have hs := (nested h₁ s₁ |>.fromEquiv u.equiv).unique (nested h₂ s₂)
α : Type
inst✝ : Hierarchical α
rtr rtr₁ : α
cpt : Component.Valued
i : ID
v : Value
c : Component.Valued
j : ID
h : c ≠ cpt ∨ j ≠ i
rtr₁✝ : α
j₁ : ID
rtr₂✝¹ : Component.type α Component.rtr
h₁ : rtr₁✝{Component.rtr}{j₁} = some rtr₂✝¹
s₁ : StrictMember (Component.val c) j rtr₂✝¹
hi :
  ∀ {rtr₂ : α},
    LawfulMemUpdate cpt i v rtr₂✝¹ rtr₂ → ∀ (s₂ : StrictMember (Component.val c) j rtr₂), object s₁ = object s₂
rtr₂ : α
u : LawfulMemUpdate cpt i v rtr₁✝ rtr₂
j₂ : ID
rtr₂✝ : Component.type α Component.rtr
s₂ : StrictMember (Component.val c) j rtr₂✝
h₂ : rtr₂{Component.rtr}{j₂} = some rtr₂✝
⊢ j₁ = j₂
α : Type
inst✝ : Hierarchical α
rtr rtr₁ : α
cpt : Component.Valued
i : ID
v : Value
c : Component.Valued
j : ID
h : c ≠ cpt ∨ j ≠ i
rtr₁✝ : α
j₁ : ID
rtr₂✝¹ : Component.type α Component.rtr
h₁ : rtr₁✝{Component.rtr}{j₁} = some rtr₂✝¹
s₁ : StrictMember (Component.val c) j rtr₂✝¹
hi :
  ∀ {rtr₂ : α},
    LawfulMemUpdate cpt i v rtr₂✝¹ rtr₂ → ∀ (s₂ : StrictMember (Component.val c) j rtr₂), object s₁ = object s₂
rtr₂ : α
u : LawfulMemUpdate cpt i v rtr₁✝ rtr₂
j₂ : ID
rtr₂✝ : Component.type α Component.rtr
s₂ : StrictMember (Component.val c) j rtr₂✝
h₂ : rtr₂{Component.rtr}{j₂} = some rtr₂✝
hs : fromEquiv ⋯ (nested h₁ s₁) = nested h₂ s₂
⊢ j₁ = j₂