Theorems · Theorem · group theory
Subgroup.set_mul_normalizer_comm
∀ {G : Type u_2} [inst : Group G] (S : Set G) (N : Subgroup G), S ⊆ ↑(Subgroup.normalizer ↑N) → S * ↑N = ↑N * S- Defined in
- Mathlib.Algebra.Group.Subgroup.Pointwise
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Subgroupstatement and proof · cited by 3,593
- Set.iUnionproof · cited by 2,483
- Set.iUnion_congr_Propproof · cited by 374
- Set.mulstatement · cited by 297
- Subgroup.normalizerstatement and proof · cited by 108
- InvMemClass.inv_memproof · cited by 52
- Set.image_mul_rightproof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.coe_mul_of_right_le_normalizer_leftproof · cited by 1
- Subgroup.set_mul_normal_commproof · cited by 0