Theorems · Theorem · group theory
Subgroup.mul_normal
∀ {G : Type u_2} [inst : Group G] (H N : Subgroup G) [hN : N.Normal], ↑(H ⊔ N) = ↑H * ↑NThe carrier of H ⊔ N is just ↑H * ↑N (pointwise set product) when N is normal.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.Normal
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Cites8
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
- Subgroup.Normalstatement and proof · cited by 334
- Set.mulstatement · cited by 297
- Subgroup.le_normalizer_of_normalproof · cited by 3
- Subgroup.coe_mul_of_left_le_normalizer_rightproof · cited by 2
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