Theorems · Theorem · combinatorics
SimpleGraph.ConnectedComponent.Represents.ncard_sdiff_of_mem
∀ {V : Type u} {G : SimpleGraph V} {C : Set G.ConnectedComponent} {s : Set V} {c : G.ConnectedComponent},
SimpleGraph.ConnectedComponent.Represents s C → c ∈ C → (c.supp \ s).ncard = c.supp.ncard - 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 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 and proof · cited by 53,352
- SimpleGraphstatement and proof · cited by 3,072
- Set.ncardstatement and proof · cited by 344
- Set.toFiniteproof · cited by 174
- SimpleGraph.ConnectedComponentstatement and proof · cited by 86
- SimpleGraph.ConnectedComponent.suppstatement and proof · cited by 42
- Set.sdiff_inter_self_eq_sdiffproof · cited by 16
- SimpleGraph.ConnectedComponent.Representsstatement and proof · cited by 10
- Set.ncard_singletonproof · cited by 8
- Set.ncard_sdiffproof · cited by 4
- SimpleGraph.ConnectedComponent.Represents.exists_inter_eq_singletonproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.ConnectedComponent.even_ncard_supp_sdiff_repproof · cited by 1