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Theorems · Theorem · group theory

nsmul_eq_zero_iff_right

∀ {M : Type u_1} [inst : AddMonoid M] [IsAddTorsionFree M] {n : ℕ} {a : M}, n ≠ 0 → (n • a = 0 ↔ a = 0)
Defined in
Mathlib.Algebra.Group.Torsion
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext
Assumes
AddMonoidIsAddTorsionFree
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Around this declaration

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

nsmul_eq_zero_iff · cited by 2nsmul_eq_zero_ifftwo_nsmul_eq_zero · cited by 1two_nsmul_eq_zeroAddMonoid · cited by 2864AddMonoidIsAddTorsionFree · cited by 155IsAddTorsionFreensmul_zero · cited by 73nsmul_zeronsmul_right_inj · cited by 21nsmul_right_injnsmul_eq_zero_iff_rightCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.