theorem extracted_formal_statement_56 : 2 ≠ 0 := sorry

State before:
E₁ : Type u_1
E₂ : Type u_2
F : Type u_3
inst✝⁹ : NormedAddCommGroup E₁
inst✝⁸ : InnerProductSpace ℝ E₁
inst✝⁷ : FiniteDimensional ℝ E₁
inst✝⁶ : NormedAddCommGroup E₂
inst✝⁵ : InnerProductSpace ℝ E₂
inst✝⁴ : FiniteDimensional ℝ E₂
inst✝³ : NormedAddCommGroup F
inst✝² : InnerProductSpace ℝ F
inst✝¹ : FiniteDimensional ℝ F
admm : ADMM E₁ E₂ F
admm_kkt : Existance_of_kkt admm
fullrank₁ : Function.Injective ⇑(OptProblem.A₁ E₂)
fullrank₂ : Function.Injective ⇑(OptProblem.A₂ E₁)
inst✝ : Setting E₁ E₂ F admm (admm_kkt₁ fullrank₁ fullrank₂)
⊢ Tendsto (fun n => ‖ey (φ n)‖ ^ 2) atTop (𝓝 0)

Tactic: rw [← zero_pow]
    apply Filter.Tendsto.pow
    apply nrm_ey_subseq_converge_zero

State after:
[E₁ : Type u_1
 E₂ : Type u_2
 F : Type u_3
 inst✝⁹ : NormedAddCommGroup E₁
 inst✝⁸ : InnerProductSpace ℝ E₁
 inst✝⁷ : FiniteDimensional ℝ E₁
 inst✝⁶ : NormedAddCommGroup E₂
 inst✝⁵ : InnerProductSpace ℝ E₂
 inst✝⁴ : FiniteDimensional ℝ E₂
 inst✝³ : NormedAddCommGroup F
 inst✝² : InnerProductSpace ℝ F
 inst✝¹ : FiniteDimensional ℝ F
 admm : ADMM E₁ E₂ F
 admm_kkt : Existance_of_kkt admm
 fullrank₁ : Function.Injective ⇑(OptProblem.A₁ E₂)
 fullrank₂ : Function.Injective ⇑(OptProblem.A₂ E₁)
 inst✝ : Setting E₁ E₂ F admm (admm_kkt₁ fullrank₁ fullrank₂)
 ⊢ 2 ≠ 0]

Relevant lemmas:
zero_pow : ∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] {n : ℕ}, n ≠ 0 → 0 ^ n = 0
Filter.Tendsto.pow : ∀ {α : Type u_2} {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : Monoid M]
  [inst_2 : ContinuousMul M] {l : Filter α} {f : α → M} {x : M},
  Tendsto f l (𝓝 x) → ∀ (n : ℕ), Tendsto (fun x => f x ^ n) l (𝓝 (x ^ n))