In some cases they have a full Lean formalization; in others they just use it for the problem statement. Getting rid of that "sorry" means you've proved the statement. I'm not a Lean expert but it reads pretty clearly as the original conjecture (though the definition of PlaneEmbedding seems quite involved!).
I think this just has to be the problem statement, there's several lemmas I would expect to see in there. Granted I know very little about Lean but it seems like the question and not the proof outlined in the paper.
Lol it should be, but it doesn't seem complete. Line 49 just says "sorry"
/-- Cubic bipartite three-vertex-connected plane graphs have a Hamiltonian cycle. -/ def MainStatement : Prop := ∀ (V : Type u) [Fintype V] [DecidableEq V] (G : SimpleGraph V) [DecidableRel G.Adj], G.IsRegularOfDegree 3 → G.IsBipartite → Planar G → ThreeVertexConnected G → HasHamiltonianCycle G
theorem main : MainStatement.{u} := by sorry
In some cases they have a full Lean formalization; in others they just use it for the problem statement. Getting rid of that "sorry" means you've proved the statement. I'm not a Lean expert but it reads pretty clearly as the original conjecture (though the definition of PlaneEmbedding seems quite involved!).
I think this just has to be the problem statement, there's several lemmas I would expect to see in there. Granted I know very little about Lean but it seems like the question and not the proof outlined in the paper.
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