Theorems · Theorem · combinatorics
SimpleGraph.isEdgeReachable_add_one
∀ {V : Type u_1} {G : SimpleGraph V} {k : ℕ} {u v : V},
k ≠ 0 → (G.IsEdgeReachable (k + 1) u v ↔ ∀ (e : Sym2 V), (G.deleteEdges {e}).IsEdgeReachable k u v)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENatproof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- Set.Nonemptyproof · cited by 2,627
- le_reflproof · cited by 2,061
- Sym2statement and proof · cited by 737
- Sym2.mkproof · cited by 332
- Set.encardproof · cited by 327
- Set.eq_empty_or_nonemptyproof · cited by 248
- SimpleGraph.Reachableproof · cited by 141
- Set.union_commproof · cited by 99
- SimpleGraph.deleteEdgesstatement and proof · cited by 64
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.isEdgeConnected_add_oneproof · cited by 0