_lean4/inductive_types.html) has a chapter about inductive datatypes.
[Theorem Proving in Lean](https://lean-lang.org/theorem_proving_in_lean4/inductive_types.html) has a chapter about inductive datatypes.

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@ -4,7 +4,7 @@ Semantic Highlighting
The Lean language server provides semantic highlighting information to editors. In order to benefit from this in VSCode, you may need to activate the "Editor > Semantic Highlighting" option in the preferences (this is translates to `"editor.semanticHighlighting.enabled": true,`
in `settings.json`). The default option here is to let your color theme decides whether it activates semantic highlighting (the default themes Dark+ and Light+ do activate it for instance).
However this may be insufficient if your color theme does not distinguish enough syntax categories or distinguishes them very subtly. For instance the default Light+ theme uses color `#001080` for variables. This is awfully close to `#000000` that is used as the default text color. This makes it very easy to miss an accidental use of [auto bound implicit arguments](https://leanprover.github.io/lean4/doc/autobound.html). For instance in
However this may be insufficient if your color theme does not distinguish enough syntax categories or distinguishes them very subtly. For instance the default Light+ theme uses color `#001080` for variables. This is awfully close to `#000000` that is used as the default text color. This makes it very easy to miss an accidental use of [auto bound implicit arguments](https://lean-lang.org/lean4/doc/autobound.html). For instance in
```lean
def my_id (n : nat) := n
```

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@ -1,5 +1,5 @@
Theorem Proving in Lean
=======================
We strongly encourage you to read the book [Theorem Proving in Lean](https://leanprover.github.io/theorem_proving_in_lean4/title_page.html).
We strongly encourage you to read the book [Theorem Proving in Lean](https://lean-lang.org/theorem_proving_in_lean4/title_page.html).
Many Lean users consider it to be the Lean Bible.

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@ -36,7 +36,7 @@ Lean has numerous features, including:
- [Monads](./monads/intro.md)
- [Extensible syntax](./syntax.md)
- Hygienic macros
- [Dependent types](https://leanprover.github.io/theorem_proving_in_lean4/dependent_type_theory.html)
- [Dependent types](https://lean-lang.org/theorem_proving_in_lean4/dependent_type_theory.html)
- [Metaprogramming](./metaprogramming.md)
- Multithreading
- Verification: you can prove properties of your functions using Lean itself

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@ -292,7 +292,7 @@ macro_rules
`conv => ...` allows the user to perform targeted rewriting on a goal or hypothesis,
by focusing on particular subexpressions.
See <https://leanprover.github.io/theorem_proving_in_lean4/conv.html> for more details.
See <https://lean-lang.org/theorem_proving_in_lean4/conv.html> for more details.
Basic forms:
* `conv => cs` will rewrite the goal with conv tactics `cs`.

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@ -127,7 +127,7 @@ calc abc
See [Theorem Proving in Lean 4][tpil4] for more information.
[tpil4]: https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#calculational-proofs
[tpil4]: https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#calculational-proofs
-/
syntax (name := calc) "calc" calcSteps : term
@ -166,7 +166,7 @@ leave a subgoal proving `z = z'`.
See [Theorem Proving in Lean 4][tpil4] for more information.
[tpil4]: https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#calculational-proofs
[tpil4]: https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#calculational-proofs
-/
syntax (name := calcTactic) "calc" calcSteps : tactic

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@ -104,7 +104,7 @@ set_option bootstrap.inductiveCheckResultingUniverse false in
The unit type, the canonical type with one element, named `unit` or `()`.
This is the universe-polymorphic version of `Unit`; it is preferred to use
`Unit` instead where applicable.
For more information about universe levels: [Types as objects](https://leanprover.github.io/theorem_proving_in_lean4/dependent_type_theory.html#types-as-objects)
For more information about universe levels: [Types as objects](https://lean-lang.org/theorem_proving_in_lean4/dependent_type_theory.html#types-as-objects)
-/
inductive PUnit : Sort u where
/-- `PUnit.unit : PUnit` is the canonical element of the unit type. -/
@ -171,7 +171,7 @@ unsafe axiom lcUnreachable {α : Sort u} : α
/--
`True` is a proposition and has only an introduction rule, `True.intro : True`.
In other words, `True` is simply true, and has a canonical proof, `True.intro`
For more information: [Propositional Logic](https://leanprover.github.io/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)
For more information: [Propositional Logic](https://lean-lang.org/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)
-/
inductive True : Prop where
/-- `True` is true, and `True.intro` (or more commonly, `trivial`)
@ -184,7 +184,7 @@ It represents a contradiction. `False` elimination rule, `False.rec`,
expresses the fact that anything follows from a contradiction.
This rule is sometimes called ex falso (short for ex falso sequitur quodlibet),
or the principle of explosion.
For more information: [Propositional Logic](https://leanprover.github.io/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)
For more information: [Propositional Logic](https://lean-lang.org/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)
-/
inductive False : Prop
@ -206,7 +206,7 @@ inductive PEmpty : Sort u where
so if your goal is `¬p` you can use `intro h` to turn the goal into
`h : p ⊢ False`, and if you have `hn : ¬p` and `h : p` then `hn h : False`
and `(hn h).elim` will prove anything.
For more information: [Propositional Logic](https://leanprover.github.io/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)
For more information: [Propositional Logic](https://lean-lang.org/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)
-/
def Not (a : Prop) : Prop := a → False
@ -228,7 +228,7 @@ Anything follows from two contradictory hypotheses. Example:
```
example (hp : p) (hnp : ¬p) : q := absurd hp hnp
```
For more information: [Propositional Logic](https://leanprover.github.io/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)
For more information: [Propositional Logic](https://lean-lang.org/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)
-/
@[macro_inline] def absurd {a : Prop} {b : Sort v} (h₁ : a) (h₂ : Not a) : b :=
(h₂ h₁).rec
@ -258,7 +258,7 @@ example (α : Type) (a b : α) (p : α → Prop)
h1 ▸ h2
```
The triangle in the second presentation is a macro built on top of `Eq.subst` and `Eq.symm`, and you can enter it by typing `\t`.
For more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
For more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
-/
inductive Eq : αα → Prop where
/-- `Eq.refl a : a = a` is reflexivity, the unique constructor of the
@ -294,7 +294,7 @@ essentially a fancy algorithm for finding good `motive` arguments to usefully
apply this theorem to replace occurrences of `a` with `b` in the goal or
hypotheses.
For more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
For more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
-/
theorem Eq.subst {α : Sort u} {motive : α → Prop} {a b : α} (h₁ : Eq a b) (h₂ : motive a) : motive b :=
Eq.ndrec h₂ h₁
@ -305,7 +305,7 @@ Equality is symmetric: if `a = b` then `b = a`.
Because this is in the `Eq` namespace, if you have a variable `h : a = b`,
`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.
For more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
For more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
-/
theorem Eq.symm {α : Sort u} {a b : α} (h : Eq a b) : Eq b a :=
h ▸ rfl
@ -317,7 +317,7 @@ Because this is in the `Eq` namespace, if you have variables or expressions
`h₁ : a = b` and `h₂ : b = c`, you can use `h₁.trans h₂ : a = c` as shorthand
for `Eq.trans h₁ h₂`.
For more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
For more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
-/
theorem Eq.trans {α : Sort u} {a b c : α} (h₁ : Eq a b) (h₂ : Eq b c) : Eq a c :=
h₂ ▸ h₁
@ -331,7 +331,7 @@ It is best to avoid this function if you can, because it is more complicated
to reason about terms containing casts, but if the types don't match up
definitionally sometimes there isn't anything better you can do.
For more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
For more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
-/
@[macro_inline] def cast {α β : Sort u} (h : Eq α β) (a : α) : β :=
h.rec a
@ -344,7 +344,7 @@ you can also use a lambda expression for `f` to prove that
internally by tactics like `congr` and `simp` to apply equalities inside
subterms.
For more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
For more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
-/
theorem congrArg {α : Sort u} {β : Sort v} {a₁ a₂ : α} (f : α → β) (h : Eq a₁ a₂) : Eq (f a₁) (f a₂) :=
h ▸ rfl
@ -354,7 +354,7 @@ Congruence in both function and argument. If `f₁ = f₂` and `a₁ = a₂` the
`f₁ a₁ = f₂ a₂`. This only works for nondependent functions; the theorem
statement is more complex in the dependent case.
For more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
For more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)
-/
theorem congr {α : Sort u} {β : Sort v} {f₁ f₂ : α → β} {a₁ a₂ : α} (h₁ : Eq f₁ f₂) (h₂ : Eq a₁ a₂) : Eq (f₁ a₁) (f₂ a₂) :=
h₁ ▸ h₂ ▸ rfl
@ -461,7 +461,7 @@ as notation for `Prod.mk a b`. Moreover, `(a, b, c)` is notation for
`Prod.mk a (Prod.mk b c)`.
Given `p : Prod α β`, `p.1 : α` and `p.2 : β`. They are short for `Prod.fst p`
and `Prod.snd p` respectively. You can also write `p.fst` and `p.snd`.
For more information: [Constructors with Arguments](https://leanprover.github.io/theorem_proving_in_lean4/inductive_types.html?highlight=Prod#constructors-with-arguments)
For more information: [Constructors with Arguments](https://lean-lang.org/theorem_proving_in_lean4/inductive_types.html?highlight=Prod#constructors-with-arguments)
-/
structure Prod (α : Type u) (β : Type v) where
/-- The first projection out of a pair. if `p : α × β` then `p.1 : α`. -/
@ -2744,7 +2744,7 @@ Like many functional programming languages, Lean makes extensive use of monads
for structuring programs. In particular, the `do` notation is a very powerful
syntax over monad operations, and it depends on a `Monad` instance.
See [the `do` notation](https://leanprover.github.io/lean4/doc/do.html)
See [the `do` notation](https://lean-lang.org/lean4/doc/do.html)
chapter of the manual for details.
-/
class Monad (m : Type u → Type v) extends Applicative m, Bind m : Type (max (u+1) v) where

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@ -60,7 +60,7 @@ def bar ⦃x : Nat⦄ : Nat := x
#check bar -- bar : ⦃x : Nat⦄ → Nat
```
See also the Lean manual: https://leanprover.github.io/lean4/doc/expressions.html#implicit-arguments
See also the Lean manual: https://lean-lang.org/lean4/doc/expressions.html#implicit-arguments
-/
inductive BinderInfo where
/-- Default binder annotation, e.g. `(x : α)` -/

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@ -166,7 +166,7 @@ inductive List (α : Type u) where
```
A list of elements of type `α` is either the empty list, `nil`,
or an element `head : α` followed by a list `tail : List α`.
For more information about [inductive types](https://leanprover.github.io/theorem_proving_in_lean4/inductive_types.html).
For more information about [inductive types](https://lean-lang.org/theorem_proving_in_lean4/inductive_types.html).
-/
def «inductive» := leading_parser
"inductive " >> declId >> ppIndent optDeclSig >> optional (symbol " :=" <|> " where") >>

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@ -38,7 +38,7 @@ example (n : Nat) : n = n := by
| i+1 => simp
```
[tpil4]: https://leanprover.github.io/theorem_proving_in_lean4/induction_and_recursion.html
[tpil4]: https://lean-lang.org/theorem_proving_in_lean4/induction_and_recursion.html
-/
@[builtin_tactic_parser] def «match» := leading_parser:leadPrec
"match " >> optional Term.generalizingParam >>

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@ -3,7 +3,7 @@
namespace lean {
options get_default_options() {
options opts;
// see https://leanprover.github.io/lean4/doc/dev/bootstrap.html#further-bootstrapping-complications
// see https://lean-lang.org/lean4/doc/dev/bootstrap.html#further-bootstrapping-complications
#if LEAN_IS_STAGE0 == 1
// switch to `true` for ABI-breaking changes affecting meta code
opts = opts.update({"interpreter", "prefer_native"}, false);

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@ -3,7 +3,7 @@
namespace lean {
options get_default_options() {
options opts;
// see https://leanprover.github.io/lean4/doc/dev/bootstrap.html#further-bootstrapping-complications
// see https://lean-lang.org/lean4/doc/dev/bootstrap.html#further-bootstrapping-complications
#if LEAN_IS_STAGE0 == 1
// switch to `true` for ABI-breaking changes affecting meta code
opts = opts.update({"interpreter", "prefer_native"}, false);

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@ -4,7 +4,7 @@
{"start": {"line": 0, "character": 54}, "end": {"line": 0, "character": 58}},
"contents":
{"value":
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"kind": "markdown"}}
{"textDocument": {"uri": "file://lean3HoverIssue.lean"},
"position": {"line": 0, "character": 52}}
@ -17,7 +17,7 @@
{"start": {"line": 4, "character": 45}, "end": {"line": 4, "character": 49}},
"contents":
{"value":
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"kind": "markdown"}}
{"textDocument": {"uri": "file://lean3HoverIssue.lean"},
"position": {"line": 7, "character": 54}}
@ -25,7 +25,7 @@
{"start": {"line": 7, "character": 53}, "end": {"line": 7, "character": 60}},
"contents":
{"value":
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"kind": "markdown"}}
{"textDocument": {"uri": "file://lean3HoverIssue.lean"},
"position": {"line": 7, "character": 65}}
@ -33,7 +33,7 @@
{"start": {"line": 7, "character": 62}, "end": {"line": 7, "character": 69}},
"contents":
{"value":
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"kind": "markdown"}}
{"textDocument": {"uri": "file://lean3HoverIssue.lean"},
"position": {"line": 7, "character": 70}}
@ -46,5 +46,5 @@
{"start": {"line": 7, "character": 72}, "end": {"line": 7, "character": 76}},
"contents":
{"value":
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://leanprover.github.io/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"```lean\nEq.symm.{u} {α : Sort u} {a b : α} (h : a = b) : b = a\n```\n***\nEquality is symmetric: if `a = b` then `b = a`.\n\nBecause this is in the `Eq` namespace, if you have a variable `h : a = b`,\n`h.symm` can be used as shorthand for `Eq.symm h` as a proof of `b = a`.\n\nFor more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n***\n*import Init.Prelude*",
"kind": "markdown"}}