∀ {α₁ : Type u_1} {α₂ : Type u_2} {β₁ : Type u_3} {β₂ : Type u_4} {γ₁ : Type u_5} {γ₂ : Type u_6}
  {f₁ f₁' : α₁ → β₁ → Finset γ₁} {f₂ f₂' : α₂ → β₂ → Finset γ₂} {g₁ g₁' : α₁ → β₂ → Finset γ₁}
  {g₂ g₂' : α₁ → β₂ → Finset γ₂},
  (∀ (a : α₁) (b : β₁), f₁ a b ⊆ f₁' a b) →
    (∀ (a : α₂) (b : β₂), f₂ a b ⊆ f₂' a b) →
      (∀ (a : α₁) (b : β₂), g₁ a b ⊆ g₁' a b) →
        (∀ (a : α₁) (b : β₂), g₂ a b ⊆ g₂' a b) →
          ∀ (a : α₁ ⊕ α₂) (b : β₁ ⊕ β₂), Finset.sumLexLift f₁ f₂ g₁ g₂ a b ⊆ Finset.sumLexLift f₁' f₂' g₁' g₂' a b