Theorems · Theorem · combinatorics
SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph
∀ {V : Type u} {G : SimpleGraph V} {v w : V} (C : G.ConnectedComponent),
C.toSimpleGraph.spanningCoe.Adj v w ↔ v ∈ C.supp ∧ G.Adj v w- Cited by
- 1 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Function.Embedding.subtypeproof · cited by 128
- SimpleGraph.ConnectedComponentstatement and proof · cited by 86
- SimpleGraph.induceproof · cited by 80
- SimpleGraph.ConnectedComponent.suppstatement and proof · cited by 42
- SimpleGraph.ConnectedComponent.toSimpleGraphstatement and proof · cited by 14
- SimpleGraph.spanningCoestatement and proof · cited by 12
- SimpleGraph.ConnectedComponent.mem_supp_congr_adjproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.IsCycles.toSimpleGraphproof · cited by 0