Theorems · Theorem · combinatorics
SimpleGraph.two_lt_edist_iff
∀ {V : Type u_1} {G : SimpleGraph V} {u v : V}, 2 < G.edist u v ↔ u ≠ v ∧ ¬G.Adj u v ∧ G.commonNeighbors u v = ∅- Defined in
- Mathlib.Combinatorics.SimpleGraph.Metric
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 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.
- Setstatement · cited by 53,352
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- Set.Nonemptyproof · cited by 2,627
- SimpleGraph.Adjstatement and proof · cited by 1,346
- lt_of_le_of_neproof · cited by 230
- one_add_one_eq_twoproof · cited by 65
- SimpleGraph.ediststatement and proof · cited by 55
- SimpleGraph.commonNeighborsstatement and proof · cited by 28
- Order.add_one_le_of_ltproof · cited by 13
- SimpleGraph.edist_selfproof · cited by 6
- SimpleGraph.edist_eq_one_iff_adjproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.IsSRGWith.ediam_eq_twoproof · cited by 0