theorem extracted_formal_statement_318.{u_3, u_2, u_1} {E₁ : Type u_1} {E₂ : Type u_2} {F : Type u_3}
  [inst : NormedAddCommGroup E₁] [inst_1 : InnerProductSpace ℝ E₁] [inst_2 : FiniteDimensional ℝ E₁]
  [inst_3 : NormedAddCommGroup E₂] [inst_4 : InnerProductSpace ℝ E₂] [inst_5 : FiniteDimensional ℝ E₂]
  [inst_6 : NormedAddCommGroup F] [inst_7 : InnerProductSpace ℝ F] [inst_8 : 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)) : Continuous ⇑(OptProblem.A₁ E₂) := sorry

State before:
case hf
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_kkt
⊢ Continuous ⇑(OptProblem.A₁ E₂)

Tactic: apply ContinuousLinearMap.continuous

State after:

Relevant lemmas:
ContinuousLinearMap.continuous : ∀ {R₁ : Type u_1} {R₂ : Type u_2} [inst : Semiring R₁] [inst_9 : Semiring R₂]
  {σ₁₂ : R₁ →+* R₂} {M₁ : Type u_4} [inst_10 : TopologicalSpace M₁] [inst_11 : AddCommMonoid M₁] {M₂ : Type u_6}
  [inst_12 : TopologicalSpace M₂] [inst_13 : AddCommMonoid M₂] [inst_14 : Module R₁ M₁] [inst_15 : Module R₂ M₂]
  (f : M₁ →SL[σ₁₂] M₂), Continuous ⇑f