have ho₂ := get?_some_to_obj?_some hc₂
case val
α : Type
inst✝ : Proper α
rtr₁ : α
hi :
  ∀ (n : Component.type α Component.rtr),
    (∃ i, rtr₁{Component.rtr}{i} = some n) →
      ∀ {rtr₂ : α},
        n ≈ rtr₂ →
          (∀ {c : Component.Valued} {i : Component.idType (Component.val c)}
              {o₁ o₂ : Component.type α (Component.val c)},
              n[Component.val c][i] = some o₁ → rtr₂[Component.val c][i] = some o₂ → o₁ = o₂) →
            n = rtr₂
rtr₂ : α
e : rtr₁ ≈ rtr₂
h :
  ∀ {c : Component.Valued} {i : Component.idType (Component.val c)} {o₁ o₂ : Component.type α (Component.val c)},
    rtr₁[Component.val c][i] = some o₁ → rtr₂[Component.val c][i] = some o₂ → o₁ = o₂
i : ID
v✝ : Component.Valued
n₁ : Component.type α (Component.val v✝)
hc₁ : rtr₁{Component.val v✝}{i} = some n₁
n₂ : Component.type α (Component.val v✝)
hc₂ : rtr₂{Component.val v✝}{i} = some n₂
ho₁ :
  rtr₁[Component.val v✝][match Component.val v✝ with
      | Component.rtr => ↑i
      | Component.rcn => i
      | Component.val v => i] =
    some n₁
⊢ n₁ = n₂
case val
α : Type
inst✝ : Proper α
rtr₁ : α
hi :
  ∀ (n : Component.type α Component.rtr),
    (∃ i, rtr₁{Component.rtr}{i} = some n) →
      ∀ {rtr₂ : α},
        n ≈ rtr₂ →
          (∀ {c : Component.Valued} {i : Component.idType (Component.val c)}
              {o₁ o₂ : Component.type α (Component.val c)},
              n[Component.val c][i] = some o₁ → rtr₂[Component.val c][i] = some o₂ → o₁ = o₂) →
            n = rtr₂
rtr₂ : α
e : rtr₁ ≈ rtr₂
h :
  ∀ {c : Component.Valued} {i : Component.idType (Component.val c)} {o₁ o₂ : Component.type α (Component.val c)},
    rtr₁[Component.val c][i] = some o₁ → rtr₂[Component.val c][i] = some o₂ → o₁ = o₂
i : ID
v✝ : Component.Valued
n₁ : Component.type α (Component.val v✝)
hc₁ : rtr₁{Component.val v✝}{i} = some n₁
n₂ : Component.type α (Component.val v✝)
hc₂ : rtr₂{Component.val v✝}{i} = some n₂
ho₁ :
  rtr₁[Component.val v✝][match Component.val v✝ with
      | Component.rtr => ↑i
      | Component.rcn => i
      | Component.val v => i] =
    some n₁
ho₂ :
  rtr₂[Component.val v✝][match Component.val v✝ with
      | Component.rtr => ↑i
      | Component.rcn => i
      | Component.val v => i] =
    some n₂
⊢ n₁ = n₂