Connected
π Source: Mathlib/Combinatorics/SimpleGraph/Connectivity/Connected.lean
Statistics
SimpleGraph
Definitions
Theorems
SimpleGraph.Adj
Theorems
| Name | Kind | Assumes | Proves | Validates | Depends On |
|---|---|---|---|---|---|
reachable π | mathematical | SimpleGraph.Adj | SimpleGraph.Reachable | β | SimpleGraph.Walk.reachable |
SimpleGraph.Connected
Theorems
SimpleGraph.ConnectedComponent
Definitions
Theorems
SimpleGraph.IsBridge
Theorems
SimpleGraph.Iso
Definitions
| Name | Category | Theorems |
|---|---|---|
connectedComponentEquiv π | CompOp |
Theorems
SimpleGraph.Preconnected
Theorems
SimpleGraph.Reachable
Theorems
| Name | Kind | Assumes | Proves | Validates | Depends On |
|---|---|---|---|---|---|
elim π | β | β | β | β | β |
elim_path π | β | β | β | β | elim |
exists_isPath π | mathematical | β | SimpleGraph.Walk.IsPath | β | SimpleGraph.Path.isPath |
map π | mathematical | β | SimpleGraph.ReachableDFunLike.coeSimpleGraph.HomRelHom.instFunLikeSimpleGraph.Adj | β | elim |
mem_subgraphVerts π | β | SimpleGraph.Subgraph.AdjSetSet.instMembershipSimpleGraph.Subgraph.verts | β | β | β |
mono π | mathematical | SimpleGraphSimpleGraph.instLE | SimpleGraph.Reachable | β | map |
mono' π | mathematical | SimpleGraphSimpleGraph.instLE | Pi.hasLeProp.leSimpleGraph.Reachable | β | mono |
of_subsingleton π | mathematical | β | SimpleGraph.Reachable | β | refl |
refl π | mathematical | β | SimpleGraph.Reachable | β | β |
rfl π | mathematical | β | SimpleGraph.Reachable | β | refl |
trans π | mathematical | β | SimpleGraph.Reachable | β | elim |
SimpleGraph.Subgraph
Definitions
SimpleGraph.Walk
Theorems
SimpleGraph.Walk.IsTrail
Theorems
SimpleGraph.reachable_deleteEdges_iff_exists_cycle
Theorems
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