Theorems · Theorem · combinatorics
Graph.exists_isLink_of_mem_edgeSet
∀ {α : Type u_1} {β : Type u_2} {e : β} {G : Graph α β}, e ∈ G.edgeSet → ∃ x y, G.IsLink e x y- Defined in
- Mathlib.Combinatorics.Graph.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Graphstatement and proof · cited by 242
- Graph.IsLinkstatement · cited by 124
- Graph.edgeSetstatement and proof · cited by 79
- Graph.edge_mem_iff_exists_isLinkproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Graph.IsSubgraph.edgeSet_monoproof · cited by 8
- Graph.eq_bouquet_of_subsingletonproof · cited by 2
- Graph.induce_vertexSetproof · cited by 1
- Graph.IsInducedSubgraph.le_of_le_subsetproof · cited by 0
- Graph.IsInducedSubgraph.ext_of_vertexSetproof · cited by 0
- Graph.vertexSet_nontrivial_of_edgeSet_nonempty_of_looplessproof · cited by 0