Theorems · Theorem · group theory
Subgroup.index_eq_two_iff_exists_notMem_and
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G}, H.index = 2 ↔ ∃ a ∉ H, ∀ (b : G), b * a ∈ H ∨ b ∈ HA subgroup H has index two if and only if there exists a ∉ H such that for all b, one
of b * a and b belongs to H.
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 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.
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
- MulMemClass.mul_memproof · cited by 173
- Subgroup.indexstatement · cited by 150
- inv_mul_cancel_leftproof · cited by 88
- InvMemClass.inv_memproof · cited by 52
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.relIndex_eq_two_iff_exists_notMem_andproof · cited by 1