Theorems · Theorem · combinatorics
SimpleGraph.Reachable.exists_walk_length_eq_dist
∀ {V : Type u_1} {G : SimpleGraph V} {u v : V}, G.Reachable u v → ∃ p, p.length = G.dist u v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Metric
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Walkstatement · cited by 915
- SimpleGraph.Walk.lengthstatement · cited by 212
- SimpleGraph.Reachablestatement and proof · cited by 141
- SimpleGraph.diststatement · cited by 40
- Nat.sInf_memproof · cited by 15
- Set.range_nonempty_iff_nonemptyproof · cited by 7
- SimpleGraph.dist_eq_sInfproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- SimpleGraph.Reachable.exists_path_of_distproof · cited by 3
- SimpleGraph.Reachable.one_lt_dist_of_ne_of_not_adjproof · cited by 2
- SimpleGraph.Connected.exists_walk_length_eq_distproof · cited by 2
- SimpleGraph.Reachable.dist_antiproof · cited by 0
- SimpleGraph.exists_walk_of_dist_ne_zeroproof · cited by 0