∀ {α : Type u_5} {β : Type u_6} {γ : Type u_7} {γ' : Type u_8} {δ : Type u_9} {δ' : Type u_10} {h : β → α} {f : γ → β}
  {f₁ : γ' → α} {f₂ : γ → γ'} {g : δ → β} {g₁ : δ' → α} {g₂ : δ → δ'},
  h ∘ f = f₁ ∘ f₂ →
    h ∘ g = g₁ ∘ g₂ →
      Set.range f ∪ Set.range g = Set.univ → ∀ (s : Set β), h '' s = f₁ '' (f₂ '' (f ⁻¹' s)) ∪ g₁ '' (g₂ '' (g ⁻¹' s))