∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Norm E] [inst_1 : Norm F] {l : Filter α} {f₁ f₂ : α → E}
  {g₁ g₂ : α → F}, f₁ =O[l] g₁ → (∀ (x : α), f₁ x = f₂ x) → (∀ (x : α), g₁ x = g₂ x) → f₂ =O[l] g₂