Theorems · Theorem · group theory
eq_addCosets_of_normal
∀ {α : Type u_1} [inst : AddGroup α] (s : AddSubgroup α), s.Normal → ∀ (g : α), g +ᵥ ↑s = AddOpposite.op g +ᵥ ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Set.extproof · cited by 2,266
- HVAdd.hVAddstatement · cited by 1,820
- AddOppositestatement · cited by 452
- Set.vaddSetstatement · cited by 403
- SetLike.mem_coeproof · cited by 302
- AddOpposite.opstatement · cited by 192
- AddSubgroup.Normalstatement and proof · cited by 183
- mem_leftAddCoset_iffproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- normal_iff_eq_addCosetsproof · cited by 0