case a.h
α : Type u_1
ι : Sort ?u.6048
κ : ι → Sort ?u.6053
inst✝¹ inst✝ : PartialOrder α
c✝ c : ClosureOperator α
x✝ : α
⊢ ↑c.toOrderHom x✝ =
    ↑(mk₃ (↑c.toOrderHom) (closed c) (_ : ∀ (x : α), x ≤ ↑c.toOrderHom x) (_ : ∀ (x : α), ↑c.toOrderHom x ∈ closed c)
            (_ : ∀ (x y : α), x ≤ y → closed c y → ↑c.toOrderHom x ≤ y)).toOrderHom
      x✝
α : Type u_1
ι : Sort ?u.6048
κ : ι → Sort ?u.6053
inst✝¹ inst✝ : PartialOrder α
c✝ c : ClosureOperator α
⊢ c =
    mk₃ (↑c.toOrderHom) (closed c) (_ : ∀ (x : α), x ≤ ↑c.toOrderHom x) (_ : ∀ (x : α), ↑c.toOrderHom x ∈ closed c)
      (_ : ∀ (x y : α), x ≤ y → closed c y → ↑c.toOrderHom x ≤ y)
ext
no goals
case a.h
α : Type u_1
ι : Sort ?u.6048
κ : ι → Sort ?u.6053
inst✝¹ inst✝ : PartialOrder α
c✝ c : ClosureOperator α
x✝ : α
⊢ ↑c.toOrderHom x✝ =
    ↑(mk₃ (↑c.toOrderHom) (closed c) (_ : ∀ (x : α), x ≤ ↑c.toOrderHom x) (_ : ∀ (x : α), ↑c.toOrderHom x ∈ closed c)
            (_ : ∀ (x y : α), x ≤ y → closed c y → ↑c.toOrderHom x ≤ y)).toOrderHom
      x✝
rfl