R03 P3-factor structural result: triangle portless side two cut impossible
ProvedR03SP06.triangle_portless_side_two_cut_impossiblegraph-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.triangle_portless_side_two_cut_impossible 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 d5c1f42c41c331b51f26cb63fa826906489e2c17631fbeebcc0c3c289460f718.
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 triangle_portless_side_two_cut_impossible
{G : SimpleGraph V} (h3 : ThreeVertexConnected G)
{A B X T : Finset V}
(hA : A.Nonempty) (hB : B.Nonempty)
(hAB : Disjoint A B) (hAX : Disjoint A X) (hBX : Disjoint B X)
(hX : X.card ≤ 2)
(hclosed : ∀ ⦃u v : V⦄, u ∈ A → G.Adj u v →
v ∈ A ∪ X ∪ T)
(hnoport : ∀ ⦃u t : V⦄, u ∈ A → t ∈ T → ¬ G.Adj u t) : False := by sorry
end R03SP06
Source
VibeMathing candidate artifact: research/artifacts/candidates/r03/parallel/sp06/q3_triangle_external_port_card.lean; source SHA-256 d5c1f42c41c331b51f26cb63fa826906489e2c17631fbeebcc0c3c289460f718; ProblemContract problem:opg-46613-p3-partition; candidate-only formalization.