Theorems · Theorem · combinatorics
Graph.IsLink.edge_mem
∀ {α : Type u_1} {β : Type u_2} {x y : α} {e : β} {G : Graph α β}, G.IsLink e x y → e ∈ G.edgeSet- Defined in
- Mathlib.Combinatorics.Graph.Basic
- Cited by
- 14 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 and proof · cited by 124
- Graph.edgeSetstatement · cited by 79
- Graph.edge_mem_iff_exists_isLinkproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- Graph.IsSubgraph.edgeSet_monoproof · cited by 8
- Graph.Inc.edge_memproof · cited by 6
- Graph.IsLink.of_compatibleproof · cited by 3
- Graph.le_iff_compatible_subset_subsetproof · cited by 1
- Graph.induce_vertexSetproof · cited by 1
- Graph.IsInducedSubgraph.not_isClosedSubgraph_iff_exists_adjproof · cited by 1
- Graph.incidenceSet_subset_edgeSetproof · cited by 0
- Graph.le_noEdge_iffproof · cited by 0
- Graph.not_isLink_of_notMem_edgeSetproof · cited by 0
- Graph.IsInducedSubgraph.le_of_le_subsetproof · cited by 0
- Graph.edgeSet_eq_emptyproof · cited by 0
- Graph.IsSubgraph.not_isInducedSubgraph_iffproof · cited by 0