Theorems · Theorem · combinatorics
SimpleGraph.dart_card_eq_sum_degrees
∀ {V : Type u} (G : SimpleGraph V) [inst : Fintype V] [inst_1 : DecidableRel G.Adj],
Fintype.card G.Dart = ∑ v, G.degree v- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Set.univproof · cited by 3,945
- Finset.univstatement and proof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- Finset.sum_congrproof · cited by 2,323
- Fintype.cardstatement · cited by 1,386
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Set.MapsToproof · cited by 732
- SimpleGraph.neighborSetstatement · cited by 257
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.sum_degrees_eq_twice_card_edgesproof · cited by 4
- SimpleGraph.natCast_card_dart_eq_dotProductproof · cited by 0