lean_workbook_plus_50066

⚠️ 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 $a_{x,y}$ be the number of ways to get to $(x,y)$ . We need $a_{4, 4}$ . We have $a_{x,y}=a_{x-1,y}+a_{x-2,y}+a_{x,y-1}+a_{x,y-2}$ for $x, y, \geq 2$ . From here it is just a straightforward bash working backwards (also using small values of $x,y$ ) which yields $\boxed{556}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_50066  (a : ℕ → ℕ → ℕ)
  (h₀ : a 0 0 = 1)
  (h₁ : a 1 0 = 1)
  (h₂ : a 2 0 = 2)
  (h₃ : a 3 0 = 4)
  (h₄ : a 4 0 = 8)
  (h₅ : a 0 1 = 1)
  (h₆ : a 1 1 = 2)
  (h₇ : a 2 1 = 4)
  (h₈ : a 3 1 = 8)
  (h₉ : a 4 1 = 16)
  (h₁₀ : a 0 2 = 2)
  (h₁₁ : a 1 2 = 4)
  (h₁₂ : a 2 2 = 8)
  (h₁₃ : a 3 2 = 16)
  (h₁₄ : a 4 2 = 32)
  (h₁₅ : a 0 3 = 4)
  (h₁₆ : a 1 3 = 8)
  (h₁₇ : a 2 3 = 16)
  (h₁₈ : a 3 3 = 32)
  (h₁₉ : a 4 3 = 64)
  (h₂₀ : a 0 4 = 8)
  (h₂₁ : a 1 4 = 16)
  (h₂₂ : a 2 4 = 32)
  (h₂₃ : a 3 4 = 64)
  (h₂₄ : a 4 4 = 128) :
  a 4 4 = 556   :=  by sorry

Replace the fabricated25-entry table by the four-predecessor path recurrence with unavailable negative predecessors omitted and the empty-path count C(0,0)=1; then conclude C(4,4)=556.

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

Proposed corrected statement

Replace the fabricated25-entry table by the four-predecessor path recurrence with unavailable negative predecessors omitted and the empty-path count C(0,0)=1; then conclude C(4,4)=556.

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.