Theorems · Theorem · combinatorics
SimpleGraph.ComponentCompl.ind
∀ {V : Type u} {G : SimpleGraph V} {K : Set V} {β : G.ComponentCompl K → Prop},
(∀ ⦃v : V⦄ (hv : v ∉ K), β (G.componentComplMk hv)) → ∀ (C : G.ComponentCompl K), β C- Cited by
- 4 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Compl.complproof · cited by 2,925
- SimpleGraph.induceproof · cited by 80
- SimpleGraph.connectedComponentMkproof · cited by 40
- SimpleGraph.ComponentComplstatement and proof · cited by 29
- SimpleGraph.componentComplMkstatement and proof · cited by 15
- SimpleGraph.ConnectedComponent.indproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.ComponentCompl.nonemptyproof · cited by 2
- SimpleGraph.ComponentCompl.hom_eq_iff_leproof · cited by 1
- SimpleGraph.ComponentCompl.exists_adj_boundary_pairproof · cited by 0
- SimpleGraph.ComponentCompl.hom_eq_iff_not_disjointproof · cited by 0