Theorems · Theorem · combinatorics
SimpleGraph.edist_anti
∀ {V : Type u_1} {G : SimpleGraph V} {u v : V} {G' : SimpleGraph V}, G ≤ G' → G'.edist u v ≤ G.edist u vSupergraphs have smaller or equal extended distances to their subgraphs.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Metric
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Walkproof · cited by 915
- le_topproof · cited by 411
- SimpleGraph.Walk.lengthproof · cited by 212
- SimpleGraph.Reachableproof · cited by 141
- SimpleGraph.Walk.mapproof · cited by 66
- SimpleGraph.ediststatement and proof · cited by 55
- SimpleGraph.Hom.ofLEproof · cited by 27
- SimpleGraph.Walk.length_mapproof · cited by 8
- SimpleGraph.edist_leproof · cited by 5
- SimpleGraph.edist_eq_top_of_not_reachableproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.ediam_antiproof · cited by 1