mathlib3 documentation

core / init.data.set

def set (α : Type u) :

A set of elements of type α; implemented as a predicate α → Prop.

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Instances for set
def set_of {α : Type u} (p : α Prop) :
set α

The set {x | p x} of elements satisfying the predicate p.

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Instances for set_of
@[protected, instance]
def set.has_mem {α : Type u} :
has_mem α (set α)
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@[simp]
theorem set.mem_set_of_eq {α : Type u} {x : α} {p : α Prop} :
x {y : α | p y} = p x
@[protected, instance]
def set.has_emptyc {α : Type u} :
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def set.univ {α : Type u} :
set α

The set that contains all elements of a type.

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Instances for set.univ
Instances for set.univ
@[protected, instance]
def set.has_insert {α : Type u} :
has_insert α (set α)
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@[protected, instance]
def set.has_singleton {α : Type u} :
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@[protected, instance]
def set.has_sep {α : Type u} :
has_sep α (set α)
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@[protected, instance]