Theorems · Theorem · combinatorics
SimpleGraph.neighborFinset_eq_filter
∀ {V : Type u_1} (G : SimpleGraph V) [inst : Fintype V] {v : V} [inst_1 : DecidableRel G.Adj],
G.neighborFinset v = {w | G.Adj v w}- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 60 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.filterstatement · cited by 949
- Finset.extproof · cited by 565
- SimpleGraph.neighborSetstatement · cited by 257
- SimpleGraph.neighborFinsetstatement · cited by 72
Cited by6
Results whose statement or proof uses this declaration.
- SimpleGraph.complete_graph_degreeproof · cited by 1
- SimpleGraph.mul_adjMatrix_applyproof · cited by 1
- SimpleGraph.adjMatrix_mul_applyproof · cited by 1
- SimpleGraph.adjMatrix_dotProductproof · cited by 1
- SimpleGraph.dotProduct_adjMatrixproof · cited by 0
- SimpleGraph.card_edgeFinset_turanGraph_addproof · cited by 0