Theorems · Theorem · combinatorics
SimpleGraph.coe_neighborFinset
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)],
↑(G.neighborFinset v) = G.neighborSet v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 59 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.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement · cited by 8,199
- 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
- Set.coe_toFinsetproof · cited by 51
Cited by9
Results whose statement or proof uses this declaration.
- SimpleGraph.disjoint_neighborFinset_of_disjointproof · cited by 1
- SimpleGraph.edgeFinset_replaceVertex_of_adjproof · cited by 1
- SimpleGraph.edgeFinset_replaceVertex_of_not_adjproof · cited by 1
- SimpleGraph.Adj.card_commonNeighbors_lt_degreeproof · cited by 0
- SimpleGraph.neighborFinset_infproof · cited by 0
- SimpleGraph.neighborFinset_sdiffproof · cited by 0
- SimpleGraph.neighborFinset_supproof · cited by 0
- SimpleGraph.neighborFinset_sup_of_disjointproof · cited by 0
- SimpleGraph.neighborFinset_topproof · cited by 0