Theorems · Theorem · order theory
Set.pair_comm
∀ {α : Type u_1} (a b : α), {a, b} = {b, a}- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.union_commproof · cited by 99
Cited by22
Results whose statement or proof uses this declaration.
- EuclideanGeometry.oangle_eq_of_dist_orthogonalProjection_eqproof · cited by 5
- vectorSpan_pair_revproof · cited by 5
- Set.pair_sdiff_rightproof · cited by 3
- EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_piproof · cited by 3
- affineCombination_mem_affineSpan_pairproof · cited by 2
- eVariationOn.pairproof · cited by 2
- Topology.CWComplex.exists_cellFrontier_one_eqproof · cited by 1
- dense_addSubgroupClosure_pair_iffproof · cited by 1
- EuclideanGeometry.Sphere.secondInter_collinearproof · cited by 1
- linearIndepOn_pair_iffproof · cited by 1
- Set.einfsep_pair_le_rightproof · cited by 1
- jacobiSym.trichotomyproof · cited by 1