Theorems · Theorem · combinatorics
SimpleGraph.card_neighborSet_eq_degree
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)],
Fintype.card ↑(G.neighborSet v) = G.degree v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 9 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
- Fintype.cardstatement · cited by 1,386
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.degreestatement · cited by 112
- Set.toFinset_cardproof · cited by 63
Cited by9
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.coe_degreeproof · cited by 3
- SimpleGraph.card_incidenceSet_eq_degreeproof · cited by 3
- SimpleGraph.Iso.degree_eqproof · cited by 2
- SimpleGraph.card_commonNeighbors_le_degree_leftproof · cited by 2
- SimpleGraph.Copy.degree_leproof · cited by 1
- SimpleGraph.degree_complproof · cited by 1
- SimpleGraph.Subgraph.degree_leproof · cited by 0
- SimpleGraph.Subgraph.degree_spanningCoeproof · cited by 0
- SimpleGraph.dart_fst_fiber_card_eq_degreeproof · cited by 0