∀ {X : Type u_1} {ι : Type u_2} {A : Set X} {U : ι → Set X} {V : ι → ι → Set X}
  (c : CompleteLattice.MulticoequalizerDiagram A U V)
  (motive :
    ((c.multispanIndex.map Set.functorToTypes).multispan.coconeTypesEquiv.symm
          (c.multicofork.map Set.functorToTypes)).pt →
      Prop)
  (x :
    ((c.multispanIndex.map Set.functorToTypes).multispan.coconeTypesEquiv.symm
        (c.multicofork.map Set.functorToTypes)).pt),
  (∀ (x : X) (hx : x ∈ c.multicofork.pt), motive ⟨x, hx⟩) → motive x