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core.​init.​funext

core.​init.​funext

source
function.​equiv
function.​equiv.​is_equivalence
function.​equiv.​refl
function.​equiv.​symm
function.​equiv.​trans
funext
pi.​subsingleton
source
def function.​equiv {α : Sort u} {β : α → Sort v} :
(Π (x : α), β x) → (Π (x : α), β x) → Prop

Equations
source
theorem function.​equiv.​refl {α : Sort u} {β : α → Sort v} (f : Π (x : α), β x) :
function.equiv f f

source
theorem function.​equiv.​symm {α : Sort u} {β : α → Sort v} {f₁ f₂ : Π (x : α), β x} :
function.equiv f₁ f₂ → function.equiv f₂ f₁

source
theorem function.​equiv.​trans {α : Sort u} {β : α → Sort v} {f₁ f₂ f₃ : Π (x : α), β x} :
function.equiv f₁ f₂ → function.equiv f₂ f₃ → function.equiv f₁ f₃

source
theorem function.​equiv.​is_equivalence (α : Sort u) (β : α → Sort v) :
equivalence function.equiv

source
@[ext]
theorem funext {α : Sort u} {β : α → Sort v} {f₁ f₂ : Π (x : α), β x} :
(∀ (x : α), f₁ x = f₂ x) → f₁ = f₂

source
@[instance]
def pi.​subsingleton {α : Sort u} {β : α → Sort v} [∀ (a : α), subsingleton (β a)] :
subsingleton (Π (a : α), β a)

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