AddSubgroup.index_dvd_two_iff

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

An additive subgroup has index dividing 2 if and only if there exists a such that for all b, at least one of b + a and b belongs to H.

Defined in: Mathlib.GroupTheory.Index
Cited by: 2 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddGroup

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