Theorems · Theorem · group theory
IsAddCyclic.exponent_eq_zero_of_infinite
∀ {α : Type u_1} [inst : AddGroup α] [IsAddCyclic α] [Infinite α], AddMonoid.exponent α = 0- Cited by
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- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupIsAddCyclicInfinite
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroup.zmultiplesproof · cited by 493
- Infinitestatement and proof · cited by 352
- AddMonoid.exponentstatement and proof · cited by 70
- IsAddCyclicstatement and proof · cited by 55
- IsAddCyclic.exists_generatorproof · cited by 8
- AddMonoid.exponent_eq_zero_addOrder_zeroproof · cited by 2
- Infinite.addOrderOf_eq_zero_of_forall_mem_zmultiplesproof · cited by 1
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