Theorems · Theorem · combinatorics
SimpleGraph.singleton_disjoint_neighborFinset
∀ {V : Type u_1} (G : SimpleGraph V) (v : V) [inst : Fintype ↑(G.neighborSet v)], Disjoint {v} (G.neighborFinset v)- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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Cites9
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
- Disjointstatement · cited by 2,201
- SimpleGraph.neighborSetstatement and proof · cited by 257
- SimpleGraph.neighborFinsetstatement · cited by 72
- Finset.disjoint_singleton_leftproof · cited by 17
- SimpleGraph.notMem_neighborFinset_selfproof · cited by 4
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