Theorems · Theorem · group theory
QuotientAddGroup.orbit_eq_out_vadd
∀ {α : Type u_1} [inst : AddGroup α] {s : AddSubgroup α} (x : α ⧸ s),
AddAction.orbitRel.Quotient.orbit x = Quotient.out x +ᵥ ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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 · cited by 8,199
- Set.ofPredproof · cited by 6,101
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement and proof · cited by 2,301
- HVAdd.hVAddstatement · cited by 1,820
- AddOppositestatement · cited by 452
- Set.vaddSetstatement · cited by 403
- QuotientAddGroup.mkproof · cited by 348
- Quotient.outstatement and proof · cited by 141
- AddSubgroup.opstatement · cited by 57
Cited by1
Results whose statement or proof uses this declaration.
- QuotientAddGroup.univ_eq_iUnion_vaddproof · cited by 1