Theorems · Theorem · group theory
IsAddTorsionFree.addOrderOf_nonpos
∀ {G : Type u_1} [inst : AddCommGroup G] [IsAddTorsionFree G] (g : G), addOrderOf g ≤ 1- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupIsAddTorsionFree
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- eq_or_neproof · cited by 1,117
- zero_leproof · cited by 382
- addOrderOfstatement · cited by 208
- IsAddTorsionFreestatement and proof · cited by 155
- addOrderOf_eq_zero_iffproof · cited by 9
- addOrderOf_zeroproof · cited by 8
- isOfFinAddOrder_iff_eq_zeroproof · cited by 1
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