Theorems · Theorem · combinatorics
SimpleGraph.mem_incidenceFinset
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)] [inst_1 : DecidableEq V] (e : Sym2 V),
e ∈ G.incidenceFinset v ↔ e ∈ G.incidenceSet v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
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
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Sym2statement and proof · cited by 737
- SimpleGraph.neighborSetstatement and proof · cited by 257
- Set.mem_toFinsetproof · cited by 47
- SimpleGraph.incidenceSetstatement · cited by 46
- SimpleGraph.incidenceFinsetstatement · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.disjoint_sdiff_neighborFinset_imageproof · cited by 2