no goals
α : Type ?u.17126
R : Type u_1
inst✝² : NonUnitalNonAssocRing R
inst✝¹ : TopologicalSpace R
inst✝ : TopologicalAddGroup R
hmul : Tendsto (uncurry fun x x_1 => x * x_1) (𝓝 0 ×ˢ 𝓝 0) (𝓝 0)
hmul_left : ∀ (x₀ : R), Tendsto (fun x => x₀ * x) (𝓝 0) (𝓝 0)
hmul_right : ∀ (x₀ : R), Tendsto (fun x => x * x₀) (𝓝 0) (𝓝 0)
⊢ Continuous fun p => p.fst * p.snd
refine continuous_of_continuousAt_zero₂ (AddMonoidHom.mul (R := R)) ?_ ?_ ?_ <;>
  simpa only [ContinuousAt, mul_zero, zero_mul, nhds_prod_eq, AddMonoidHom.mul_apply]