Theorems · Theorem · group theory
AddAction.univ_eq_iUnion_orbit
∀ (G : Type u_1) (α : Type u_2) [inst : AddGroup G] [inst_1 : AddAction G α], Set.univ = ⋃ x, x.orbit
Decomposition of a type X as a disjoint union of its orbits under an additive
group action. Phrased as a set union. See AddAction.selfEquivSigmaOrbits for the type
isomorphism.
- Defined in
- Mathlib.GroupTheory.GroupAction.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement · cited by 3,945
- Set.iUnionstatement · cited by 2,483
- Set.extproof · cited by 2,266
- AddActionstatement and proof · cited by 820
- Set.mem_univproof · cited by 416
- Set.mem_iUnionproof · cited by 212
- Quotient.mk''proof · cited by 132
- AddAction.orbitRel.Quotientstatement and proof · cited by 17
- AddAction.orbitRel.Quotient.orbitstatement and proof · cited by 15
- AddAction.mem_orbit_selfproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- QuotientAddGroup.univ_eq_iUnion_vaddproof · cited by 1