AddSubgroup.index_eq_two_iff_exists_notMem_and

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

An additive 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 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup

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