Theorems · Theorem · combinatorics
SimpleGraph.edgeFinset_eq_empty
∀ {V : Type u_1} {G : SimpleGraph V} [inst : Fintype ↑G.edgeSet], G.edgeFinset = ∅ ↔ G = ⊥- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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.
- Finsetstatement and proof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Bot.botstatement and proof · cited by 4,720
- SimpleGraphstatement and proof · cited by 3,072
- Sym2statement and proof · cited by 737
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.edgeFinsetstatement and proof · cited by 116
- SimpleGraph.edgeFinset_injproof · cited by 3
- SimpleGraph.edgeFinset_botproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.edgeFinset_nonemptyproof · cited by 0