Theorems · Definition · combinatorics
Graph.IsNonloopAt
{α : Type u_1} → {β : Type u_2} → Graph α β → β → α → PropG.IsNonloopAt e x means that the vertex x is one but not both of the ends of the edge =e,
or equivalently that e is incident with x but not a loop at x -
see Graph.isNonloopAt_iff_inc_not_isLoopAt.
- Defined in
- Mathlib.Combinatorics.Graph.Basic
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 3 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 by16
Results whose statement or proof uses this declaration.
- Graph.IsNonloopAt.incstatement and proof · cited by 3
- Graph.Inc.isLoopAt_or_isNonloopAtstatement · cited by 1
- Graph.IsLoopAt.not_isNonloopAtstatement and proof · cited by 1
- Graph.IsNonloopAt.not_isLoopAtstatement and proof · cited by 1
- Graph.IsSubgraph.isNonloopAt_congrstatement · cited by 1
- Graph.not_isNonloopAt_bouquetstatement · cited by 0
- Graph.Inc.isNonloopAtstatement · cited by 0
- Graph.inf_isNonloopAt_iffstatement · cited by 0
- Graph.banana_isNonloopAtstatement · cited by 0
- Graph.IsNonloopAt.edge_memstatement and proof · cited by 0
- Graph.IsNonloopAt.monostatement and proof · cited by 0
- Graph.IsNonloopAt.of_compatiblestatement and proof · cited by 0