Theorems · Theorem · combinatorics
SimpleGraph.EdgeDisjointTriangles.mem_sym2_subsingleton
∀ {α : Type u_1} {G : SimpleGraph α},
G.EdgeDisjointTriangles → ∀ ⦃e : Sym2 α⦄, ¬e.IsDiag → {s | s ∈ G.cliqueSet 3 ∧ e ∈ s.sym2}.SubsingletonAlias of the forward direction of SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.ofPredstatement · cited by 6,101
- SimpleGraphstatement and proof · cited by 3,072
- Sym2statement · cited by 737
- Set.Subsingletonstatement · cited by 276
- Finset.sym2statement · cited by 43
- Sym2.IsDiagstatement · cited by 43
- SimpleGraph.cliqueSetstatement · cited by 18
- SimpleGraph.EdgeDisjointTrianglesstatement · cited by 8
- SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingletonproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_leproof · cited by 1