∀ {X : Type u} [inst : TopologicalSpace X],
  (∀ (s : Set X),
      (∀ (K : Type u) [inst_1 : TopologicalSpace K] [CompactSpace K] (f : K → X), Continuous f → IsOpen (f ⁻¹' s)) →
        IsOpen s) →
    CompactlyCoherentSpace X