26 lines
No EOL
688 B
Text
26 lines
No EOL
688 B
Text
universes u v w
|
||
|
||
structure equiv (α : Type u) (β : Type v) :=
|
||
(f : α → β) (g : β → α)
|
||
|
||
infix ` ≃ `:50 := equiv
|
||
|
||
variables {α : Type u} {β : Type v} {γ : Type w}
|
||
|
||
instance: has_coe_to_fun (α ≃ β) := {
|
||
F := λ _, α → β,
|
||
coe := equiv.f,
|
||
}
|
||
|
||
@[symm] def equiv.inv : α ≃ β → β ≃ α
|
||
| ⟨f,g⟩ := ⟨g,f⟩
|
||
|
||
local postfix `⁻¹` := equiv.inv
|
||
|
||
-- coe_fn should be applied at function arguments
|
||
def equiv.trans (f : α ≃ β) (g : β ≃ γ) : α ≃ γ :=
|
||
⟨g ∘ f, f⁻¹ ∘ g⁻¹⟩
|
||
|
||
example (f : α ≃ β) := function.bijective f
|
||
example (f : α ≃ β) (a : α) := f a
|
||
example (f : (α ≃ β) ≃ (β ≃ α)) (g : α ≃ β) (b : β) := f g b |