Theorems · Definition · combinatorics
Finset.sym2
{α : Type u_1} → Finset α → Finset (Sym2 α)s.sym2 is the finset of all unordered pairs of elements from s.
It is the image of s ×ˢ s under the quotient α × α → Sym2 α.
- Defined in
- Mathlib.Data.Finset.Sym
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Sym2statement · cited by 737
- Finset.valproof · cited by 438
- Multiset.sym2proof · cited by 17
Cited by44
Results whose statement or proof uses this declaration.
- Finsupp.sym2Mulproof · cited by 5
- Finset.sym2_valstatement and proof · cited by 4
- Finset.sym2_consstatement and proof · cited by 3
- Finset.coe_sym2statement · cited by 2
- SimpleGraph.map_edgeFinset_inducestatement · cited by 2
- QuadraticMap.map_sumstatement and proof · cited by 2
- Finset.mk_mem_sym2_iffstatement · cited by 1
- Finset.monotone_sym2statement · cited by 1
- QuadraticMap.apply_linearCombinationstatement and proof · cited by 1
- SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingletonstatement and proof · cited by 1
- QuadraticMap.apply_linearCombination'proof · cited by 1
- SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_leproof · cited by 1