theorem extracted_formal_statement_433 (C : ℝ) : C * 0 = 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)
C : ℝ
this : Tendsto (fun n => ‖(OptProblem.A₁ E₂) (e₁ n)‖) atTop (𝓝 0)
⊢ C * 0 = 0

Tactic: simp only [mul_zero]

State after:

Relevant lemmas:
MulZeroClass.mul_zero : ∀ {M₀ : Type u} [self : MulZeroClass M₀] (a : M₀), a * 0 = 0