Intersection_with_Normal_Subgroup_is_Normal
Disproved⚠️ Retired — specification defect
The Lean statement below does not encode the problem shown on this page, so its
Disprovedstatus carries no information about that problem. Do not import this node or use it as a dependency.
Let G be a group, H a subgroup, N a normal subgroup. Then H ∩ N is normal in H.
Why this node was retired
The posted statement is
theorem Intersection_with_Normal_Subgroup_is_Normal {G : Type _} [Group G] (H N : Subgroup G) (hN : N.Normal) (g h : G) (hh : h ∈ H ⊓ N) : g * h * g⁻¹ ∈ H ⊓ N := by sorry
The conjugating element ranges over all of G rather than H.
The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.
Proposed corrected statement
Add g∈H to the displayed conjugation statement. Equivalently, H∩N is normal in H whenever N is normal in G.
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.
import Mathlib.Analysis.Complex.Basic
theorem Intersection_with_Normal_Subgroup_is_Normal {G : Type _} [Group G] (H N : Subgroup G) (hN : N.Normal) (g h : G) (hh : h ∈ H ⊓ N) : g * h * g⁻¹ ∈ H ⊓ N := by sorry