Theorems · Theorem · combinatorics
Graph.IsClosedSubgraph.isLink_congr
∀ {α : Type u_1} {β : Type u_2} {x y : α} {e : β} {G H : Graph α β},
x ∈ H.vertexSet → H.IsClosedSubgraph G → (H.IsLink e x y ↔ G.IsLink e x y)- Defined in
- Mathlib.Combinatorics.Graph.Subgraph
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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.vertexSetstatement and proof · cited by 87
- Graph.IsClosedSubgraphstatement and proof · cited by 17
- Graph.IsInducedSubgraph.leproof · cited by 12
- Graph.IsLink.monoproof · cited by 11
- Graph.IsLink.inc_leftproof · cited by 8
- Graph.IsClosedSubgraph.isInducedSubgraphproof · cited by 6
- Graph.Inc.edge_memproof · cited by 6
- Graph.IsClosedSubgraph.inc_congrproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Graph.IsClosedSubgraph.mem_iff_of_isLinkproof · cited by 2
- Graph.IsClosedSubgraph.adj_congrproof · cited by 0
- Graph.IsClosedSubgraph.mem_tfae_of_isLinkproof · cited by 0