Theorems · Theorem · combinatorics
SimpleGraph.diam_ne_zero_of_ediam_ne_top
∀ {α : Type u_1} {G : SimpleGraph α} [Nontrivial α], G.ediam ≠ ⊤ → G.diam ≠ 0- Defined in
- Mathlib.Combinatorics.SimpleGraph.Diam
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Nontrivialstatement and proof · cited by 2,416
- lt_of_lt_of_leproof · cited by 438
- pos_iff_ne_zeroproof · cited by 180
- SimpleGraph.ediamstatement and proof · cited by 44
- exists_pair_neproof · cited by 32
- SimpleGraph.diamstatement and proof · cited by 15
- SimpleGraph.connected_of_ediam_ne_topproof · cited by 2
- SimpleGraph.dist_le_diamproof · cited by 1
- SimpleGraph.Connected.pos_dist_of_neproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.diam_eq_zero_iff_ediam_eq_topproof · cited by 1