Theorems · Theorem · combinatorics
SimpleGraph.exists_walk_of_edist_ne_top
∀ {V : Type u_1} {G : SimpleGraph V} {u v : V}, G.edist u v ≠ ⊤ → ∃ p, ↑p.length = G.edist u v- Defined in
- Mathlib.Combinatorics.SimpleGraph.Metric
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 36 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.
- Top.topstatement and proof · cited by 9,680
- ENatstatement · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Walkstatement · cited by 915
- SimpleGraph.Walk.lengthstatement · cited by 212
- SimpleGraph.ediststatement and proof · cited by 55
- SimpleGraph.Reachable.exists_walk_length_eq_edistproof · cited by 3
- SimpleGraph.reachable_of_edist_ne_topproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.edist_eq_one_iff_adjproof · cited by 5
- SimpleGraph.edist_triangleproof · cited by 2
- SimpleGraph.exists_walk_of_edist_eq_coeproof · cited by 1
- SimpleGraph.edist_boxProdproof · cited by 0