Theorems · Theorem · combinatorics
Graph.eq_bouquet_of_subsingleton
∀ {α : Type u_1} {β : Type u_2} {v : α} {G : Graph α β},
v ∈ G.vertexSet → G.vertexSet.Subsingleton → G = Graph.bouquet v G.edgeSetEvery graph on just one vertex is a bouquet on that vertex.
- Defined in
- Mathlib.Combinatorics.Graph.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Subsingletonstatement and proof · cited by 276
- Graphstatement and proof · cited by 242
- Graph.IsLinkproof · cited by 124
- Set.insert_eq_of_memproof · cited by 118
- Graph.vertexSetstatement and proof · cited by 87
- Graph.edgeSetstatement and proof · cited by 79
- Graph.Incproof · cited by 42
- Set.Subsingleton.eq_singleton_of_memproof · cited by 16
- Graph.IsLink.left_memproof · cited by 14
- Graph.bouquetstatement and proof · cited by 11
- Graph.IsLink.inc_leftproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Graph.exists_eq_bouquetproof · cited by 0
- Graph.eq_bouquet_iffproof · cited by 0