Theorems · Theorem · combinatorics
SimpleGraph.card_edgeFinset_le_card_choose_two
∀ {V : Type u_1} {G : SimpleGraph V} [inst : Fintype ↑G.edgeSet] [inst_1 : Fintype V],
G.edgeFinset.card ≤ (Fintype.card V).choose 2Any graph on n vertices has at most n.choose 2 edges.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Fintype.cardstatement · cited by 1,386
- Sym2statement · cited by 737
- Nat.choosestatement · cited by 494
- le_topproof · cited by 411
- SimpleGraph.edgeSetstatement and proof · cited by 199
- Finset.card_le_cardproof · cited by 118
- SimpleGraph.edgeFinsetstatement and proof · cited by 116
- SimpleGraph.edgeFinset_monoproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.FarFromTriangleFree.lt_halfproof · cited by 1
- SimpleGraph.CliqueFree.card_edgeFinset_leproof · cited by 0