-- File: optlib/Optlib/Algorithm/ADMM/Theroem_converge.lean
Theorem statement:
theorem extracted_formal_statement_96.{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} : 0 < ADMM.τ E₁ E₂ F * ADMM.ρ E₁ E₂ F := sorry

Tactic state before:
E₁ : Type u_1
E₂ : Type u_2
F : Type u_3
inst✝⁸ : NormedAddCommGroup E₁
inst✝⁷ : InnerProductSpace ℝ E₁
inst✝⁶ : FiniteDimensional ℝ E₁
inst✝⁵ : NormedAddCommGroup E₂
inst✝⁴ : InnerProductSpace ℝ E₂
inst✝³ : FiniteDimensional ℝ E₂
inst✝² : NormedAddCommGroup F
inst✝¹ : InnerProductSpace ℝ F
inst✝ : FiniteDimensional ℝ F
admm : ADMM E₁ E₂ F
⊢ 0 < ADMM.τ E₁ E₂ F * ADMM.ρ E₁ E₂ F

Tactic: exact mul_pos tau_pos rho_pos

Tactic state after:

Premises used:
mul_pos : ∀ {α : Type u_3} {a b : α} [inst : MulZeroClass α] [inst_9 : Preorder α] [inst_10 : PosMulStrictMono α],
  0 < a → 0 < b → 0 < a * b