Theorems · Theorem · combinatorics
SimpleGraph.card_neighborFinset_eq_degree
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)], (G.neighborFinset v).card = G.degree v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardstatement · cited by 2,327
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.degreestatement · cited by 112
- SimpleGraph.neighborFinsetstatement · cited by 72
Cited by5
Results whose statement or proof uses this declaration.
- SimpleGraph.card_edgeFinset_replaceVertex_of_not_adjproof · cited by 2
- SimpleGraph.card_edgeFinset_replaceVertex_of_adjproof · cited by 1
- SimpleGraph.degree_completeEquipartiteGraphproof · cited by 1
- SimpleGraph.isBipartiteWith_degree_leproof · cited by 0
- SimpleGraph.isBipartiteWith_degree_le'proof · cited by 0