Use the elementwise
attribute to create applied versions of lemmas. #
Usually we would use @[elementwise]
at the point of definition,
however some early parts of the category theory library are imported by Tactic.Elementwise
,
so we need to add the attribute after the fact.
We now add some elementwise
attributes to lemmas that were proved earlier.
@[simp]
theorem
CategoryTheory.Iso.hom_inv_id_apply
{C : Type u}
[CategoryTheory.Category.{v, u} C]
{X : C}
{Y : C}
(self : X ≅ Y)
[inst : CategoryTheory.ConcreteCategory C]
(x : (CategoryTheory.forget C).obj X)
:
self.inv (self.hom x) = x
@[simp]
theorem
CategoryTheory.Iso.inv_hom_id_apply
{C : Type u}
[CategoryTheory.Category.{v, u} C]
{X : C}
{Y : C}
(self : X ≅ Y)
[inst : CategoryTheory.ConcreteCategory C]
(x : (CategoryTheory.forget C).obj Y)
:
self.hom (self.inv x) = x
@[simp]
theorem
CategoryTheory.IsIso.inv_hom_id_apply
{C : Type u}
[CategoryTheory.Category.{v, u} C]
{X : C}
{Y : C}
(f : X ⟶ Y)
[I : CategoryTheory.IsIso f]
[inst : CategoryTheory.ConcreteCategory C]
(x : (CategoryTheory.forget C).obj Y)
:
f ((CategoryTheory.inv f) x) = x
@[simp]
theorem
CategoryTheory.IsIso.hom_inv_id_apply
{C : Type u}
[CategoryTheory.Category.{v, u} C]
{X : C}
{Y : C}
(f : X ⟶ Y)
[I : CategoryTheory.IsIso f]
[inst : CategoryTheory.ConcreteCategory C]
(x : (CategoryTheory.forget C).obj X)
:
(CategoryTheory.inv f) (f x) = x