Theorems · Theorem · combinatorics
Graph.IsClosedSubgraph.mem_tfae_of_isLink
∀ {α : Type u_1} {β : Type u_2} {x y : α} {e : β} {G H : Graph α β},
G.IsLink e x y → H.IsClosedSubgraph G → [x ∈ H.vertexSet, y ∈ H.vertexSet, e ∈ H.edgeSet].TFAE- Defined in
- Mathlib.Combinatorics.Graph.Subgraph
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- List.TFAEstatement · cited by 102
- Graph.vertexSetstatement and proof · cited by 87
- List.tfae_of_cycleproof · cited by 83
- Graph.edgeSetstatement and proof · cited by 79
- Graph.IsClosedSubgraphstatement and proof · cited by 17
- Graph.IsLink.edge_memproof · cited by 14
- Graph.IsLink.left_memproof · cited by 14
- Graph.IsInducedSubgraph.leproof · cited by 12
- Graph.IsLink.symmproof · cited by 11
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