Theorems · Theorem · group theory
Subgroup.relIndex_eq_two_iff_exists_notMem_and
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G}, H.relIndex K = 2 ↔ ∃ a ∈ K, a ∉ H ∧ ∀ b ∈ K, b * a ∈ H ∨ b ∈ HRelative version of Subgroup.index_eq_two_iff_exists_notMem_and.
- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 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.
Cites4
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
- Subgroup.relIndexstatement · cited by 72
- Subgroup.index_eq_two_iff_exists_notMem_andproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.relindex_adjoinNegOne_eq_twoproof · cited by 1