case nested.mem_get?_iff j _ _ _ _ e h₁ h₂ _ _ =>
  intro c j'
  by_cases hc : c = .rtr <;> try subst hc
  case neg => exact e.mem_iff (.inl hc)
  case pos => 
    by_cases hj : j' = j <;> try subst hj
    case neg => exact e.mem_iff (.inr hj)
    case pos => simp [Partial.mem_iff, h₁, h₂]
α : Type
inst✝ : Reactor α
cpt : Component.Valued
i : ID
v : Value
rtr₂ rtr₁ : α
j : ID
rtr₁✝ rtr₂✝ : α
n₁✝ n₂✝ : Component.type α Component.rtr
e : rtr₁✝ ≃[Component.rtr][j] rtr₂✝
h₁ : rtr₁✝{Component.rtr}{j} = some n₁✝
h₂ : rtr₂✝{Component.rtr}{j} = some n₂✝
a✝ : LawfulMemUpdate cpt i v n₁✝ n₂✝
a_ih✝ : n₁✝ ≈ n₂✝
⊢ ∀ (cpt : Component) (i : ID), i ∈ rtr₁✝{cpt} ↔ i ∈ rtr₂✝{cpt}
no goals