∀ {α : Type u_4} [inst : TopologicalSpace α] (carrier : Set α) (isIrreducible' : IsIrreducible carrier)
  (isClosed' : IsClosed carrier) (carrier_1 : Set α) (isIrreducible'_1 : IsIrreducible carrier_1)
  (isClosed'_1 : IsClosed carrier_1),
  ({ carrier := carrier, isIrreducible' := isIrreducible', isClosed' := isClosed' } =
      { carrier := carrier_1, isIrreducible' := isIrreducible'_1, isClosed' := isClosed'_1 }) =
    (carrier = carrier_1)