Theorems · Theorem · combinatorics
SimpleGraph.mem_neighborFinset
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)] (w : V),
w ∈ G.neighborFinset v ↔ G.Adj v w- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 58 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement · cited by 1,346
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.neighborFinsetstatement · cited by 72
- Set.mem_toFinsetproof · cited by 47
Cited by6
Results whose statement or proof uses this declaration.
- SimpleGraph.isBipartiteWith_neighborFinsetproof · cited by 2
- SimpleGraph.isBipartiteWith_neighborFinset'proof · cited by 2
- SimpleGraph.union_eq_univ_of_forall_ncard_leproof · cited by 2
- SimpleGraph.exists_bijective_of_forall_ncard_leproof · cited by 1
- SimpleGraph.IsSRGWith.param_eqproof · cited by 0
- SimpleGraph.exists_isMatching_of_forall_ncard_leproof · cited by 0