R03 P3-factor structural result: neighbor card of cubic
ProvedR03SP06.neighbor_card_of_cubicgraph-theoryopg-46613p3-factorsource-faithful-candidate
This is a source-faithful auxiliary theorem from the candidate formalization of the cubic P3-partition problem. It records the structural result R03SP06.neighbor_card_of_cubic under exactly the explicit hypotheses in the Lean statement. It is a conditional reusable result and does not claim that the open root problem has been solved.
Formalization Note The Lean statement and direct proof were extracted from the cited candidate artifact; its source digest is 04ca22c9ca4f49f2bf87ecf9b084f5f0c8d4ef55932daf6265571b9feb721bf2.
Formal statement
import Mathlib
import Definitions.Def_cubic_p3_partition_models
namespace R03SP06
open R03SP06
open CubicP3Partition
variable {V : Type} [Fintype V] [DecidableEq V]
theorem neighbor_card_of_cubic
{G : SimpleGraph V} [DecidableRel G.Adj]
(hC : Cubic G) : ∀ v : V, (G.neighborFinset v).card = 3 := by sorry
end R03SP06
Source
VibeMathing candidate artifact: research/artifacts/candidates/r03/parallel/sp06/p3_external_budget_exact.lean; source SHA-256 04ca22c9ca4f49f2bf87ecf9b084f5f0c8d4ef55932daf6265571b9feb721bf2; ProblemContract problem:opg-46613-p3-partition; candidate-only formalization.