lean_workbook_plus_65913

⚠️ 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.

Let $P_n$ denote the probability of Yizheng winning given that $n$ is the number of points Yizheng has minus the number of points Jennifer has. Then: $P_0=3/10P_1+7/10P_{-1}$, $P_1=3/10P_2+7/10P_0$, $P_{-1}=3/10P_0+7/10P_{-2}$, $P_2=1$, $P_{-2}=0$. Solve this linear system.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_65913 (P : ℤ → ℚ) (h₀ : P 0 = 3/10 * P 1 + 7/10 * P (-1)) (h₁ : P 1 = 3/10 * P 2 + 7/10 * P 0) (h₂ : P (-1) = 3/10 * P 0 + 7/10 * P (-2)) (h₃ : P 2 = 1) (h₄ : P (-2) = 0) : P = fun n => (1/2)^(n+1)   :=  by sorry

Five equations do not determine an entire function, and the invented geometric formula violates P(2)=1.

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

Proposed corrected statement

State only P(−2)=0,P(−1)=27/580,P(0)=9/58,P(1)=237/580,P(2)=1; leave other indices unconstrained.

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.