α : Type u_1
β : Type u_2
inst✝ : NormedField β
t u v w : α → β
l : Filter α
hz : ∀ᶠ (x : α) in l, v x = 0 → u x = 0
huv : Tendsto (u / v) l (𝓝 1)
⊢ ∃ φ x, u =ᶠ[l] φ * v
α : Type u_1
β : Type u_2
inst✝ : NormedField β
t u v w : α → β
l : Filter α
hz : ∀ᶠ (x : α) in l, v x = 0 → u x = 0
huv : Tendsto (u / v) l (𝓝 1)
⊢ u ~[l] v
rw [isEquivalent_iff_exists_eq_mul]
no goals
α : Type u_1
β : Type u_2
inst✝ : NormedField β
t u v w : α → β
l : Filter α
hz : ∀ᶠ (x : α) in l, v x = 0 → u x = 0
huv : Tendsto (u / v) l (𝓝 1)
⊢ ∃ φ x, u =ᶠ[l] φ * v
refine' ⟨u / v, huv, hz.mono fun x hz' ↦ (div_mul_cancel_of_imp hz').symm⟩