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[Merged by Bors] - doc: explain extended set notation #8425

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[Merged by Bors] - doc: explain extended set notation #8425

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8 changes: 8 additions & 0 deletions Mathlib/Init/Set.lean
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Expand Up @@ -20,6 +20,7 @@ Given a type `X` and a predicate `p : X → Prop`:
* `Set X` : the type of sets whose elements have type `X`
* `{a : X | p a} : Set X` : the set of all elements of `X` satisfying `p`
* `{a | p a} : Set X` : a more concise notation for `{a : X | p a}`
* `{f x y | (x : X) (y : Y)} : Set Z` : a more concise notation for `{z : Z | ∃ x y, f x y = z}`
* `{a ∈ S | p a} : Set X` : given `S : Set X`, the subset of `S` consisting of
its elements satisfying `p`.

Expand Down Expand Up @@ -84,6 +85,13 @@ def setOf.unexpander : Lean.PrettyPrinter.Unexpander
| _ => throw ()

open Std.ExtendedBinder in
/--
`{ f x y | (x : X) (y : Y) }` is notation for the set of elements `f x y` constructed from the
binders `x` and `y`, equivalent to `{z : Z | ∃ x y, f x y = z}`.

If `f x y` is a single identifier, it must be parenthesized to avoid ambiguity with `{x | p x}`;
for instance, `{(x) | (x : Nat) (y : Nat) (_hxy : x = y^2)}`.
-/
macro (priority := low) "{" t:term " | " bs:extBinders "}" : term =>
`({x | ∃ᵉ $bs:extBinders, $t = x})

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