∀ {H : Type u_1} [inst : TopologicalSpace H] (PG : Pregroupoid H) (e : OpenPartialHomeomorph H H),
  (∀ x ∈ e.source,
      ∃ s, IsOpen s ∧ x ∈ s ∧ e.restr s ∈ {e | PG.property (↑e) e.source ∧ PG.property (↑e.symm) e.target}) →
    e ∈ {e | PG.property (↑e) e.source ∧ PG.property (↑e.symm) e.target}