Theorems · Theorem · combinatorics
SimpleGraph.ConnectedComponent.mem_supp_congr_adj
∀ {V : Type u} {G : SimpleGraph V} {v w : V} (c : G.ConnectedComponent), G.Adj v w → (v ∈ c.supp ↔ w ∈ c.supp)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.ConnectedComponentstatement and proof · cited by 86
- SimpleGraph.Adj.symmproof · cited by 66
- SimpleGraph.ConnectedComponent.suppstatement · cited by 42
- SimpleGraph.connectedComponentMkproof · cited by 40
- SimpleGraph.ConnectedComponent.connectedComponentMk_eq_of_adjproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraphproof · cited by 1
- SimpleGraph.ConnectedComponent.mem_supp_of_adj_mem_suppproof · cited by 0