Theorems · Theorem · combinatorics
SimpleGraph.Iso.connectedComponentEquiv_apply
∀ {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} (φ : G ≃g G') (C : G.ConnectedComponent),
φ.connectedComponentEquiv C = SimpleGraph.ConnectedComponent.map (RelIso.toRelEmbedding φ).toRelHom C- Cited by
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- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement · cited by 8,337
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement · cited by 1,346
- SimpleGraph.Isostatement and proof · cited by 99
- SimpleGraph.ConnectedComponentstatement and proof · cited by 86
- RelIso.toRelEmbeddingstatement · cited by 34
- RelEmbedding.toRelHomstatement · cited by 15
- SimpleGraph.ConnectedComponent.mapstatement · cited by 11
- SimpleGraph.Iso.connectedComponentEquivstatement and proof · cited by 5
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