theorem extracted_formal_statement_51 : StrictMono fun x => x := 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_kkt
⊢ Tendsto (fun n => (OptProblem.A₁ E₂) (ADMM.x₁ E₂ F (φ n))) atTop (𝓝 ((OptProblem.A₁ E₂) x₁''))

Tactic: apply tendsto_iff_seq_tendsto.1 (Satisfying_equational_constraint1' fullrank₁ fullrank₂) (x₁ ∘ φ)
    apply tendsto_iff_seq_tendsto.1 (x₁_subseq_converge fullrank₁ fullrank₂)
    apply StrictMono.tendsto_atTop

State after:
[case a.h
 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
 ⊢ StrictMono fun x => x]

Relevant lemmas:
Filter.tendsto_iff_seq_tendsto : ∀ {α : Type u_1} {β : Type u_2} {f : α → β} {k : Filter α} {l : Filter β}
  [inst : k.IsCountablyGenerated], Tendsto f k l ↔ ∀ (x : ℕ → α), Tendsto x atTop k → Tendsto (f ∘ x) atTop l
StrictMono.tendsto_atTop : ∀ {φ : ℕ → ℕ}, StrictMono φ → Tendsto φ atTop atTop