α : Type u_1
β : Type ?u.73089
γ : Type ?u.73092
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
x y z ε ε₁ ε₂ : ℝ≥0∞
s : Set ℝ≥0∞
f : Filter α
u : α → ℝ≥0∞
a : ℝ≥0∞
h : ∀ (ε : ℝ≥0∞), ε > 0 → ∀ᶠ (x : α) in f, u x ∈ Icc (a - ε) (a + ε)
⊢ Tendsto u f (⨅ (ε : ℝ≥0∞) (_ : ε > 0), 𝓟 (Icc (a - ε) (a + ε)))
α : Type u_1
β : Type ?u.73089
γ : Type ?u.73092
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
x y z ε ε₁ ε₂ : ℝ≥0∞
s : Set ℝ≥0∞
f : Filter α
u : α → ℝ≥0∞
a : ℝ≥0∞
h : ∀ (ε : ℝ≥0∞), ε > 0 → ∀ᶠ (x : α) in f, u x ∈ Icc (a - ε) (a + ε)
⊢ Tendsto u f (𝓝 a)
refine Tendsto.mono_right ?_ (biInf_le_nhds _)
no goals
α : Type u_1
β : Type ?u.73089
γ : Type ?u.73092
a✝ b c d : ℝ≥0∞
r p q : ℝ≥0
x y z ε ε₁ ε₂ : ℝ≥0∞
s : Set ℝ≥0∞
f : Filter α
u : α → ℝ≥0∞
a : ℝ≥0∞
h : ∀ (ε : ℝ≥0∞), ε > 0 → ∀ᶠ (x : α) in f, u x ∈ Icc (a - ε) (a + ε)
⊢ Tendsto u f (⨅ (ε : ℝ≥0∞) (_ : ε > 0), 𝓟 (Icc (a - ε) (a + ε)))
simpa only [tendsto_iInf, tendsto_principal]