Fishers_Inequality

⚠️ 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.

For any BIBD $\struct {v, k, \lambda}$, the number of blocks $b$ must be greater then or equal to the number of points $v$ $b \ge v$

Why this node was retired

The posted statement is

theorem Fishers_Inequality (v k l b r : ℕ) (hk : 1 < k) (hk2 : k < v) (hr : b * k = v * r) (hlam : r * (k - 1) = l * (v - 1)) : v ≤ b := by sorry

Necessary parameter equations are used without assuming existence of a balanced incomplete block design.

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

Proposed corrected statement

Assume an actual finite incidence design with v points, b blocks, block size k, replication r and pair multiplicity λ, with1<k<v and λ>0; then conclude v≤b.

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.