Theorems · Theorem · group theory
Subgroup.Normal.mem_comm
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, H.Normal → ∀ {a b : G}, a * b ∈ H → b * a ∈ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- inv_invproof · cited by 494
- Subgroup.Normalstatement and proof · cited by 334
- inv_mul_cancel_leftproof · cited by 88
- Subgroup.Normal.conj_memproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.Normal.mem_comm_iffproof · cited by 4
- Subgroup.smul_diff_smul'statement and proof · cited by 0