Theorems · Theorem · combinatorics
SimpleGraph.edgeFinset_nonempty
∀ {V : Type u_1} {G : SimpleGraph V} [inst : Fintype ↑G.edgeSet], G.edgeFinset.Nonempty ↔ G ≠ ⊥- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Finset.Nonemptystatement · cited by 1,001
- Sym2statement · cited by 737
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.edgeFinsetstatement · cited by 116
- Iff.neproof · cited by 52
- Finset.nonempty_iff_ne_emptyproof · cited by 34
- SimpleGraph.edgeFinset_eq_emptyproof · cited by 1
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