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core.​init.​data.​subtype.​basic

core.​init.​data.​subtype.​basic

source
subtype.​eq
subtype.​eta
subtype.​exists_of_subtype
subtype.​inhabited
subtype.​tag_irrelevant
source
def subtype.​exists_of_subtype {α : Type u} {p : α → Prop} :
{x // p x} → (∃ (x : α), p x)

Equations
  • _ = _
source
theorem subtype.​tag_irrelevant {α : Type u} {p : α → Prop} {a : α} (h1 h2 : p a) :
⟨a, h1⟩ = ⟨a, h2⟩

source
theorem subtype.​eq {α : Type u} {p : α → Prop} {a1 a2 : {x // p x}} :
a1.val = a2.val → a1 = a2

source
@[simp]
theorem subtype.​eta {α : Type u} {p : α → Prop} (a : {x // p x}) (h : p a.val) :
⟨a.val, h⟩ = a

source
@[instance]
def subtype.​inhabited {α : Type u} {p : α → Prop} {a : α} :
p a → inhabited {x // p x}

Equations

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