Module: Mathlib.Analysis.Calculus.LHopital

Goal state before:
pp: case hff'
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ ∀ᶠ (x : ℝ) in 𝓝[≠] a, HasDerivAt f (f' x) x

pp: case hgg'
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ ∀ᶠ (x : ℝ) in 𝓝[≠] a, HasDerivAt g (g' x) x

pp: case hg'
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ ∀ᶠ (x : ℝ) in 𝓝[≠] a, g' x ≠ 0

pp: case hfa
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ Tendsto f (𝓝[≠] a) (𝓝 0)

pp: case hga
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ Tendsto g (𝓝[≠] a) (𝓝 0)

pp: case hdiv
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ Tendsto (fun x ↦ f' x / g' x) (𝓝[≠] a) l

Tactic:
<;>

Goal state after:
case hff'
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ ∀ᶠ (x : ℝ) in 𝓝[≠] a, HasDerivAt f (f' x) x

case hgg'
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ ∀ᶠ (x : ℝ) in 𝓝[≠] a, HasDerivAt g (g' x) x

case hg'
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ ∀ᶠ (x : ℝ) in 𝓝[≠] a, g' x ≠ 0

case hfa
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ Tendsto f (𝓝[≠] a) (𝓝 0)

case hga
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ Tendsto g (𝓝[≠] a) (𝓝 0)

case hdiv
a : ℝ
l : Filter ℝ
f f' g g' : ℝ → ℝ
hff' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt f (f' x) x
hgg' : ∀ᶠ (x : ℝ) in 𝓝 a, HasDerivAt g (g' x) x
hg' : ∀ᶠ (x : ℝ) in 𝓝 a, g' x ≠ 0
hfa : Tendsto f (𝓝 a) (𝓝 0)
hga : Tendsto g (𝓝 a) (𝓝 0)
hdiv : Tendsto (fun x ↦ f' x / g' x) (𝓝 a) l
⊢ Tendsto (fun x ↦ f' x / g' x) (𝓝[≠] a) l