theorem extracted_formal_statement_62.{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} (h1 : 0 < ADMM.τ E₁ E₂ F) (h2 : ADMM.τ E₁ E₂ F ≤ 1) :
  1 ⊓ (1 + 1 / ADMM.τ E₁ E₂ F - ADMM.τ E₁ E₂ F) = 1 := sorry

State before:
case intro
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
inst✝ : Setting E₁ E₂ F admm admm_kkt
h1 : 0 < ADMM.τ E₁ E₂ F
h2 : ADMM.τ E₁ E₂ F ≤ 1
⊢ 1 ⊓ (1 + 1 / ADMM.τ E₁ E₂ F - ADMM.τ E₁ E₂ F) = 1

Tactic: apply min_eq_left
    have h3 : τ ≤ 1 / τ :=
  calc
    _ ≤ 1 := h2
    _ ≤ 1 / τ := by apply one_le_one_div h1 h2
    linarith

State after:

Relevant lemmas:
error