Theorems · Theorem · combinatorics
SimpleGraph.Subgraph.connected_sup
∀ {V : Type u} {G : SimpleGraph V} {H K : G.Subgraph},
H.Preconnected → K.Preconnected → (H ⊓ K).verts.Nonempty → (H ⊔ K).Connected- Cited by
- 3 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Set.Nonemptystatement and proof · cited by 2,627
- SimpleGraph.Subgraphstatement and proof · cited by 326
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- SimpleGraph.Subgraph.vertsstatement and proof · cited by 210
- SimpleGraph.Subgraph.coeproof · cited by 89
- SimpleGraph.Subgraph.Connectedstatement · cited by 24
- SimpleGraph.Reachable.mapproof · cited by 14
- SimpleGraph.Subgraph.Preconnectedstatement and proof · cited by 14
- SimpleGraph.connected_iff_exists_forall_reachableproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.toSubgraph_connectedproof · cited by 3
- SimpleGraph.Subgraph.induce_union_connectedproof · cited by 1
- SimpleGraph.Subgraph.connected_induce_top_supproof · cited by 1