Theorems · Definition · group theory
AddSubgroup.leftCosetEquivAddSubgroup
{α : Type u_1} → [inst : AddGroup α] → {s : AddSubgroup α} → (g : α) → ↑(g +ᵥ ↑s) ≃ ↥sThe natural bijection between the cosets g + s and s.
- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HVAdd.hVAddstatement and proof · cited by 1,820
- Set.vaddSetstatement · cited by 403
Cited by2
Results whose statement or proof uses this declaration.
- AddSubgroup.addGroupEquivQuotientProdAddSubgroupproof · cited by 5
- AddMonoidHom.fiberEquivKerproof · cited by 2