Theorems · Theorem · combinatorics
SimpleGraph.card_incidenceSet_eq_degree
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)] [inst_1 : DecidableEq V],
Fintype.card ↑(G.incidenceSet v) = G.degree v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Sym2statement · cited by 737
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.degreestatement and proof · cited by 112
- Fintype.card_congrproof · cited by 67
- SimpleGraph.incidenceSetstatement · cited by 46
- SimpleGraph.card_neighborSet_eq_degreeproof · cited by 9
- SimpleGraph.incidenceSetEquivNeighborSetproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.card_incidenceFinset_eq_degreeproof · cited by 4
- SimpleGraph.IsEdgeReachable.le_degreeproof · cited by 1
- SimpleGraph.sum_incMatrix_applyproof · cited by 1