Theorems · Theorem · combinatorics
SimpleGraph.Subgraph.degree_of_notMem_verts
∀ {V : Type u} {G : SimpleGraph V} {G' : G.Subgraph} {v : V} [inst : Fintype ↑(G'.neighborSet v)],
v ∉ G'.verts → G'.degree v = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Subgraphstatement and proof · cited by 326
- SimpleGraph.Subgraph.vertsstatement and proof · cited by 210
- SimpleGraph.Subgraph.neighborSetstatement and proof · cited by 46
- SimpleGraph.Subgraph.degreestatement · cited by 14
- Fintype.card_eq_zero_iffproof · cited by 14
- SimpleGraph.Subgraph.Adj.fst_memproof · cited by 7
- isEmpty_subtypeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.degree_eq_zero_of_subsingletonproof · cited by 2