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Commit 2022-10-24 07:29 3882aaf6

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feat(group_theory/index): criterion for subgroups of index two (#16629)

  • A subgroup has index two if and only if there exists a such that for all b, b * a ∈ H is equivalent to b ∉ H.
  • For a subgroup of index two, a * b ∈ H ↔ (a ∈ H ↔ b ∈ H).

Estimated changes

modified theorem xor_comm
added theorem xor_iff_iff_not
added theorem xor_iff_not_iff'
modified theorem xor_iff_not_iff
added theorem xor_not_left
added theorem xor_not_not
added theorem xor_not_right