α : Type u_1
f : Filter α
inst✝ : CountableInterFilter f
u v : α → ℝ≥0∞
⊢ u * v ≤ᶠ[f] fun x => limsup u f * v x
α : Type u_1
f : Filter α
inst✝ : CountableInterFilter f
u v : α → ℝ≥0∞
⊢ limsup (u * v) f ≤ limsup (fun x => limsup u f * v x) f
refine limsup_le_limsup ?_
no goals
α : Type u_1
f : Filter α
inst✝ : CountableInterFilter f
u v : α → ℝ≥0∞
⊢ u * v ≤ᶠ[f] fun x => limsup u f * v x
filter_upwards [@eventually_le_limsup _ f _ u] with x hx using mul_le_mul' hx le_rfl