Theorems · Theorem · group theory
normal_iff_eq_cosets
∀ {α : Type u_1} [inst : Group α] (s : Subgroup α), s.Normal ↔ ∀ (g : α), g • ↑s = MulOpposite.op g • ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- Group
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Cites10
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
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- MulOppositestatement · cited by 1,135
- Set.smulSetstatement · cited by 608
- MulOpposite.opstatement · cited by 520
- Subgroup.Normalstatement · cited by 334
- eq_cosets_of_normalproof · cited by 1
- normal_of_eq_cosetsproof · cited by 1
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