brualdi-ch12-62

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal brualdi-ch12-62

What it runs

The Lean statement the swarm must prove — kernel-verified at Gate A. The trailing sorry is the open obligation a proof replaces.

goals/brualdi-ch12-62.lean

import Mathlib

structure TwoConnected {V : Type*} (G : SimpleGraph V) : Prop where
  selfconnected : G.Connected
  remains_connected : ∀ x : V, ((⊤ : SimpleGraph.Subgraph G).deleteVerts {x}).coe.Connected

theorem brualdi_ch12_62 {V : Type*} (G : SimpleGraph V) : TwoConnected G ↔ ∀ x : V, ∀ e ∈ G.edgeSet,
    ∃ G' : SimpleGraph.Subgraph G, x ∈ G'.verts ∧ e ∈ G'.edgeSet ∧ G'.coe.IsCycles := by
  sorry

Runs (0)

No runs recorded for this suite yet — they appear here as the swarm attempts the benchmarks.