Theorems · Theorem · group theory
AddSubgroup.add_mem_iff_of_index_two
∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, H.index = 2 → ∀ {a b : G}, a + b ∈ H ↔ (a ∈ H ↔ b ∈ H)- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- add_assocproof · cited by 746
- AddSubgroup.indexstatement and proof · cited by 104
- Xorproof · cited by 56
- add_mem_cancel_rightproof · cited by 10
- add_mem_cancel_leftproof · cited by 8
- Xor.orproof · cited by 7
- AddSubgroup.index_eq_two_iffproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.add_self_mem_of_index_twoproof · cited by 1