Theorems · Definition · combinatorics
SimpleGraph.ComponentCompl.hom
{V : Type u} → {G : SimpleGraph V} → {K L : Set V} → K ⊆ L → G.ComponentCompl L → G.ComponentCompl KIf K ⊆ L, the components outside of L are all contained in a single component outside of K.
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SimpleGraph.ComponentComplstatement and proof · cited by 29
- SimpleGraph.Hom.idproof · cited by 11
- SimpleGraph.ConnectedComponent.mapproof · cited by 11
- SimpleGraph.induceHomproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- SimpleGraph.componentComplFunctorproof · cited by 6
- SimpleGraph.ComponentCompl.subset_homstatement · cited by 3
- SimpleGraph.ComponentCompl.infinite_iff_in_all_rangesstatement and proof · cited by 2
- SimpleGraph.ComponentCompl.hom_eq_iff_lestatement and proof · cited by 1
- SimpleGraph.ComponentCompl.hom_mkstatement · cited by 1
- SimpleGraph.componentComplFunctor_mapstatement · cited by 1
- SimpleGraph.infinite_iff_in_eventualRangeproof · cited by 0
- SimpleGraph.ComponentCompl.hom_eq_iff_not_disjointstatement and proof · cited by 0
- SimpleGraph.ComponentCompl.hom_infinitestatement · cited by 0
- SimpleGraph.ComponentCompl.hom_reflstatement · cited by 0
- SimpleGraph.ComponentCompl.hom_transstatement · cited by 0
- SimpleGraph.ComponentCompl.hom.congr_simpstatement and proof · cited by 0