Theorems · Theorem · combinatorics
SimpleGraph.degree_eq_zero_of_subsingleton
∀ {V : Type u_1} {G : SimpleGraph V} (v : V) [inst : Fintype ↑(G.neighborSet v)] [Subsingleton V], G.degree v = 0- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeSubsingleton
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.degreestatement · cited by 112
- SimpleGraph.IsIsolated.degree_eq_zeroproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.degree_eq_zero_of_subsingletonproof · cited by 2