Theorems · Theorem · combinatorics
SimpleGraph.mem_edgeFinset
∀ {V : Type u_1} {G : SimpleGraph V} {e : Sym2 V} [inst : Fintype ↑G.edgeSet], e ∈ G.edgeFinset ↔ e ∈ G.edgeSet- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 61 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Sym2statement and proof · cited by 737
- SimpleGraph.edgeSetstatement and proof · cited by 199
- SimpleGraph.edgeFinsetstatement · cited by 116
- Set.mem_toFinsetproof · cited by 47
Cited by6
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.IsTrail.length_le_card_edgeFinsetproof · cited by 2
- SimpleGraph.dart_card_eq_twice_card_edgesproof · cited by 2
- SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_leproof · cited by 1
- SimpleGraph.not_isDiag_of_mem_edgeFinsetproof · cited by 1
- SimpleGraph.edgeFinset_deleteIncidenceSet_eq_filterproof · cited by 1
- SimpleGraph.card_edgeFinset_bipartiteDoubleCoverproof · cited by 1