Theorems · Theorem · combinatorics
SimpleGraph.IsTree.card_edgeFinset
∀ {V : Type u_1} {G : SimpleGraph V} [inst : Fintype V] [inst_1 : Fintype ↑G.edgeSet],
G.IsTree → G.edgeFinset.card + 1 = Fintype.card V- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites56
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
- Compl.complproof · cited by 2,925
- zero_addproof · cited by 2,366
- Finset.cardstatement and proof · cited by 2,327
- Fintype.cardstatement and proof · cited by 1,386
- SimpleGraph.Adjproof · cited by 1,346
- SimpleGraph.Walkproof · cited by 915
- Sym2statement and proof · cited by 737
- Sym2.mkproof · cited by 332
- SimpleGraph.Walk.supportproof · cited by 307
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.Connected.card_vert_le_card_edgeSet_add_oneproof · cited by 1
- SimpleGraph.isTree_iff_connected_and_cardproof · cited by 0
- SimpleGraph.IsTree.minDegree_eq_one_of_nontrivialproof · cited by 0