have lim_u_φ' : seq_limit (u ∘ φ) l := subseq_tendsto_of_tendsto' hl φ_extr
case intro.intro
u : ℕ → ℝ
l a : ℝ
hl : seq_limit u l
φ : ℕ → ℕ
φ_extr : extraction φ
lim_u_φ : seq_limit (u ∘ φ) a
⊢ a = l
case intro.intro
u : ℕ → ℝ
l a : ℝ
hl : seq_limit u l
φ : ℕ → ℕ
φ_extr : extraction φ
lim_u_φ : seq_limit (u ∘ φ) a
lim_u_φ' : seq_limit (u ∘ φ) l
⊢ a = l