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Theorems · Theorem · group theory

AddMonoid.exponent_eq_zero_iff_range_addOrderOf_infinite

∀ {G : Type u} [inst : AddMonoid G],
  (∀ (g : G), 0 < addOrderOf g) → (AddMonoid.exponent G = 0 ↔ (Set.range addOrderOf).Infinite)
Defined in
Mathlib.GroupTheory.Exponent
Cited by
1 results in Mathlib
Foundations
Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddMonoid.exponent_eq_iSup_addOrderOf · cited by 2AddMonoid.exponent_eq_iSu…Set.range · cited by 4705Set.rangeAddMonoid · cited by 2864AddMonoidSet.Finite · cited by 1814Set.FiniteSet.Infinite · cited by 263Set.InfiniteaddOrderOf · cited by 208addOrderOfAddMonoid.exponent · cited by 70AddMonoid.exponentnot_iff_comm · cited by 32not_iff_commAddMonoid.exponent_ne_zero_iff_range_addOrderOf_finite · cited by 3AddMonoid.exponent_ne_zer…AddMonoid.exponent_eq_zero_if…CITED BYCITES

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Cited by1

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