Theorems · Theorem · combinatorics
SimpleGraph.neighborFinset_disjoint_singleton
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)], Disjoint (G.neighborFinset v) {v}- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Disjointstatement · cited by 2,201
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.neighborFinsetstatement · cited by 72
- Finset.disjoint_singleton_rightproof · cited by 12
- SimpleGraph.notMem_neighborFinset_selfproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.neighborFinset_boxProdstatement and proof · cited by 1
- SimpleGraph.degree_boxProdproof · cited by 0