Theorems · Theorem · combinatorics
SimpleGraph.card_edgeFinset_top_eq_card_choose_two
∀ {V : Type u_1} [inst : Fintype V] [inst_1 : DecidableEq V], ⊤.edgeFinset.card = (Fintype.card V).choose 2The complete graph on n vertices has n.choose 2 edges.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement · cited by 3,072
- Compl.complproof · cited by 2,925
- Finset.cardstatement · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- Sym2statement · cited by 737
- Nat.choosestatement and proof · cited by 494
- SimpleGraph.edgeSetproof · cited by 199
- SimpleGraph.edgeFinsetstatement · cited by 116
- Set.toFinset_cardproof · cited by 63
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.card_edgeFinset_le_card_choose_twoproof · cited by 2
- SimpleGraph.card_topEdgeLabelingproof · cited by 0