∀ {α : Type u_2} {α' : Type u_3} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace α']
  [inst_2 : One β] {f : α → β},
  HasCompactMulSupport f → ∀ {g : α' → α}, Topology.IsClosedEmbedding g → HasCompactMulSupport (f ∘ g)