Theorems · Theorem · group theory
normal_iff_eq_addCosets
∀ {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
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
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Cites11
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
- HVAdd.hVAddstatement · cited by 1,820
- AddOppositestatement · cited by 452
- Set.vaddSetstatement · cited by 403
- AddOpposite.opstatement · cited by 192
- AddSubgroup.Normalstatement · cited by 183
- eq_addCosets_of_normalproof · cited by 1
- normal_of_eq_addCosetsproof · cited by 1
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