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Theorems · Theorem · combinatorics

SimpleGraph.Reachable.coe_subgraphMap

∀ {V : Type u} {G : SimpleGraph V} {G' : G.Subgraph} {G'' : G'.coe.Subgraph} (f : G'.coe →g G) {u v : ↑G''.verts},
  G''.coe.Reachable u v → (SimpleGraph.Subgraph.map f G'').coe.Reachable ⟨f ↑u, ⋯⟩ ⟨f ↑v, ⋯⟩
Defined in
Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
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Around this declaration

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

SimpleGraph.Subgraph.Preconnected.map · cited by 2Preconnected.mapSimpleGraph.Reachable.coe_coeSubgraph · cited by 0Reachable.coe_coeSubgraphDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSubtype.prop · cited by 505Subtype.propSet.mem_image_of_mem · cited by 371Set.mem_image_of_memSimpleGraph.Subgraph · cited by 326SimpleGraph.SubgraphSimpleGraph.Subgraph.verts · cited by 210Subgraph.vertsSimpleGraph.Reachable · cited by 141SimpleGraph.ReachableSimpleGraph.Hom · cited by 139SimpleGraph.HomSimpleGraph.Subgraph.coe · cited by 89Subgraph.coeSimpleGraph.Subgraph.map · cited by 24Subgraph.mapSimpleGraph.Reachable.map · cited by 14Reachable.mapSimpleGraph.Subgraph.vert · cited by 3Subgraph.vertReachable.coe_subgraphMapCITED BYCITES

Cites16

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Cited by2

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