Theorems · Theorem · group theory
MulAction.univ_eq_iUnion_orbit
∀ (G : Type u_1) (α : Type u_2) [inst : Group G] [inst_1 : MulAction G α], Set.univ = ⋃ x, x.orbit
Decomposition of a type X as a disjoint union of its orbits under a group action.
Phrased as a set union. See MulAction.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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.univstatement · cited by 3,945
- Set.iUnionstatement · cited by 2,483
- Set.extproof · cited by 2,266
- MulActionstatement and proof · cited by 1,294
- Quotient.mk''proof · cited by 132
- MulAction.orbitRel.Quotientstatement and proof · cited by 28
- MulAction.orbitRel.Quotient.orbitstatement and proof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- QuotientGroup.univ_eq_iUnion_smulproof · cited by 0