Theorems · Theorem · combinatorics
SimpleGraph.Preconnected.support_eq_univ
∀ {V : Type u} [Nontrivial V] {G : SimpleGraph V}, G.Preconnected → G.support = Set.univ- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.univstatement · cited by 3,945
- SimpleGraphstatement and proof · cited by 3,072
- Nontrivialstatement and proof · cited by 2,416
- SimpleGraph.Adjproof · cited by 1,346
- SimpleGraph.Walkproof · cited by 915
- exists_neproof · cited by 101
- SimpleGraph.Walk.casesOnproof · cited by 59
- SimpleGraph.Preconnectedstatement and proof · cited by 49
- SimpleGraph.supportstatement · cited by 43
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.Preconnected.degree_pos_of_nontrivialproof · cited by 2
- SimpleGraph.Preconnected.not_isIsolatedproof · cited by 0