Theorems · Theorem · combinatorics
SimpleGraph.card_incidenceFinset_eq_degree
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)] [inst_1 : DecidableEq V],
(G.incidenceFinset v).card = G.degree v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 72 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
- Finset.cardstatement and proof · cited by 2,327
- Sym2statement · cited by 737
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.degreestatement · cited by 112
- Set.toFinset_cardproof · cited by 63
- SimpleGraph.incidenceSetproof · cited by 46
- SimpleGraph.incidenceFinsetstatement and proof · cited by 15
- SimpleGraph.card_incidenceSet_eq_degreeproof · cited by 3
Cited by4
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.Walk.IsEulerian.even_degree_iffproof · cited by 1
- SimpleGraph.degree_le_card_edgeFinsetproof · cited by 0