Theorems · Theorem · combinatorics
SimpleGraph.notMem_neighborFinset_self
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)], v ∉ G.neighborFinset v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 60 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.
Cites6
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
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.neighborFinsetstatement · cited by 72
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.degree_lt_card_vertsproof · cited by 3
- SimpleGraph.neighborFinset_disjoint_singletonproof · cited by 2
- SimpleGraph.IsSRGWith.param_eqproof · cited by 0
- SimpleGraph.singleton_disjoint_neighborFinsetproof · cited by 0