∀ {A : Type u_4} {B : Type u_5} {C : Type u_6} {D : Type u_7} [inst : TopologicalSpace A] [inst_1 : TopologicalSpace B]
  [inst_2 : TopologicalSpace C] [inst_3 : TopologicalSpace D] (f : A → B) (g : C → D) (p : A → C) (q : B → D),
  g ∘ p = q ∘ f →
    Topology.IsInducing f →
      Function.Surjective p →
        IsOpenQuotientMap q → Topology.IsEmbedding g → q ⁻¹' (q '' Set.range f) ⊆ Set.range f → Topology.IsQuotientMap p