lean_workbook_plus_19846

⚠️ 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.

Given $a_{1}= 1$ and $a_{n+1}= 1+\frac{1}{a_{n}}$ , then $a_{2}= 2 ,a_{3}= \frac{3}{2},a_{4}= \frac{5}{3},a_{5}= \frac{8}{5}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_19846 (a : ℕ → ℚ) (a1 : a 0 = 1) (a_rec : ∀ n, a (n + 1) = 1 + 1 / a n) : a 2 = 2 ∧ a 3 = 3 / 2 ∧ a 4 = 5 / 3 ∧ a 5 = 8 / 5   :=  by sorry

Initial value was shifted to index0 while all later named indices stayed unchanged.

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

Proposed corrected statement

Either keep source a₁=1 and conclude a₂=2,a₃=3/2,a₄=5/3,a₅=8/5, or use a₀=1 and shift every conclusion down one index.

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.