lean_workbook_plus_44687

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Using the same strategy, we get $T_3=\frac{5}{9}T_4$ and $T_4 = \frac{9}{17}T_5=\frac{9}{17}$ . Working backwards, we get $T_1 = \frac{2}{17}$ and $H = \frac{1}{17}$ . When we start, we have a $\frac{1}{2}$ chance of going to $T_1$ and a $\frac{1}{2}$ chance of going to $H$ , so our final answer is $\frac{1}{2}\cdot\frac{2}{17}+\frac{1}{2}\cdot\frac{1}{17} = \boxed{\frac{3}{34}}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_44687  (t₁ t₂ t₃ t₄ t₅ h : ℝ)
  (h₀ : 0 < t₁ ∧ 0 < t₂ ∧ 0 < t₃ ∧ 0 < t₄ ∧ 0 < t₅ ∧ 0 < h)
  (h₁ : t₁ + t₂ + t₃ + t₄ + t₅ + h = 1)
  (h₂ : t₁ = 1 / 2 * t₂)
  (h₃ : t₂ = 1 / 2 * t₃)
  (h₄ : t₃ = 5 / 9 * t₄)
  (h₅ : t₄ = 9 / 17 * t₅)
  (h₆ : t₅ = 1 / 17 * h) :
  t₁ + h = 3 / 34   :=  by sorry

The snippet does not provide the full original stochastic system.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Restore the actual state-probability equations and the final weighted value(1/2)T1+(1/2)H, using the source values T1=2/17,H=1/17. Remove the unrelated sum-normalization and fabricated ratios.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.