Theorems · Theorem · group theory
nsmul_inj_iff_of_addOrderOf_eq_zero
∀ {G : Type u_1} [inst : AddLeftCancelMonoid G] {x : G}, addOrderOf x = 0 → ∀ {n m : ℕ}, n • x = m • x ↔ n = m- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddLeftCancelMonoid
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.ModEqproof · cited by 225
- addOrderOfstatement and proof · cited by 208
- AddLeftCancelMonoidstatement and proof · cited by 37
- Nat.modEq_zero_iffproof · cited by 8
- nsmul_eq_nsmul_iff_modEqproof · cited by 4
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