Theorems · Theorem · combinatorics
SimpleGraph.ConnectedComponent.ind
∀ {V : Type u} {G : SimpleGraph V} {β : G.ConnectedComponent → Prop},
(∀ (v : V), β (G.connectedComponentMk v)) → ∀ (c : G.ConnectedComponent), β c- Cited by
- 7 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.ConnectedComponentstatement and proof · cited by 86
- SimpleGraph.connectedComponentMkstatement and proof · cited by 40
Cited by7
Results whose statement or proof uses this declaration.
- SimpleGraph.ComponentCompl.indproof · cited by 4
- SimpleGraph.ConnectedComponent.map_compproof · cited by 1
- SimpleGraph.ConnectedComponent.map_idproof · cited by 1
- SimpleGraph.ConnectedComponent.maximal_connected_induce_suppproof · cited by 1
- SimpleGraph.ConnectedComponent.maximal_connected_toSubgraphproof · cited by 1
- SimpleGraph.ConnectedComponent.iso_image_comp_eq_map_iff_eq_compproof · cited by 0
- SimpleGraph.ConnectedComponent.iso_inv_image_comp_eq_iff_eq_mapproof · cited by 0