Theorems · Theorem · combinatorics
SimpleGraph.degree_lt_card_verts
∀ {V : Type u_1} {G : SimpleGraph V} [inst : Fintype V] [inst_1 : DecidableRel G.Adj] (v : V),
G.degree v < Fintype.card V- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 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.
Cites9
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
- SimpleGraphstatement and proof · cited by 3,072
- Fintype.cardstatement · cited by 1,386
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.neighborSetstatement · cited by 257
- SimpleGraph.degreestatement · cited by 112
- SimpleGraph.notMem_neighborFinset_selfproof · cited by 4
- Finset.card_lt_univ_of_notMemproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.card_commonNeighbors_lt_card_vertsproof · cited by 0
- SimpleGraph.maxDegree_lt_card_vertsproof · cited by 0
- SimpleGraph.minDegree_lt_cardproof · cited by 0