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Theorems · Theorem · combinatorics

SimpleGraph.Reachable.map

∀ {V : Type u} {V' : Type v} {u v : V} {G : SimpleGraph V} {G' : SimpleGraph V'} (f : G →g G'),
  G.Reachable u v → G'.Reachable (f u) (f v)
Defined in
Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
Cited by
14 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.Reachable.mono · cited by 10Reachable.monoSimpleGraph.Subgraph.connected_sup · cited by 3Subgraph.connected_supSimpleGraph.Reachable.coe_subgraphMap · cited by 2Reachable.coe_subgraphMapSimpleGraph.induce_connected_of_patches · cited by 2SimpleGraph.induce_connec…SimpleGraph.Subgraph.Connected.exists_verts_eq_connectedComponentSupp · cited by 1Connected.exists_verts_eq…SimpleGraph.ConnectedComponent.maximal_connected_induce_supp · cited by 1ConnectedComponent.maxima…SimpleGraph.ConnectedComponent.maximal_connected_toSubgraph · cited by 1ConnectedComponent.maxima…SimpleGraph.Preconnected.sum_sup_edge · cited by 1Preconnected.sum_sup_edgeSimpleGraph.Iso.reachable_iff · cited by 1Iso.reachable_iffSimpleGraph.Reachable.sum_sup_edge · cited by 1Reachable.sum_sup_edgeSimpleGraph.Reachable.coe_toSubgraph · cited by 1Reachable.coe_toSubgraphSimpleGraph.Subgraph.preconnected_iff_forall_exists_walk_subgraph · cited by 1Subgraph.preconnected_iff…SimpleGraph.ConnectedComponent.maximal_connected_induce_iff · cited by 0ConnectedComponent.maxima…SimpleGraph.ConnectedComponent.maximal_subgraph_connected_iff · cited by 0ConnectedComponent.maxima…DFunLike.coe · cited by 62936DFunLike.coeSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.Walk · cited by 915SimpleGraph.WalkSimpleGraph.Reachable · cited by 141SimpleGraph.ReachableSimpleGraph.Hom · cited by 139SimpleGraph.HomSimpleGraph.Walk.map · cited by 66Walk.mapSimpleGraph.Reachable.elim · cited by 7Reachable.elimReachable.mapCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by14

Results whose statement or proof uses this declaration.