Theorems · Theorem · group theory
QuotientGroup.orbit_mk_eq_smul
∀ {α : Type u_1} [inst : Group α] {s : Subgroup α} (x : α), MulAction.orbitRel.Quotient.orbit ↑x = x • ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Set.extproof · cited by 2,266
- MulOppositestatement and proof · cited by 1,135
- Set.smulSetstatement · cited by 608
- QuotientGroup.mkstatement · cited by 196
- MulAction.orbitRelproof · cited by 114
- Subgroup.opstatement and proof · cited by 58
- MulAction.orbitRel.Quotient.orbitstatement · cited by 15
- Setoid.comm'proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- QuotientGroup.orbit_eq_out_smulproof · cited by 1