Theorems · Theorem · group theory
QuotientAddGroup.univ_eq_iUnion_vadd
∀ {α : Type u_1} [inst : AddGroup α] (H : AddSubgroup α), Set.univ = ⋃ x, Quotient.out x +ᵥ ↑HAn additive group is made up of a disjoint union of cosets of an additive subgroup.
- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 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.
Cites17
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
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement · cited by 3,945
- AddSubgroupstatement and proof · cited by 3,232
- Set.iUnionstatement and proof · cited by 2,483
- HasQuotient.Quotientstatement and proof · cited by 2,301
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionproof · cited by 820
- AddOppositeproof · cited by 452
- Set.vaddSetstatement · cited by 403
- Quotient.outstatement and proof · cited by 141
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.univ_eq_iUnion_image_addproof · cited by 1