No_Group_has_Two_Order_2_Elements_v2

⚠️ 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.

A group cannot contain exactly two distinct elements of order 2. If there are three elements of order 2, at least two must be equal.

Why this node was retired

The posted statement is

import Mathlib.Analysis.Complex.Basic

theorem No_Group_has_Two_Order_2_Elements_v2 {G : Type _} [Group G] (a b c : G) (ha : orderOf a = 2) (hb : orderOf b = 2) (hc : orderOf c = 2) : a = b ∨ a = c ∨ b = c := by sorry

The formula prohibits three distinct involutions, whereas the source prohibits exactly two.

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

Proposed corrected statement

If a,b are distinct group elements with orderOf a=orderOf b=2, then there exists c different from both with orderOf c=2. Equivalently, the set of involutions cannot have cardinality exactly two.

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.