Theorems · Definition · combinatorics
Graph.IsLoopAt
{α : Type u_1} → {β : Type u_2} → Graph α β → β → α → PropG.IsLoopAt e x means that both ends of the edge e are equal to the vertex x.
- Defined in
- Mathlib.Combinatorics.Graph.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Graphstatement and proof · cited by 242
- Graph.IsLinkproof · cited by 124
Cited by32
Results whose statement or proof uses this declaration.
- Graph.Loopless.not_isLoopAtstatement · cited by 3
- Graph.IsLoopAt.incstatement and proof · cited by 2
- Graph.loopSetproof · cited by 2
- Graph.Inc.isLoopAt_or_isNonloopAtstatement and proof · cited by 1
- Graph.IsLoopAt.edge_memstatement and proof · cited by 1
- Graph.IsLoopAt.eq_of_incstatement and proof · cited by 1
- Graph.IsLoopAt.not_isNonloopAtstatement and proof · cited by 1
- Graph.IsNonloopAt.not_isLoopAtstatement and proof · cited by 1
- Graph.loopless_iff_forall_ne_of_adjproof · cited by 1
- Graph.IsSubgraph.isLoopAt_congrstatement · cited by 1
- Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iffstatement · cited by 1
- Topology.CWComplex.OneSkeletonGraph.exists_isLoopAt_iff_subsingletonstatement · cited by 1