AddSubgroup.index_eq_two_iff

∀ {G : Type u_1} [inst : AddGroup G] {H : AddSubgroup G}, H.index = 2 ↔ ∃ a, ∀ (b : G), Xor (b + a ∈ H) (b ∈ H)

An additive subgroup has index two if and only if there exists a such that for all b, exactly one of b + a and b belong to H.

Defined in: Mathlib.GroupTheory.Index
Cited by: 5 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup

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