Theorems · Theorem · combinatorics
SimpleGraph.dart_card_eq_twice_card_edges
∀ {V : Type u} (G : SimpleGraph V) [inst : Fintype V] [inst_1 : DecidableRel G.Adj],
Fintype.card G.Dart = 2 * G.edgeFinset.card- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 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.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardstatement and proof · cited by 2,327
- mul_commproof · cited by 2,262
- Fintype.cardstatement · cited by 1,386
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.filterproof · cited by 949
- Sym2statement and proof · cited by 737
- SimpleGraph.edgeFinsetstatement and proof · cited by 116
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.sum_degrees_eq_twice_card_edgesproof · cited by 4
- SimpleGraph.two_mul_card_edgeFinsetproof · cited by 2