mk — Mathlib · SciLib

English

There is a colimit structure on the cocone over diagram U.

Русский

Существует структура колимита на коконе над диаграммой диаграмма(U).

LaTeX

$$$\mathrm{coconeIsColimit}(U) : \mathrm{IsColimit}(\mathrm{cocone}(U)).$$$

Lean4

/-- Constructs a partial function isomorphism between types from an equivalence between them. -/
@[simps]
def mk {α β : PartialFun.{u}} (e : α ≃ β) : α ≅ β where
  hom x := e x
  inv x := e.symm x
  hom_inv_id :=
    (PFun.coe_comp _ _).symm.trans
      (by
        simp only [Equiv.symm_comp_self, PFun.coe_id]
        rfl)
  inv_hom_id :=
    (PFun.coe_comp _ _).symm.trans
      (by
        simp only [Equiv.self_comp_symm, PFun.coe_id]
        rfl)

Похожие утверждения