∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C}
  (f : X ⟶ Y) [inst_2 : CategoryTheory.Limits.HasKernel f] {X' Y' : C} (f' : X' ⟶ Y')
  [inst_3 : CategoryTheory.Limits.HasKernel f'] (p : X ≅ X') (q : Y ≅ Y')
  (w : CategoryTheory.CategoryStruct.comp f q.hom = CategoryTheory.CategoryStruct.comp p.hom f'),
  (CategoryTheory.Limits.kernel.mapIso f f' p q w).hom = CategoryTheory.Limits.kernel.map f f' p.hom q.hom w